Year 7 Unit on Fractions

1. Fractions and Percentages
Topics we will cover:
• Naming Fractions.
• Highest Common Factor (HCF) and Lowest Common Multiple
(LCM).
• Equivalent Fractions.
• Simplifying Fractions.
• Ordering Fractions.
• Adding and Subtracting Fractions.
• Adding and Subtracting Mixed Numerals.
• Finding a Fraction of a Quantity.
• Multiplying Fractions.
• Dividing Fractions.
• Percentages and Fractions.
• Percentages and Decimals.
• Converting Percentages.
• Finding a Percentage of a Quantity.

2. Naming Fractions a
Definition: A fraction is a number usually expressed in the form
b
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3. Naming Fractions a
Definition: A fraction is a number usually expressed in the form
b
The top number is called the numerator
The line in
3 between is
4 called the
vinculum.
The bottom number is called the denominator.
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4. Naming Fractions a
Definition: A fraction is a number usually expressed in the form
b
The top number is called the numerator
The line in
3 between is
4 called the
vinculum.
The bottom number is called the denominator.
Always remember a fraction is the same thing as a division the above fraction
could be written as 3 ÷ 4 .
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5. Naming Fractions a
Definition: A fraction is a number usually expressed in the form
b
The top number is called the numerator
The line in
3 between is
4 called the
vinculum.
The bottom number is called the denominator.
Always remember a fraction is the same thing as a division the above fraction
could be written as 3 ÷ 4 .
11
Proper Fractions have a numerator less than the denominator e.g.
200
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6. Naming Fractions a
Definition: A fraction is a number usually expressed in the form
b
The top number is called the numerator
The line in
3 between is
4 called the
vinculum.
The bottom number is called the denominator.
Always remember a fraction is the same thing as a division the above fraction
could be written as 3 ÷ 4 .
11
Proper Fractions have a numerator less than the denominator e.g.
200
31
Improper Fractions have a numerator greater than the denominator e.g.
4
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7. Naming Fractions a
Definition: A fraction is a number usually expressed in the form
b
The top number is called the numerator
The line in
3 between is
4 called the
vinculum.
The bottom number is called the denominator.
Always remember a fraction is the same thing as a division the above fraction
could be written as 3 ÷ 4 .
11
Proper Fractions have a numerator less than the denominator e.g.
200
31
Improper Fractions have a numerator greater than the denominator e.g.
4
5
Mixed Numerals have a whole part and a fraction part e.g. 3
8 HOME

8. Naming Fractions
It is possible to convert between mixed numerals and improper fractions.
Examples:
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9. Naming Fractions
It is possible to convert between mixed numerals and improper fractions.
Examples:
3 3
Write 1 as an improper fraction (how many quarters are in 1 ?)
4 4
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10. Naming Fractions
It is possible to convert between mixed numerals and improper fractions.
Examples:
3 3
Write 1 as an improper fraction (how many quarters are in 1 ?)
4 4
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11. Naming Fractions
It is possible to convert between mixed numerals and improper fractions.
Examples:
3 3
Write 1 as an improper fraction (how many quarters are in 1 ?)
4 4
3 7
1 =
4 4
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12. Naming Fractions
It is possible to convert between mixed numerals and improper fractions.
Examples:
3 3
Write 1 as an improper fraction (how many quarters are in 1 ?)
4 4
3 7
1 =
4 4
+ 3 4 × 1+ 3 7
Quick Solution: 1 = =
4 4 4
×
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13. Naming Fractions
Examples:
14
Write as a mixed numeral (we need to do a division).
3
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14. Naming Fractions
Examples:
14
Write as a mixed numeral (we need to do a division).
3
Solution: 14
= 14 ÷ 3
3
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15. Naming Fractions
Examples:
14
Write as a mixed numeral (we need to do a division).
3
Solution: 14
= 14 ÷ 3
3
= 4 remainder 2
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16. Naming Fractions
Examples:
14
Write as a mixed numeral (we need to do a division).
3
Solution: 14
= 14 ÷ 3
3
= 4 remainder 2
2
=4
3
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17. Highest Common Factors and
Lowest Common Multiples
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18. Highest Common Factors and
Lowest Common Multiples
Finding the HCF and LCM of two numbers are useful skills when calculating with
fractions.
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19. Highest Common Factors and
Lowest Common Multiples
Finding the HCF and LCM of two numbers are useful skills when calculating with
fractions.
The HCF of two or more numbers is the largest factor that divides evenly into
all of those numbers.
HOME

