A whole number can be written as a fraction with denominator 1. Then use the same multiplication rule.

Worked Example

Calculate: $\frac{2}{3} \times 12$

Solution

Write 12 as a fraction: $12 = \frac{12}{1}$

$\frac{2}{3} \times 12 = \frac{2}{3} \times \frac{12}{1} = \frac{2 \times 12}{3 \times 1} = \frac{24}{3}$

Now simplify: $\frac{24}{3} = 8$

Therefore, $\frac{2}{3} \times 12 = 8$

To divide a fraction by a whole number, write the whole number as a fraction, flip it (write its reciprocal), and multiply.

Steps:

1. Write the whole number as a fraction (with denominator 1)
2. Flip the divisor (swap numerator and denominator)
3. Multiply the fractions

Worked Example

Calculate: $\frac{1}{2} \div 3$

Solution

Write 3 as a fraction: $3 = \frac{3}{1}$

Flip the divisor: $\frac{3}{1}$ becomes $\frac{1}{3}$

Multiply: $\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}$

Therefore, $\frac{1}{2} \div 3 = \frac{1}{6}$

To divide one fraction by another, flip the divisor and multiply.

Steps:

1. Flip the second fraction (the divisor)
2. Multiply the two fractions

Worked Example

Calculate: $\frac{3}{8} \div \frac{4}{6}$

Solution

Flip the divisor: $\frac{4}{6}$ becomes $\frac{6}{4}$

Multiply: $\frac{3}{8} \times \frac{6}{4} = \frac{3 \times 6}{8 \times 4} = \frac{18}{32}$

Simplify: $\frac{18}{32} = \frac{9}{16}$

Therefore, $\frac{3}{8} \div \frac{4}{6} = \frac{9}{16}$

• Always simplify your answer if possible
• When multiplying fractions: multiply top × top and bottom × bottom
• When dividing fractions: flip the second fraction and multiply
• A whole number is also a fraction with denominator 1

In Tanzanian markets, multiplication and division of fractions are useful for everyday transactions. For example, if a trader at Buguruni market has $\frac{3}{4}$ of a 50 kg bag of maize flour left and wants to divide it equally among 3 customers, the trader calculates $\frac{3}{4} \div 3 = \frac{1}{4}$, so each customer gets $\frac{1}{4}$ of the 50 kg bag, which is 12.5 kg of maize flour.