This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authored by Darren Rigby
Math Basics Learning Centre
Working with Fractions
ADDITION AND SUBTRACTION OF FRACTIONS
For fractions having the same denominator:
a. Add or subtract the numerators.
b. Keep the same denominator.
For fractions having different denominators:
a. Convert to equivalent fractions having their LCD.
b. Add or subtract the numerators of the new
fractions.
c. Keep the LCD as the denominator.
For problems involving mixed numerals:
a. Add or subtract the fraction parts of the numbers,
as above.
If you need to borrow:
a. Subtract one from the whole number part of
the top number.
b. Add 1 (i.e.,
n
⁄
n
) to the fraction part of the top
number.
c. Continue with the problem.
b. Add or subtract the whole numbers in the problem.
c. Add the two results at the end.
MULTIPLICATION OF FRACTIONS
To multiply a fraction by a whole number:
a. Multiply the numerator by the whole number.
b. Write the result over the denominator.
To multiply a fraction by another fraction:
a. Multiply the numerators.
b. Multiply the denominators.
When a multiplication problem involves a mixed numeral,
convert it to an improper fraction* first.
DIVISION OF FRACTIONS
To divide with fractions, or fractions and whole numbers:
a. Invert the divisor. Remember that whole
numbers can be written as fractions over 1.
b. Multiply the fractions.
1
6
3
6
4
6
2
3
+ = =
Example 1:
3
4
5
8
6
8
5
8
3
8
1
+ =
=
=
Example 2:
3
5
8
24
5
4
5
× = =
4
Example 4:
1
2
7
8
7
16
× =
Example 5:
4
9
5
6
4
9
÷ = × = =
6
5
24
45
8
15
Example 6:
2
3
2
3
÷ = × = =
1
8
2
24
1
12
8
Example 7:
1
3
2
5
5
15
6
15
14
15
−1 = 1 = 1
3 = 3 = 2
Example 3:
20
15
6
15
. 2
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
When a division problem involves a mixed numeral, convert it to an improper fraction
first.
* For help with converting to improper fractions, see the Equivalent Fractions worksheet
.
EXERCISES
A. Add or subtract:
1)
3
⁄
7
+
2
⁄
7
= 3) 5
7
⁄
8
− 2
5
⁄
8
=
2)
13
⁄
16
−
3
⁄
16
= 4) 2
3
⁄
5
+ 5
2
⁄
5
=
B. Add or subtract:
1)
1
⁄
5
+
1
⁄
2
= 5) 5
1
⁄
4
+
3
⁄
8
=
2)
1
⁄
3
−
2
⁄
7
= 6) 8
11
⁄
14
+ 7
1
⁄
2
=
3) 1
1
⁄
8
+ 2
3
⁄
5
= 7) 14 − 3
7
⁄
8
=
4) 7
1
⁄
2
− 5
4
⁄
15
= 8) 14
1
⁄
6
− 11
1
⁄
2
=
C. Multiply:
1)
4
⁄
5
× 2 = 5)
5
⁄
2
×
2
⁄
5
=
2) 15 ×
2
⁄
5
= 6)
3
⁄
8
×
16
⁄
21
=
3)
3
⁄
10
×
5
⁄
6
= 7) 5
1
⁄
8
× 16 =
4)
1
⁄
2
×
1
⁄
8
= 8) 13
1
⁄
3
× 1
1
⁄
2
D. Divide:
1)
8
⁄
27
÷
2
⁄
9
= 5)
1
⁄
2
÷ 16 =
2)
3
⁄
5
÷
6
⁄
25
= 6) 5
1
⁄
2
÷ 11 =
3)
3
⁄
4
÷
9
⁄
16
= 7) 5 ÷ 7
1
⁄
7
=
4) 16 ÷
1
⁄
2
= 8) 5
3
⁄
5
÷ 2
1
⁄
2
=
SOLUTIONS
A. (1)
5
⁄
7
(2)
5
⁄
8
(3) 3
2
⁄
8
3
1
⁄
4
(4) 7
5
⁄
5
8
B. (1)
2
⁄
10
+
5
⁄
10
=
7
⁄
10
(2)
7
⁄
21
−
6
⁄
21
=
1
⁄
21
(3) 1
5
⁄
40
+ 2
24
⁄
40
= 3
29
⁄
40
(4) 7
15
⁄
30
− 5
8
⁄
30
= 2
7
⁄
30
(5) 5
2
⁄
8
+
3
⁄
8
= 5
5
⁄
8
(6) 8
11
⁄
14
+ 7
7
⁄
14
= 15
18
⁄
14
16
4
⁄
14
16
2
⁄
7
(7) 13
8
⁄
8
− 3
7
⁄
8
= 10
1
⁄
8
(8) 14
1
⁄
6
− 11
3
⁄
6
13
7
⁄
6
− 11
3
⁄
6
= 2
4
⁄
6
2
2
⁄
3
C. (1)
8
⁄
5
1
3
⁄
5
(2)
30
⁄
5
6 (3)
15
⁄
60
1
⁄
4
(4)
1
⁄
16
(5)
10
⁄
10
1 (6)
48
⁄
168
2
⁄
7
(7)
41
⁄
8
×
16
⁄
1
=
656
⁄
8
82 (8)
40
⁄
3
×
3
⁄
2
=
120
⁄
6
20
D. (1)
72
⁄
54
1
18
⁄
54
1
1
⁄
3
(2)
75
⁄
30
2
15
⁄
30
2
1
⁄
2
(3)
48
⁄
36
1
12
⁄
36
1
1
⁄
3
(4)
16
⁄
1
×
2
⁄
1
=
32
⁄
1
32 (5)
1
⁄
2
×
1
⁄
16
=
1
⁄
32
(6)
11
⁄
2
×
1
⁄
11
=
11
⁄
22
1
⁄
2
(7)
5
⁄
1
×
7
⁄
50
=
35
⁄
50
7
⁄
10
(8)
28
⁄
5
×
2
⁄
5
=
56
⁄
25
= 2
6
⁄
25