20. Highest Common Factors and
Lowest Common Multiples
Finding the HCF and LCM of two numbers are useful skills when calculating with
fractions.
The HCF of two or more numbers is the largest factor that divides evenly into
all of those numbers.
Example
Find the HCF of 24 and 32, (list the factors and find the largest number in both
lists).
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21. Highest Common Factors and
Lowest Common Multiples
Finding the HCF and LCM of two numbers are useful skills when calculating with
fractions.
The HCF of two or more numbers is the largest factor that divides evenly into
all of those numbers.
Example
Find the HCF of 24 and 32, (list the factors and find the largest number in both
lists).
24: 1, 2, 3, 4, 6, 8, 12, 24.
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22. Highest Common Factors and
Lowest Common Multiples
Finding the HCF and LCM of two numbers are useful skills when calculating with
fractions.
The HCF of two or more numbers is the largest factor that divides evenly into
all of those numbers.
Example
Find the HCF of 24 and 32, (list the factors and find the largest number in both
lists).
24: 1, 2, 3, 4, 6, 8, 12, 24.
32: 1, 2, 4, 8, 16, 32.
HOME

23. Highest Common Factors and
Lowest Common Multiples
Finding the HCF and LCM of two numbers are useful skills when calculating with
fractions.
The HCF of two or more numbers is the largest factor that divides evenly into
all of those numbers.
Example
Find the HCF of 24 and 32, (list the factors and find the largest number in both
lists).
24: 1, 2, 3, 4, 6, 8, 12, 24.
32: 1, 2, 4, 8, 16, 32.
HOME

24. Highest Common Factors and
Lowest Common Multiples
Finding the HCF and LCM of two numbers are useful skills when calculating with
fractions.
The HCF of two or more numbers is the largest factor that divides evenly into
all of those numbers.
Example
Find the HCF of 24 and 32, (list the factors and find the largest number in both
lists).
24: 1, 2, 3, 4, 6, 8, 12, 24.
32: 1, 2, 4, 8, 16, 32.
The HCF of 24 and 32 is 8.
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25. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
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26. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
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27. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
4: 4, 8, 12, 16........
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28. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
4: 4, 8, 12, 16........
6: 6, 12, 18......
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29. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
4: 4, 8, 12, 16........
6: 6, 12, 18......
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30. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
4: 4, 8, 12, 16........ The LCM of 4 and 6 is 12
6: 6, 12, 18......
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31. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
4: 4, 8, 12, 16........ The LCM of 4 and 6 is 12
6: 6, 12, 18......
Find the LCM of:
b) 3 and 9
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32. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
4: 4, 8, 12, 16........ The LCM of 4 and 6 is 12
6: 6, 12, 18......
Find the LCM of:
b) 3 and 9
3: 3, 6, 9, 12........
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33. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
4: 4, 8, 12, 16........ The LCM of 4 and 6 is 12
6: 6, 12, 18......
Find the LCM of:
b) 3 and 9
3: 3, 6, 9, 12........
9: 9, 18, 27.....
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34. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
4: 4, 8, 12, 16........ The LCM of 4 and 6 is 12
6: 6, 12, 18......
Find the LCM of:
b) 3 and 9
3: 3, 6, 9, 12........
9: 9, 18, 27.....
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35. Highest Common Factors and
Lowest Common Multiples
The LCM of two or more numbers is the smallest number that is a multiple of
all those numbers.
Example
Find the LCM of:
a) 4 and 6 (list the multiples of each number and choose the smallest number in
both lists).
4: 4, 8, 12, 16........ The LCM of 4 and 6 is 12
6: 6, 12, 18......
Find the LCM of:
b) 3 and 9
3: 3, 6, 9, 12........ The LCM of 3 and 9 is 9
9: 9, 18, 27.....
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36. Equivalent Fractions
Equivalent fractions have the same value even though they may look different.
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37. Equivalent Fractions
Equivalent fractions have the same value even though they may look different.
1 2 6 are equivalent fractions.
= =
2 4 12
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38. Equivalent Fractions
Equivalent fractions have the same value even though they may look different.
