Multiplying & dividing fractions
🎯 In this topic you will
- Multiply a proper fraction by a whole number.
- Divide a proper fraction by a whole number.
🧠 Key Words
- denominator
- numerator
- operator
- proper fraction
- unit fraction
Show Definitions
- denominator: The number below the fraction bar that shows how many equal parts the whole is divided into.
- numerator: The number above the fraction bar that shows how many parts of the whole are being considered.
- operator: A symbol or number that tells you to perform a mathematical action such as multiplying or dividing a quantity.
- proper fraction: A fraction in which the numerator is smaller than the denominator, so the value is less than one.
- unit fraction: A fraction that has 1 as its numerator, representing one equal part of a whole.
➗ Dividing Fractions by Whole Numbers
Mia is dividing a fraction by a whole number.
📚 Learning About Fraction Operations
In this unit you will learn about multiplying and dividing fractions by a whole number.
❓ EXERCISES
1. Write an addition sentence and a multiplication sentence for this diagram.
👀 Show answer
Multiplication sentence: $ 3 \times \frac{4}{6} $.
2. Write a multiplication sentence that is equivalent to this addition diagram.
👀 Show answer
3. Calculate.
a. $ \frac{3}{5} \times 2 $
b. $ \frac{7}{8} \times 5 $
c. $ \frac{5}{6} \times 4 $
Check your answers with your partner.
👀 Show answer
b. $ \frac{7}{8} \times 5 = \frac{35}{8} = 4\frac{3}{8} $.
c. $ \frac{5}{6} \times 4 = \frac{20}{6} = \frac{10}{3} = 3\frac{1}{3} $.
4. Copy the sorting table and write the letter of each expression in the correct place.
A. $ \frac{2}{8} \times 4 $
B. $ 3 \times \frac{2}{3} $
C. $ \frac{3}{4} \times 4 $
D. $ \frac{2}{8} \text{ of } 4 $
E. $ \frac{2}{3} \times 3 $
F. $ \frac{2}{8} + \frac{2}{8} + \frac{2}{8} + \frac{2}{8} $
G. $ \frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4} $
H. $ \frac{2}{3} \text{ of } 3 $
| Answer = $1$ | Answer = $2$ | Answer = $3$ |
|---|---|---|
| $A, D$ | $B, E, H$ | $C, F, G$ |
👀 Show answer
Answer $=2$: $B, E, H$.
Answer $=3$: $C, F, G$.
5. Saif writes the calculation $ 5 \times \frac{2}{3} $. Which of the following statements are true for his calculation?
A. The answer is between $1$ and $2$.
B. The answer is between $2$ and $3$.
C. The answer is between $3$ and $4$.
D. The answer is between $4$ and $5$.
👀 Show answer
Correct statement: $C$.
6. Oscar, Bruno and Ali equally share $ \frac{2}{3} $ of a large pie. What fraction of the whole pie did each boy get? Draw a diagram to show your answer.
👀 Show answer
7. Calculate.
a. $ \frac{5}{8} \div 2 $
b. $ \frac{2}{3} \div 4 $
👀 Show answer
b. $ \frac{2}{3} \div 4 = \frac{2}{12} = \frac{1}{6} $.
8. Calculate.
a. $ \frac{4}{5} \div 2 $
b. $ \frac{5}{8} \div 2 $
c. $ \frac{3}{5} \div 5 $
Check your answers with your partner.
👀 Show answer
b. $ \frac{5}{8} \div 2 = \frac{5}{16} $.
c. $ \frac{3}{5} \div 5 = \frac{3}{25} $.
9. Write a whole number less than $10$ in each box to make these number sentences correct.
a. $ \frac{2}{3} \div \square = \frac{1}{9} $
b. $ \frac{3}{4} \div \square = \frac{1}{12} $
👀 Show answer
b. $9$.
🧠 Think like a Mathematician
Challenge: Find values that make this number sentence correct.
□$\div$□$=$$\frac{5}{24}$
The first box represents a fraction and the second box represents a whole number.
Your Task:
- Choose a fraction for the first box.
- Choose a whole number for the second box.
- Check whether dividing the fraction by the whole number gives $\frac{5}{24}$.
- Try to find more than one possible pair of values that makes the number sentence correct.
Follow-up Questions:
Show Answers
- 1: One possible solution is $\frac{5}{12} \div 2 = \frac{5}{24}$.
- 2: Another example is $\frac{5}{8} \div 3 = \frac{5}{24}$.
- 3: Dividing a fraction by a whole number multiplies the denominator by that number. In general, $\frac{a}{b} \div n = \frac{a}{bn}$.