Generate Equivalent Fractions with a Common Denominator

Students convert two or more fractions with unlike denominators into equivalent fractions that share a common denominator, preparing them to add or subtract. Students multiply numerator and denominator by the same factor to maintain equivalence.

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Grade 5 · Adding and Subtracting Fractions with Unlike Denominators · question 1 of 3

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20 rungs. A star at the top.

8 = 15/40

How it is taught

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Equivalent fractions name the same amount with a new bottom.

You multiply the top and the bottom by the same number.

Read it: Make one cut, then count

1/5 and 3/10 are cut differently: one bar in fifths, one in tenths. Cut each fifth into 2 and 1/5 is 2/10. Now the pieces line up: 2/10 + 3/10 = 5/10, which is 1/2.

Find a cut both bottom numbers go into: 5 and 10 both go into 10.
Write each fraction in that cut: 1/5 is 2/10, and 3/10 stays 3/10.
Add or take away the top numbers and keep the cut: 2/10 + 3/10 = 5/10, which is 1/2.

Pieces of different sizes cannot be counted together, so both bars are cut into the same pieces first.

Cutting a piece into smaller pieces does not change the amount: 1/5 and 2/10 shade the same part of a bar.

The least common denominator is the smallest cut both go into, so its pieces are the biggest that line up.

To add or subtract fractions with different denominators, write both in a common denominator, then add or subtract the numerators.

Adding the tops and the bottoms: 1/5 + 3/10 = 4/15.

4/15 is less than 3/10 alone, because fifteenths are smaller pieces. Cut both into tenths: 2/10 + 3/10 = 5/10, which is 1/2.

Write 7/12 and 7/8 with one denominator, 24. 7/8 = ___/24 — 21. 12 and 8 both go into 24: 7/12 is 14/24 and 7/8 is 21/24.

1/3 and 1/4 → twelfths

Today we'll turn two fractions with different bottoms into matching ones — fractions that share a denominator.

Here's one-third and one-fourth. Their denominators — three and four — are different sizes.

We need a number that both three and four fit into. Three times four is twelve. Twelve is our common denominator!

Start with one-third. To turn the bottom into twelve, multiply by four. Whatever we do to the bottom, we do to the top.

One times four is four. So one-third equals four-twelfths.

Now one-fourth. To turn the bottom into twelve, multiply by three. The top must get times three too.

One times three is three. So one-fourth equals three-twelfths.

Look! Four-twelfths and three-twelfths — both have the same denominator now.

Grade 5 · Make the denominators match

Same-size pieces! Now we're ready to add or subtract. That's how we build equivalent fractions with a common denominator.

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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