1 2 6 are equivalent fractions.
= =
2 4 12
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39. Equivalent Fractions
Equivalent fractions have the same value even though they may look different.
1 2 6 are equivalent fractions.
= =
2 4 12
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40. Equivalent Fractions
Equivalent fractions have the same value even though they may look different.
1 2 6 are equivalent fractions.
= =
2 4 12
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41. Equivalent Fractions
Equivalent fractions are found by multiplying the numerator and denominator by
the same number.
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42. Equivalent Fractions
Equivalent fractions are found by multiplying the numerator and denominator by
the same number.
Examples
a) Write equivalent fractions for
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43. Equivalent Fractions
Equivalent fractions are found by multiplying the numerator and denominator by
the same number.
Examples
a) Write equivalent fractions for
4
=
5
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44. Equivalent Fractions
Equivalent fractions are found by multiplying the numerator and denominator by
the same number.
Examples
a) Write equivalent fractions for
4
=
5
b) Find the missing term in each of these pairs of equivalent fractions
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45. Equivalent Fractions
Equivalent fractions are found by multiplying the numerator and denominator by
the same number.
Examples
a) Write equivalent fractions for
4
=
5
b) Find the missing term in each of these pairs of equivalent fractions
3
i) =
4 20
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46. Equivalent Fractions
Equivalent fractions are found by multiplying the numerator and denominator by
the same number.
Examples
a) Write equivalent fractions for
4
=
5
b) Find the missing term in each of these pairs of equivalent fractions
3 5 35
i) = ii) =
4 20 9
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47. Equivalent Fractions
Equivalent fractions are found by multiplying the numerator and denominator by
the same number.
Examples
a) Write equivalent fractions for
4
=
5
b) Find the missing term in each of these pairs of equivalent fractions
3 5 35 16
i) = ii) = iii) =
4 20 9 24 6
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48. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
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49. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
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50. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a)
5
=
10
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51. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a)
5 5 ×1
=
10 5 × 2
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52. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a)
5 5 ×1
=
10 5 × 2
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53. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a)
5 5 ×1
=
10 5 × 2
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54. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a)
5 5 ×1
=
10 5 × 2
1
=
2
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55. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a)
5 5 ×1
=
10 5 × 2
1
=
2
HCF of 5
and 10 is 5
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56. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b)
5 5 ×1 4
= =
10 5 × 2 6
1
=
2
HCF of 5
and 10 is 5
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57. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b)
5 5 ×1 4 2×2
= =
10 5 × 2 6 2×3
1
=
2
HCF of 5
and 10 is 5
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58. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b)
5 5 ×1 4 2×2
= =
10 5 × 2 6 2×3
1
=
2
HCF of 5
and 10 is 5
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59. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b)
5 5 ×1 4 2×2
= =
10 5 × 2 6 2×3
1
=
2
HCF of 5
and 10 is 5
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60. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b)
5 5 ×1 4 2×2
= =
10 5 × 2 6 2×3
1 2
= =
2 3
HCF of 5
and 10 is 5
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61. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b)
5 5 ×1 4 2×2
= =
10 5 × 2 6 2×3
1 2
= =
2 3
HCF of 5 HCF of 4
and 10 is 5 and 6 is 2
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62. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b) c)
5 5 ×1 4 2×2 18
= = =
10 5 × 2 6 2×3 42
1 2
= =
2 3
HCF of 5 HCF of 4
and 10 is 5 and 6 is 2
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63. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b) c)
5 5 ×1 4 2×2 18 6×3
= = =
10 5 × 2 6 2×3 42 6×7
1 2
= =
2 3
HCF of 5 HCF of 4
and 10 is 5 and 6 is 2
HOME

64. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b) c)
5 5 ×1 4 2×2 18 6×3
= = =
10 5 × 2 6 2×3 42 6×7
1 2
= =
2 3
HCF of 5 HCF of 4
and 10 is 5 and 6 is 2
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65. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b) c)
5 5 ×1 4 2×2 18 6×3
= = =
10 5 × 2 6 2×3 42 6×7
1 2
= =
2 3
HCF of 5 HCF of 4
and 10 is 5 and 6 is 2
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66. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b) c)
5 5 ×1 4 2×2 18 6×3
= = =
10 5 × 2 6 2×3 42 6×7
1 2 3
= = =
2 3 7
HCF of 5 HCF of 4
and 10 is 5 and 6 is 2
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67. Simplifying Fractions
In a list of equivalent fractions the one with the smallest possible numerator
and denominator is called the most simple fraction.
To find the most simple fraction or to simplify fractions one needs to find the
HCF of the numerator and denominator and cancel it out of both.
Examples
Simplify:
a) b) c)
5 5 ×1 4 2×2 18 6×3
= = =
10 5 × 2 6 2×3 42 6×7
1 2 3
= = =
2 3 7
HCF of 5 HCF of 4 HCF of 18
and 10 is 5 and 6 is 2 and 42 is 6
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68. Simplifying Fractions
Improper fractions are simplified in the same manner as proper fractions. They
then should be written as mixed numerals.
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69. Simplifying Fractions
Improper fractions are simplified in the same manner as proper fractions. They
then should be written as mixed numerals.
Example
Simplify:
36
=
27
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70. Simplifying Fractions
Improper fractions are simplified in the same manner as proper fractions. They
then should be written as mixed numerals.
Example
Simplify:
36 9 × 4
=
27 9 × 3
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71. Simplifying Fractions
Improper fractions are simplified in the same manner as proper fractions. They
then should be written as mixed numerals.
Example
Simplify:
36 9 × 4
=
27 9 × 3
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72. Simplifying Fractions
Improper fractions are simplified in the same manner as proper fractions. They
then should be written as mixed numerals.
Example
Simplify:
36 9 × 4
=
27 9 × 3
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73. Simplifying Fractions
Improper fractions are simplified in the same manner as proper fractions. They
then should be written as mixed numerals.
Example
Simplify:
36 9 × 4
=
27 9 × 3
4
=
3
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74. Simplifying Fractions
Improper fractions are simplified in the same manner as proper fractions. They
then should be written as mixed numerals.
Example
Simplify:
36 9 × 4
=
27 9 × 3
4
=
3
1
=1
3
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75. Simplifying Fractions
Mixed numerals can have their fraction part simplified.
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76. Simplifying Fractions
Mixed numerals can have their fraction part simplified.
Examples
Simplify:
11
6 =
33
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77. Simplifying Fractions
Mixed numerals can have their fraction part simplified.
Examples
Simplify:
11 11× 1
6 =6
33 11× 3
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78. Simplifying Fractions
Mixed numerals can have their fraction part simplified.
Examples
Simplify:
11 11× 1
6 =6
33 11× 3
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79. Simplifying Fractions
Mixed numerals can have their fraction part simplified.
Examples
Simplify:
11 11× 1
6 =6
33 11× 3
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80. Simplifying Fractions
Mixed numerals can have their fraction part simplified.
Examples
Simplify:
11 11× 1
6 =6
33 11× 3
1
=6
3
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81. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
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82. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ?
7 7
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83. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task)
7 7
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84. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task)
7 7
6 6 2
is larger, or we may write >
7 7 7
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85. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task)
7 7
6 6 2
is larger, or we may write >
7 7 7
3 4
b) Which is smaller or ?
8 9
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86. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task)
7 7
6 6 2
is larger, or we may write >
7 7 7
3 4 (Denominators are different, we need equivalent fractions
b) Which is smaller or ? with a common denominator. Multiply both fractions by the
8 9
denominator of the other)
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87. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task)
7 7
6 6 2
is larger, or we may write >
7 7 7
3 4 (Denominators are different, we need equivalent fractions
b) Which is smaller or ? with a common denominator. Multiply both fractions by the
8 9
denominator of the other)
3 3 × 9 27
= =
8 8 × 9 72
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88. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task)
7 7
6 6 2
is larger, or we may write >
7 7 7
3 4 (Denominators are different, we need equivalent fractions
b) Which is smaller or ? with a common denominator. Multiply both fractions by the
8 9
denominator of the other)
3 3 × 9 27
= =
8 8 × 9 72
4 4 × 8 32
= =
9 9 × 8 72
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89. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task)
7 7
6 6 2
is larger, or we may write >
7 7 7
3 4 (Denominators are different, we need equivalent fractions
b) Which is smaller or ? with a common denominator. Multiply both fractions by the
8 9
denominator of the other)
3 3 × 9 27 27 32
= = <
8 8 × 9 72 72 72
4 4 × 8 32
= =
9 9 × 8 72
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90. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task)
7 7
6 6 2
is larger, or we may write >
7 7 7
3 4 (Denominators are different, we need equivalent fractions
b) Which is smaller or ? with a common denominator. Multiply both fractions by the
8 9
denominator of the other)
3 3 × 9 27 27 32
= = <
8 8 × 9 72 72 72
4 4 × 8 32 3 4
= = ∴ <
9 9 × 8 72 8 9
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91. Ordering Fractions
Ordering fractions is simply placing them in order from smallest to largest or vice
versa.
Examples:
a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task)
7 7
6 6 2
is larger, or we may write >
7 7 7
3 4 (Denominators are different, we need equivalent fractions
b) Which is smaller or ? with a common denominator. Multiply both fractions by the
8 9
denominator of the other)
3 3 × 9 27 27 32
= = <
8 8 × 9 72 72 72
4 4 × 8 32 3 4
= = ∴ < (Always refer back to original fractions)
9 9 × 8 72 8 9
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92. Adding and Subtracting Fractions
Fractions with the same denominator, simply add or subtract the numerators.
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93. Adding and Subtracting Fractions
Fractions with the same denominator, simply add or subtract the numerators.
Examples:
a) 1 2 3
+ =
5 5 5
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94. Adding and Subtracting Fractions
Fractions with the same denominator, simply add or subtract the numerators.
Examples:
a) 1 2 3
+ =
5 5 5
+
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95. Adding and Subtracting Fractions
Fractions with the same denominator, simply add or subtract the numerators.
Examples:
a) 1 2 3
+ =
5 5 5
+ =
HOME

