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Fraction foundations · Lesson 3 of 3

Equivalent fractions

Change the number of pieces without changing the amount. See why one half is also two fourths.

Explore it

More pieces. The same amount.

Split each half into smaller equal pieces. Both bars represent the same-sized whole.

Start with one half 1/2
Split each half into 2 pieces 2/4

1/2 = 2/4
(1 × 2) / (2 × 2) = 2/4

The shaded length never changes. Both the shaded parts and the total parts are multiplied by 2.

Look a little closer

New names for the same amount.

Start with 1/2 of a bar. Split each half into 2 equal pieces. The whole now has 4 parts, and 2 are shaded.

You have not added or removed any of the bar. That is why 1/2 = 2/4. These are called equivalent fractions.

In numbers: multiply both the numerator and denominator by 2. Multiplying only one of them would change the amount.

Give the idea a try.

Take your time. Each answer comes with an explanation, and you can try again.

Think it through · 1Split every third into 2 equal pieces. What is another name for 2/3?
Think it through · 2Why are 1/2 and 3/6 equal?

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Try fresh questions on this idea, or keep exploring the series.

Revisit fraction foundations