Equivalent fractions (age 9+)
Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths
What a learner can do afterwards
- Use a fraction strip to show 2/3 = 4/6 = 6/9
- Explain that multiplying numerator and denominator by the same number gives an equivalent fraction because the size of the whole is unchanged
- Generate three fractions equivalent to 3/5 and verify with diagrams
The lesson
You already know 2/3 and 4/6 name the same amount. Here's why: if you cut every part of a fraction into the same number of smaller pieces, the shaded amount doesn't change, only the number of pieces does. Multiply the numerator and the denominator by the same number, and you get an equivalent fraction.
Priya wants a fraction equivalent to 3/5. She multiplies the numerator and denominator by 2: 3 x 2 = 6, and 5 x 2 = 10. So 3/5 = 6/10.
Always multiply both the numerator and the denominator by the same number. If you multiply only one of them, the value of the fraction changes.
Multiply the numerator and denominator by the same number, and the fraction's value stays exactly the same.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.