2. EQUIVALENT FRACTIONS

3. Definition:
– Equivalent fractions are fractions having the same
values.
– It can be obtained by multiplying both the
numerator and the denominator of the given
fraction by the same non-zero whole number.
Example :

4. Determining equivalent fractions
– To determine whether two fractions are equivalent,
convert each fraction into fractions with a common
(same) denominator. Then, compare the numerators.
Example :

5. Comparing two fractions
– If two fractions have the same denominators, their
values can be compared by comparing
their numerators or by using a number line.
Example :

6. – If two fractions have different denominators, convert
both fractions into their respective
equivalent fractions with the common denominator.
Example :

7. Arranging fractions in order
– To arrange fractions in order, convert the given
fractions into equivalent fractions with
the common denominator and then compare the
numerators.

8. Example :

9. Lowest terms
– To simplify a fraction to its lowest terms, divide the
numerator and the denominator of
the fraction by their HCF.
Example :

10. Mixed Numbers
Definition:
– A mixed number is a number consisting of a whole
number and a fraction
Example :

11. Comparing and arranging
mixed numbers
– Like fractions, mixed numbers can be arranged and
compared on a number line. Any number on the
number line is greater than numbers to its left.
Example :

13. PROPER FRACTIONS AND
IMPROPER FRACTIONS

14. • Definition:
– A proper fraction is a fraction whose numerator is
less than the denominator
• example:

15. • Definition
– An improper fraction is a fraction whose numerator is
equal to or greater than the denominator
• example:

17. • Changing mixed numbers into improper fractions
– To change a mixed number into an improper fraction,
multiply the whole number by the denominator and
then add the numerator to it. The denominator
remains the same.

18. • example:

19. • Changing improper fractions into mixed
numbers
– To change an improper fraction into a mixed
number, divide the numerator by the
denominator. The quotient obtained is the whole
number part and the remainder is the numerator
of the fractional part.

20. • example:

21. 17
6

22. ADDITION OF FRACTIONS

23. • Definition:
– Addition of fractions is a process of finding the sum of
two or more fractions
• Adding two fractions with the same denominator
– To add two fractions with the same denominator,
keep the denominator and add the numerators.

24. • Example 1:

25. • Example 2:

26. • Adding two fractions with different denominators
– To add two fractions with different denominators,
convert both the fractions into their respective
equivalent fractions with the same denominators.
• example:

27. • Adding whole numbers and fractions
– A mixed number is produced when adding a whole
number and a fraction.
• example:

28. • Adding fractions and mixed numbers
– To add a fraction and a mixed number, keep the
whole number part and add the fractional
parts like adding two fractions.
• example:

29. • Adding two mixed numbers
– Convert mixed numbers into improper fractions. Then
perform the addition
like adding two fractions.
• example:

30. • Adding three fractions
– Convert the fractions so that they have a common
denominator before performing the addition.
• example: