Multiplying Fractions
Multiply numerators and denominators.
Key idea
Multiply numerators and denominators.
In depth
Multiplying means taking a fraction of a fraction. Multiply the numerators and denominators across: (a/b)(c/d) = ac/bd. Cancel common factors first to keep numbers small.
Worked example
2/3 × 3/8 = 6/24 = 1/4. Or cancel the 3s first: 2/8 = 1/4.
Formula
Real-world uses
- Finding a fraction of an amount such as 2/3 of a class
- Scaling recipes
- Calculating areas of rectangles
Common mistake
Looking for a common denominator. You do not need one for multiplication.
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 Multiplying Fractions?
Multiply numerators and denominators. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Multiplying Fractions?
The key formula is (a/b)(c/d) = ac/bd.
Where is Multiplying Fractions used in real life?
Real-world examples: Finding a fraction of an amount such as 2/3 of a class; Scaling recipes; Calculating areas of rectangles.
What should I learn before Multiplying Fractions?
Make sure you are comfortable with Subtracting Fractions, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Multiplying Fractions?
Looking for a common denominator. You do not need one for multiplication.
How can I practise Multiplying 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 Multiplying Fractions?
Move on to Dividing Fractions 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.