Dividing Fractions
Multiply by the reciprocal of the divisor.
Key idea
Multiply by the reciprocal of the divisor.
In depth
Dividing by a fraction asks how many of it fit. Equivalent to multiplying by its reciprocal: a/b ÷ c/d = a/b × d/c. Division by 1/2 doubles because two halves fit in each whole.
Worked example
3/4 ÷ 1/2 = 3/4 × 2 = 3/2 = 1½.
Formula
Real-world uses
- Working out how many 3/4-metre pieces come from a 6-metre board
- Dosage and portion calculations
Common mistake
Flipping the wrong fraction. Only flip the divisor (the second one).
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Dividing Fractions?
Multiply by the reciprocal of the divisor. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Dividing Fractions?
The key formula is (a/b) ÷ (c/d) = ad/bc.
Where is Dividing Fractions used in real life?
Real-world examples: Working out how many 3/4-metre pieces come from a 6-metre board; Dosage and portion calculations.
What should I learn before Dividing Fractions?
Make sure you are comfortable with Multiplying Fractions, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Dividing Fractions?
Flipping the wrong fraction. Only flip the divisor (the second one).
How can I practise Dividing Fractions?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Dividing Fractions?
Move on to Mixed Numbers next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.