96. Adding and Subtracting Fractions
Fractions with the same denominator, simply add or subtract the numerators.
Examples:
a) 1 2 3
+ =
5 5 5
+ =
b) 5 2 3
− =
7 7 7
HOME

97. Adding and Subtracting Fractions
Fractions with the same denominator, simply add or subtract the numerators.
Examples:
a) 1 2 3
+ =
5 5 5
+ =
b) 5 2 3
− =
7 7 7
−
HOME

98. Adding and Subtracting Fractions
Fractions with the same denominator, simply add or subtract the numerators.
Examples:
a) 1 2 3
+ =
5 5 5
+ =
b) 5 2 3
− =
7 7 7
− =
HOME

99. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
HOME

100. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10
+ = +
4 6 12 12
HOME

101. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
HOME

102. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
HOME

103. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
3 + 10
=
12
HOME

104. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
3 + 10
=
12
13 1
= =1
12 12
HOME

105. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
3 + 10
=
12
13 1
= =1
12 12
Examples:
b) 2 3 8 3
− = −
5 20 20 20
HOME

106. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
3 + 10
=
12
13 1
= =1
12 12
Examples:
b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new
− = − denominator)
5 20 20 20
HOME

107. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
3 + 10
=
12
13 1
= =1
12 12
Examples:
b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new
− = − denominator)
5 20 20 20
HOME

108. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
3 + 10
=
12
13 1
= =1
12 12
Examples:
b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new
− = − denominator)
5 20 20 20
8−3
=
20
HOME

109. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
3 + 10
=
12
13 1
= =1
12 12
Examples:
b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new
− = − denominator)
5 20 20 20
8−3
=
20
5 1
= = HOME
20 4

110. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
3 + 10
=
12
13 1
= =1
12 12
Examples:
b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new
− = − denominator)
5 20 20 20
8−3
=
20
5 1
= = HOME
20 4

111. Adding and Subtracting Fractions
Fractions with different denominators need to be converted to equivalent
fractions with the same denominator. This common denominator should be
the LCM of the original denominators.
Examples:
a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new
+ = + denominator)
4 6 12 12
3 + 10
=
12
13 1
= =1
12 12
Examples:
b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new
− = − denominator)
5 20 20 20
8−3
=
20 (Always simplify fractions if you can)
5 1
= = HOME
20 4

112. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
HOME

113. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1
1− =
8
HOME

114. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1
1− = −
8 1 8
HOME

115. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1
1− = −
8 1 8
8 1
= −
8 8
HOME

116. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1
1− = −
8 1 8
8 1
= −
8 8
7
=
8
HOME

117. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1 b) 3
1− = − 7− =
8 1 8 5
8 1
= −
8 8
7
=
8
HOME

118. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1 b) 3 7 3
1− = − 7− = −
8 1 8 5 1 5
8 1
= −
8 8
7
=
8
HOME

119. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1 b) 3 7 3
1− = − 7− = −
8 1 8 5 1 5
8 1 35 3
= − = −
8 8 5 5
7
=
8
HOME

120. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1 b) 3 7 3
1− = − 7− = −
8 1 8 5 1 5
8 1 35 3
= − = −
8 8 5 5
7 32
= =
8 5
HOME

121. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1 b) 3 7 3
1− = − 7− = −
8 1 8 5 1 5
8 1 35 3
= − = −
8 8 5 5
7 32
= =
8 5
2
=6
5
HOME

122. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1 b) 3 7 3 c) 1 1
1− = − 7− = − 6 −4 =
8 1 8 5 1 5 3 2
8 1 35 3
= − = −
8 8 5 5
7 32
= =
8 5
2
=6
5
HOME

123. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
Examples
Evaluate the following:
a) 1 1 1 b) 3 7 3 c) 1 1 19 9
1− = − 7− = − 6 −4 = −
8 1 8 5 1 5 3 2 3 2
8 1 35 3
= − = −
8 8 5 5
7 32
= =
8 5
2
=6
5
HOME

124. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
LCM of 2
Examples and 3 is 6
Evaluate the following:
a) 1 1 1 b) 3 7 3 c) 1 1 19 9
1− = − 7− = − 6 −4 = −
8 1 8 5 1 5 3 2 3 2
8 1 35 3 19 × 2 9 × 3
= − = − = −
8 8 5 5 3× 2 2 × 3
7 32
= =
8 5
2
=6
5
HOME

125. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
LCM of 2
Examples and 3 is 6
Evaluate the following:
a) 1 1 1 b) 3 7 3 c) 1 1 19 9
1− = − 7− = − 6 −4 = −
8 1 8 5 1 5 3 2 3 2
8 1 35 3 19 × 2 9 × 3
= − = − = −
8 8 5 5 3× 2 2 × 3
7 32 38 27
= = = −
8 5 6 6
2
=6
5
HOME

126. Adding and Subtracting Mixed
Numerals
To add or subtract mixed numerals convert them to improper fractions and follow
the rules adding and subtracting proper fractions.
LCM of 2
Examples and 3 is 6
Evaluate the following:
a) 1 1 1 b) 3 7 3 c) 1 1 19 9
1− = − 7− = − 6 −4 = −
8 1 8 5 1 5 3 2 3 2
8 1 35 3 19 × 2 9 × 3
= − = − = −
8 8 5 5 3× 2 2 × 3
7 32 38 27
= = = −
8 5 6 6
2 11
=6 =
5 6
5
=1
6 HOME

127. Adding and Subtracting Mixed
Numerals
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128. Adding and Subtracting Mixed
Numerals
Examples
Evaluate the following:
a)
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129. Adding and Subtracting Mixed
Numerals
Examples
Evaluate the following:
a)
5 1
6 +4
6 9
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130. Adding and Subtracting Mixed
Numerals
Examples
Evaluate the following:
a)
5 1 41 37
6 +4 = +
6 9 6 9
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131. Adding and Subtracting Mixed
Numerals
Examples
Evaluate the following:
a)
5 1 41 37
6 +4 = +
6 9 6 9
41× 3 37 × 2
= +
6×3 9×2
LCM of 6
and 9 is 18
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132. Adding and Subtracting Mixed
Numerals
Examples
Evaluate the following:
a)
5 1 41 37
6 +4 = +
6 9 6 9
41× 3 37 × 2
= +
6×3 9×2
LCM of 6
=
123 74
+ and 9 is 18
18 18
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133. Adding and Subtracting Mixed
Numerals
Examples
Evaluate the following:
a)
5 1 41 37
6 +4 = +
6 9 6 9
41× 3 37 × 2
= +
6×3 9×2
LCM of 6
=
123 74
+ and 9 is 18
18 18
197
=
18
17
= 10
18
HOME

134. Adding and Subtracting Mixed
Numerals
Examples
Evaluate the following:
a) Your Turn! b)
5 1 41 37 2 3
6 +4 = + 5 +3 =
6 9 6 9 3 4
41× 3 37 × 2
= +
6×3 9×2
LCM of 6
=
123 74
+ and 9 is 18
18 18
197
=
18
17
= 10
18
HOME

135. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
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136. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
3 3
of 12 = × 12
4 4
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137. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
3 3
of 12 = × 12
4 4
So the problem of finding becomes, what is ?
HOME

138. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
3 3
of 12 = × 12
4 4
So the problem of finding becomes, what is ?
3 12
= ×
4 1
HOME

139. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
3 3
of 12 = × 12
4 4
So the problem of finding becomes, what is ?
3 12
= ×
4 1
3 12
= ×
1 4
HOME

140. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
3 3
of 12 = × 12
4 4
So the problem of finding becomes, what is ?
3 12
= ×
4 1
3 12
= ×
1 4
36
=
4
=9
HOME

141. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
3 3
of 12 = × 12
4 4
So the problem of finding becomes, what is ?
3 12
= × or
4 1
3 12
= ×
1 4
36
=
4
=9
HOME

142. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
3 3
of 12 = × 12
4 4
So the problem of finding becomes, what is ?
3 12 1
= × or Find of 12 and multiply by 3.
4 1 4
3 12
= ×
1 4
36
=
4
=9
HOME

143. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
3 3
of 12 = × 12
4 4
So the problem of finding becomes, what is ?
3 12 1
= × or Find of 12 and multiply by 3.
4 1 4
3 12
= × ⎛ 1 ⎞
1 4 ⎜ × 12 ⎟ × 3 = 3 × 3
⎝ 4 ⎠
36
=
4
=9
HOME

