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Generate and Recognize Equivalent Fractions

Students practice creating multiple equivalent fractions for a given fraction, recognize equivalent fractions in sets, and use their understanding to simplify and rename fractions in real-world contexts.

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Generate and Recognize Equivalent Fractions

Grade 4 · Equivalent Fractions · question 1 of 3

0 of 20

20 rungs. A star at the top.

1/2 = 4.

How it is taught

0:00 of 4:40

One amount can be written as many equivalent fractions.

Multiply or divide both parts by the same number.

Read it: Same amount, different name

Two friends share a chocolate bar. Leo breaks his half into two pieces and says he has more, because two is more than one. Look at the chocolate, not the pieces.

  1. Maya has one piece out of two: 1/2.
  2. Leo cut his half into two, so he has two pieces out of four: 2/4.
  3. Slide Leo's two pieces together. They are exactly the size of Maya's one.

Cutting a piece into more pieces changes how many pieces there are. It does not change how much chocolate there is.

A fraction is a name for an amount. The same amount can carry more than one name — 1/2, 2/4, 3/6, 4/8 all name Maya's half.

When the top and the bottom are both multiplied by the same number, the name changes and the amount stays.

Multiply the top and the bottom by the same number: the fraction has a new name and the same value.

Reading 2/4 as more than 1/2 because 2 is more than 1.

The bottom number says how small the pieces are. Fourths are smaller than halves, so two of them are only worth one half.

___/12 = 3/4 — 9. Since 4 × 3 = 12, multiply 3 × 3 to get 9.

2/3 = 4/6

Today we'll learn about equivalent fractions — fractions that look different but show the exact same amount.

Here's a bar split into three equal parts, with two parts shaded.

We write that as two over three — two-thirds.

Here's another bar, split into six equal parts, with four shaded.

We write that as four over six — four-sixths.

Look — the shaded areas are exactly the same length! Two-thirds and four-sixths are equivalent.

Here's the trick. Multiply the top number — the numerator — by two: two times two is four.

Now multiply the bottom number — the denominator — by the same two: three times two is six.

Equivalent FractionsSame amount, different names=2346× 2× 2Multiply top and bottom by the same numberEQUIVALENT23 = 46same amount
Grade 4 · Same amount, different names

The big idea: multiply the top and bottom by the same number, and the fraction stays equivalent.

So two-thirds equals four-sixths. Same amount, just a different name. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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