Mathematics · Fractions and decimals

Equivalent fractions

Are 1/2 and 2/4 the same amount? Learn to find equivalent fractions by multiplying or dividing the numerator and denominator by the same number, to simplify fractions, and to find the simplest form.

15 min
1 simulation
Mini quiz

Updated: 15 October 2026

Preview

The question

Zeynep is making biscuits with her mum. The recipe asks for "half a glass of milk", but the measuring jug at home only has lines for quarter glasses. Up to which line should Zeynep pour the milk? And what if the recipe said "three quarters of a glass of sugar" and the jug had lines for eighths?

Can two fractions that look different show the same amount? In this lesson we'll look for the answer.

Try it yourself

No account needed: change the values and check your answer. Some simulations ask for a prediction before they start; it doesn't matter whether it's right or wrong.

Fraction model

How many eighths equal 3/4?

Set the number of parts to 8, tap the slices you want and press Check.

Predict first

If you cut the pizza into 8 slices instead of 4, what happens to the number of slices you need for 3/4 of the pizza?

It doesn’t matter whether you’re right; the simulation opens once you choose.

Lab

The divided water tank

Open full page in the Lab →

Fig. 1The divided water tank

Pull the lever: the parts get finer, the water stays put

1/2 · 50%

Starting fraction (×1)

Numerator

parts filled

Denominator

number of parts

Split lever (factor)

Split every part into how many pieces?

Same amount

Water level: 50%

Pull the lever and watch the water: the numerator and denominator grow together.

Simplest form: 1/2

Learn

Progress is kept on this page only; no points are given.

1Predict
2Try
3Explain

The tank is 1/2 full. If you pull the lever to ×3 and split every part into 3 pieces, what happens to the water level?

The height from the tank’s floor up to the “1 whole” line is split into as many equal parts as the denominator, and the water fills as many parts as the numerator. When the lever splits every part into k equal pieces, both the denominator and the number of filled parts are multiplied by k, so the water level (numerator ÷ denominator) does not change: a/b = (a × k)/(b × k), k ≠ 0. Adding the same number to the top and bottom does change the level.

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Frequently asked

5 questions

What are equivalent fractions?

Fractions that are written differently but show the same amount. 1/2, 2/4 and 3/6 all show half of the same strip, so they are equivalent.

How do I find an equivalent fraction?

Multiply or divide the numerator and the denominator by the same number, as long as it is not zero. For example, multiplying the top and bottom of 2/3 by 4 gives 8/12; both are the same amount.

What do simplifying and simplest form mean?

Simplifying means dividing the numerator and the denominator by a common factor. A fraction is in simplest form when the two have no common factor other than 1: dividing 12/18 by 6 gives 2/3.

If I add the same number to the top and bottom, do I get an equivalent fraction?

No. Adding 1 to the top and bottom of 1/2 gives 2/3, which is more than a half. For equivalent fractions you only multiply or divide.

Can I multiply the top and bottom by 0?

No. A denominator of 0 makes the fraction undefined, because you cannot split a whole into zero equal parts. The number you multiply or divide by must not be 0.