144. Finding a Fraction of a Quantity
In mathematics the word “of” can be replaced by a multiplication symbol.
For example:
3 3
of 12 = × 12
4 4
So the problem of finding becomes, what is ?
3 12 1
= × or Find of 12 and multiply by 3.
4 1 4
3 12
= × ⎛ 1 ⎞
1 4 ⎜ × 12 ⎟ × 3 = 3 × 3
⎝ 4 ⎠
36
= =9
4
=9
HOME

145. Finding a Fraction of a Quantity
Find:
a) 1
of 1 kilometre in metres
10
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146. Finding a Fraction of a Quantity
Find:
a) 1
of 1 kilometre in metres
10
1
= × 1000m
10
HOME

147. Finding a Fraction of a Quantity
Find:
a) 1
of 1 kilometre in metres
10
1
= × 1000m
10
1 1000
= ×
10 1
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148. Finding a Fraction of a Quantity
Find:
a) 1
of 1 kilometre in metres
10
1
= × 1000m
10
1 1000
= ×
10 1
1 1000
= ×
1 10
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149. Finding a Fraction of a Quantity
Find:
a) 1
of 1 kilometre in metres
10
1
= × 1000m
10
1 1000
= ×
10 1
1 1000
= ×
1 10
= 100m
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150. Finding a Fraction of a Quantity
Find:
a) 1 b)
of 1 kilometre in metres 5
10 of 7.2cm
8
1
= × 1000m
10
1 1000
= ×
10 1
1 1000
= ×
1 10
= 100m
HOME

151. Finding a Fraction of a Quantity
Find:
a) 1 b)
of 1 kilometre in metres 5
10 of 7.2cm
8
1
= × 1000m 5 72
10 = × mm
8 1
1 1000
= ×
10 1
1 1000
= ×
1 10
= 100m
HOME

152. Finding a Fraction of a Quantity
Find:
a) 1 b)
of 1 kilometre in metres 5
10 of 7.2cm
8
1
= × 1000m 5 72
10 = × mm
8 1
1 1000 5 72
= × = × mm
10 1 1 8
1 1000
= ×
1 10
= 100m
HOME

153. Finding a Fraction of a Quantity
Find:
a) 1 b)
of 1 kilometre in metres 5
10 of 7.2cm
8
1
= × 1000m 5 72
10 = × mm
8 1
1 1000 5 72
= × = × mm
10 1 1 8
1 1000 = 45mm
= ×
1 10
= 100m
HOME

154. Finding a Fraction of a Quantity
Find:
a) 1 b)
of 1 kilometre in metres 5
10 of 7.2cm
8
1
= × 1000m 5 72
10 = × mm
8 1
1 1000 5 72
= × = × mm
10 1 1 8
1 1000 = 45mm or = 4.5cm
= ×
1 10
= 100m
HOME

155. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples
Find:
3 7
a) ×
5 8
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156. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples
Find:
3 7 3× 7
a) × =
5 8 5×8
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157. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples
Find:
3 7 3× 7
a) × =
5 8 5×8
21
=
40
HOME

158. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples
Find:
3 7 3× 7 2 5
a) × = b) ×
5 8 5×8 5 7
21
=
40
HOME

159. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples
Find:
3 7 3× 7 2 5 2×5
a) × = b) × =
5 8 5×8 5 7 5×7
21
=
40
HOME

160. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples
Find:
3 7 3× 7 2 5 2×5
a) × = b) × =
5 8 5×8 5 7 5×7
21 10
= =
40 35
HOME

161. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples
Find:
3 7 3× 7 2 5 2×5
a) × = b) × =
5 8 5×8 5 7 5×7
21 10
= =
40 35
2
=
7
HOME

162. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples
or
Find:
3 7 3× 7 2 5 2×5
a) × = b) × =
5 8 5×8 5 7 5×7
21 10
= =
40 35
2
=
7
HOME

163. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5
or ×
Find: 5 7
3 7 3× 7 2 5 2×5
a) × = b) × =
5 8 5×8 5 7 5×7
21 10
= =
40 35
2
=
7
HOME

164. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5
a) × = b) × =
5 8 5×8 5 7 5×7
21 10
= =
40 35
2
=
7
HOME

165. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5
a) × = b) × =
5 8 5×8 5 7 5×7
21 10
= =
40 35
2
=
7
HOME

166. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5
a) × = b) × =
5 8 5×8 5 7 5×7
21 10
= =
40 35
2
=
7
HOME

167. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5 2
a) × = b) × = =
5 8 5×8 5 7 5×7 7
21 10
= =
40 35
2
=
7
HOME

168. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5 2
a) × = b) × = =
5 8 5×8 5 7 5×7 7
21 10 Why?
= =
40 35
2
=
7
HOME

169. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5 2
a) × = b) × = =
5 8 5×8 5 7 5×7 7
21 10 Why?
= =
40 35 2 5
= ×
2 5 7
=
7
HOME

170. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5 2
a) × = b) × = =
5 8 5×8 5 7 5×7 7
21 10 Why?
= =
40 35 2 5
= ×
2 5 7
=
7 2×5
=
5×7
HOME

171. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5 2
a) × = b) × = =
5 8 5×8 5 7 5×7 7
21 10 Why?
= =
40 35 2 5
= ×
2 5 7
=
7 2×5
=
5×7
5×2
=
5×7
HOME

172. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5 2
a) × = b) × = =
5 8 5×8 5 7 5×7 7
21 10 Why?
= =
40 35 2 5
= ×
2 5 7
=
7 2×5
=
5×7
5×2
=
5×7
2
= 1×
7
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173. Multiplying Fractions
To multiply Fractions, multiply the numbers in the numerator and then multiply the
numbers in the denominator.
Examples 2 5 2 5
or × = ×
Find: 5 7 5 7
3 7 3× 7 2 5 2×5 2
a) × = b) × = =
5 8 5×8 5 7 5×7 7
21 10 Why?
= =
40 35 2 5
= ×
2 5 7
=
7 2×5
=
5×7
5×2
=
5×7
2
= 1×
7
2
=
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174. Dividing Fractions
Consider the following examples:
Examples:
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175. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 =
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176. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = b) 4 ÷ 2 =
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177. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = b) 4 ÷ 2 = c) 6 ÷ 2 =
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178. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = b) 4 ÷ 2 = c) 6 ÷ 2 = d) 8 ÷ 2 =
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179. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = b) 4 ÷ 2 = c) 6 ÷ 2 = d) 8 ÷ 2 = e)10 ÷ 2 =
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180. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
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181. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1
f) 2 ÷ =
2
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182. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1
f) 2 ÷ = g) 4 ÷ =
2 2
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183. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1
f) 2 ÷ = g) 4 ÷ = h) 6 ÷ =
2 2 2
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184. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1 1
f) 2 ÷ = g) 4 ÷ = h) 6 ÷ = i) 8 ÷ =
2 2 2 2
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185. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1 1 1
f) 2 ÷ = g) 4 ÷ = h) 6 ÷ = i) 8 ÷ = j) 10 ÷ =
2 2 2 2 2
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186. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1 1 1
f) 2 ÷ = 4 g) 4 ÷ = 8 h) 6 ÷ = 12 i) 8 ÷ = 16 j) 10 ÷ = 20
2 2 2 2 2
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187. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1 1 1
f) 2 ÷ = 4 g) 4 ÷ = 8 h) 6 ÷ = 12 i) 8 ÷ = 16 j) 10 ÷ = 20
2 2 2 2 2
Conclusion:
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188. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1 1 1
f) 2 ÷ = 4 g) 4 ÷ = 8 h) 6 ÷ = 12 i) 8 ÷ = 16 j) 10 ÷ = 20
2 2 2 2 2
Conclusion: Dividing by a half is the same as multiplying by 2
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189. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1 1 1
f) 2 ÷ = 4 g) 4 ÷ = 8 h) 6 ÷ = 12 i) 8 ÷ = 16 j) 10 ÷ = 20
2 2 2 2 2
Conclusion: Dividing by a half is the same as multiplying by 2
1
f) 2 ÷ =
2
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190. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1 1 1
f) 2 ÷ = 4 g) 4 ÷ = 8 h) 6 ÷ = 12 i) 8 ÷ = 16 j) 10 ÷ = 20
2 2 2 2 2
Conclusion: Dividing by a half is the same as multiplying by 2
1
f) 2 ÷ = 2 × 2
2
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191. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1 1 1
f) 2 ÷ = 4 g) 4 ÷ = 8 h) 6 ÷ = 12 i) 8 ÷ = 16 j) 10 ÷ = 20
2 2 2 2 2
Conclusion: Dividing by a half is the same as multiplying by 2
1 1
f) 2 ÷ = 2 × 2 g) 4 ÷ =
2 2
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192. Dividing Fractions
Consider the following examples:
Examples:
a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5
1 1 1 1 1
f) 2 ÷ = 4 g) 4 ÷ = 8 h) 6 ÷ = 12 i) 8 ÷ = 16 j) 10 ÷ = 20
2 2 2 2 2
Conclusion: Dividing by a half is the same as multiplying by 2
1 1
f) 2 ÷ = 2 × 2 g) 4 ÷ = 4 × 2
2 2
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