Multiply a Fraction by a Fraction

Students learn to multiply two fractions by multiplying numerators together and denominators together, then simplify. They use visual models like area diagrams to confirm understanding of 'a fraction of a fraction'.

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Real questions from this skill, graded here. No account, and nothing is saved.

Grade 5 · Multiplying Fractions · question 1 of 3

0 of 20

20 rungs. A star at the top.

1/9 × = 1/36

How it is taught

0:00 of 4:15

Times means multiply tops, then multiply bottoms.

The product of two unit fractions is a smaller unit.

Read it: A part of a part

2/3 × 3/4 is 2/3 of 3/4. Cut a whole 3 down and 4 across: 12 cells. The two shades cross on 6 of them, so 2/3 × 3/4 = 6/12, which is 1/2 in simplest form.

Shade the first fraction one way: 2 of the 3 rows.
Shade the second fraction the other way: 3 of the 4 columns.
The cells inside both shades, over all the cells, are the product: 6/12 = 1/2.

Multiplying the denominators counts the cells in the whole: 3 × 4 = 12.

Multiplying the numerators counts the cells inside both shades: 2 × 3 = 6.

A part of a part is smaller than either part: 1/2 is less than 2/3 and less than 3/4.

Multiply the numerators for the top and the denominators for the bottom, then simplify: 2/3 × 3/4 = 6/12 = 1/2.

Adding the fractions instead of multiplying them: 2/3 + 3/4 = 17/12, more than either.

Multiplying takes a part of a part, so the product is smaller: 2/3 × 3/4 = 1/2.

1/3 × 2/11 = ___ — 2/33. Cut the whole 3 by 11: 33 cells. The shades cross on 2 cells: 2/33.

1/2 × 2/3

Today we'll multiply a fraction by a fraction. What is one-half of two-thirds?

First, let's draw two-thirds. We split a whole into three equal parts and shade two of them.

Now we want one-half of that. So we split the same whole the other way — into two equal rows.

The piece that's shaded BOTH ways is one-half of two-thirds.

The whole is now split into six equal pieces, and two of them are double-shaded. That's two-sixths.

Grade 5 · A fraction of a fraction

Let's write it with numbers. One-half times two-thirds.

Multiply the numerators: one times two is two.

Multiply the denominators: two times three is six.

So one-half times two-thirds equals two-sixths.

Two-sixths simplifies to one-third — both top and bottom share a factor of two.

One-half of two-thirds is one-third. Multiply across the top, multiply across the bottom!

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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Standard

CCSS.5.NF.B.4

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction

Grade 5

Quoted from the Common Core State Standards.

Where this sits

Comes after

Interpret (a/b) × q as Parts of a Partition

Leads to

What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 5

This is one rung of 81 in Grade 5 mathematics, in the order they build on each other.

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