2. Integers: …, -3, -2, -1, 0, 1, 2, 3, …
A Rational Number can be written in the
form a , where a and b are integers and
b ≠ 0. b
2
3
www.visualfractions.com
4. Equivalent (equal) fractions represent the same
number.
2 2 4
3 2 6
2 3 6
3 3 9
Fundamental Law of Fractions a a c
b b c
5. 2 6
Show that and are equal by finding
3 9
a common denominator.
The least common denominator of two
fractions is the LCM of their denominators.
LCM(3,9) = 9
2 3 6
3 3 9
6. 2 6
Show that and are equal by
3 9
simplifying both fractions.
A fraction is in simplest form if its
numerator and denominator have no
common factor other than 1.
2 is simplified
6 3 2
3 9 3 3
7. 2 6
Show that and
3 9 are equal by cross
multiplying.
a c
if ad bc
b d
18 18 18 = 18
2 6 so 2 6
3 9 3 9
8. Ordering rational numbers
Place <, > or = between the two numbers:
2 3
< 0 1 2 3 4 5 6
1
7 7 7 7 7 7 7 7 7
1 3
> 7
5 5
1
1 1
< 5
5 4 1
4
9. 1 1
Find one rational number between and
5 4
1 4 1 5 LCD = 20
5 4 4 5
4 2 5 2
20 2 20 2
9
8 10
40
40 40
11. A mixed number represents the sum of an integer
and a fraction.
1 1
1 2 1 2
1 1
1 2 1 2
-2 11
2 -1 0
1
1 1 2
2
12. 2
Change 1 3
to an improper fraction.
An improper fraction has a numerator that is greater
than or equal to its denominator.
2 3 2
1 3 3 3
2
1 3 5
3
24. Dividing rational numbers
6 3
=2 3 3
How many threes are in six?
6 2
=3 2 2 2
How many twos are in six?
25. 6 ½
= 12
How many one-halfs are in six?
6 ¼
= 24
How many one-fourths are in six?
26. 1 1
3 6
=2
How many one-sixths are in one-third?
a c a d
b d b c
1 1 1 6 6
2
3 6 3 1 3
27. Jane has 20 yards of fabric. How many blouses
can she make if each blouse requires:
a) 2 yards of fabric
20 2 = 10 blouses
28. Jane has 20 yards of fabric. How many blouses
can she make if each blouse requires:
b) 2 ½ yards of fabric 8 blouses
1 5 20 2 40
20 2 2 20 2 1 5 5 =8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
29. Jane has 20 yards of fabric. How many blouses
can she make if each blouse requires:
c) 2 1
yards of fabric 8 blouses
3
1 7 20 3 60 4
20 2 3 20 3 1 7 7 8 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
d) How many yards of fabric is left over?
1 7 56 2
Fabric used: 8 2 3 8 3 3 18 3 yards
Fabric left: 20 18 2 1 1 yards
3 3