Create Common Denominators to Compare Fractions

Students use equivalent fractions to rewrite two fractions with a common denominator, enabling direct comparison. They use visual models and the multiplication rule to find common denominators.

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Grade 4 · Comparing Fractions · question 1 of 3

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20 rungs. A star at the top.

Omar sells 2/3 of a pie and 1/2 of a pie at the market. He cuts both pies into 6 equal slices. The half pie is 3 slices. How many slices is the 2/3 pie?

How it is taught

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Fractions compare easily when bottoms match.

A common denominator lets the tops decide.

Rename both fractions, then compare the tops.

Read it: Same-size pieces, then compare

Which is more, 2/3 or 3/4? Cut both into twelfths: 8/12 and 9/12. 9 twelfths is more, so 3/4 > 2/3.

Find a denominator both go into: 12.
Rename both: 2/3 = 8/12 and 3/4 = 9/12.
Compare the numerators: 9 twelfths is more than 8 twelfths.

Thirds and fourths are different sizes, so their numerators cannot be compared yet.

Cutting every piece again makes twelfths, the same size on both bars.

With the same pieces, the fraction with more of them is the greater fraction.

Rename to a common denominator, then compare the numerators.

Comparing 2 and 3 when the pieces are different sizes.

Rename first: 8/12 and 9/12. 9 twelfths is more, so 3/4 > 2/3.

Which is greater, 5/6 or 3/4? Rename both to twelfths first. — 5/6. 5/6 = 10/12 and 3/4 = 9/12. 10 twelfths is more than 9 twelfths, so 5/6 > 3/4.

Compare 2/3 and 3/4

Today we'll compare two fractions. Which is bigger — two-thirds or three-fourths?

Here they are. The trouble is, the bottom numbers — the denominators — are different. So we can't tell just by looking.

Let's give both fractions the same bottom. If we multiply the two denominators, three times four, we get twelve. So we'll rewrite both fractions in twelfths.

To turn two-thirds into twelfths, we multiply the top and the bottom by four.

Two times four is eight. Three times four is twelve. So two-thirds equals eight-twelfths.

Now for three-fourths. To make twelfths, we multiply the top and the bottom by three.

Three times three is nine. Four times three is twelve. So three-fourths equals nine-twelfths.

Both fractions are now in twelfths. When the bottoms match, we just compare the tops. Eight is less than nine.

Grade 4 · Rewriting fractions in twelfths to compare

So eight-twelfths is less than nine-twelfths, which means two-thirds is less than three-fourths. Three-fourths is the bigger fraction!

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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