Operations on Fractions – JSS1 Mathematics Lesson Note (First Term)

Operations on fractions are addition, subtraction, multiplication and division. To add or subtract fractions with the same denominator, add or subtract the numerators and keep the denominator. If the denominators differ, find their LCM first. To multiply, multiply the numerators together and the denominators together. To divide, change the sign to multiplication and turn the second fraction upside down.

Behavioural objectives

By the end of the lesson, students should be able to:

• add and subtract fractions with the same denominator;
• add and subtract mixed numbers by using the LCM of the denominators;
• multiply fractions, including mixed numbers changed to improper fractions;
• divide one fraction by another by multiplying by the inverse.

How do you add and subtract fractions?

Example 1

Find the value of the following: (a) 4/9 + 5/9 + 7/9 (b) 5/8 – 3/8 (c) 1 + 4/7

Solution

(a) 4/9 + 5/9 + 7/9 = 16/9 (the denominators are the same, so we add the numerators together).

(b) 5/8 – 3/8 = 2/8 (the denominator is the same, so we subtract the numerators from each other).

Try (c) yourself.

Example 2

Simplify the following: (a) 33/4 + 5/8 + 17/12 (b) 2 + 4 2/5 – 5 3/5

Solution

(a) Find the LCM of the denominators 4, 8 and 12. The LCM is 24. Then add the fractions together:

33/4 + 5/8 + 17/12 = (198 + 15 + 34)/24 = 247/24

Convert the improper fraction to a mixed number.

(b) Rearrange the sum by separating the whole numbers from the fractions.

• Whole numbers: 2 + 4 – 5 = 1
• Fractions (same denominator): 2/5 – 3/5 = -1/5
• Answer: 1 – 1/5 = 4/5

How do you multiply and divide fractions?

Example 1

Simplify the following:

1. 4/5 × 2/3
2. Find the product of 3 5/17, 2 5/6 and 4/8.
3. 3/5 ÷ 4/9
4. 2 4/5 × 5 6/8 ÷ 5 1/9

Solution

(a) 4/5 × 2/3 = 8/15 (multiply the numerators together and the denominators together).

(b) Change the mixed numbers to improper fractions:

3 5/17 × 2 5/6 × 4/8 = 56/17 × 17/6 × 4/8

Cancel where you can: the 17s cancel, 4/8 becomes 1/2, and 56 and 6 are both divisible by 2.

= 14/3 = 4 2/3

(d) Change the mixed numbers to improper fractions. Change the division sign to multiplication and turn the last fraction upside down:

2 4/5 × 5 6/8 ÷ 5 1/9 = 14/5 × 46/8 × 9/46

Cancel the 46s (46 divides 46):

= 63/20 = 3 3/20

Evaluation

1. How do you add fractions that have the same denominator?
2. What do you do before adding fractions with different denominators?
3. Solve Example 1(c) under addition and subtraction: 1 + 4/7.
4. Solve 3/5 ÷ 4/9, and state how you changed the division sign.