Multiply a Fraction by a Whole Number

Students multiply a fraction a/b by a whole number n by understanding that n × (a/b) = (n × a)/b. They use models, repeated addition, and equations to build fluency, including results greater than 1 that require conversion to mixed numbers.

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

Grade 4 · Multiplying Fractions by Whole Numbers · question 1 of 3

0 of 20

20 rungs. A star at the top.

= 6 × 1/12

How it is taught

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To multiply a fraction by a whole number, multiply the top only.

The bottom stays the same.

Read it: Copies make a longer run

4/5 is 4 pieces of a bar cut into 5. Take 2 copies of it and the run is 8 pieces, each still 1/5: 2 × 4/5 = 8/5, which is more than 1 bar.

Shade 1 copy: 4/5 is 4 pieces of 1/5.
Take it 2 times: 2 copies of 4 pieces make 8 pieces.
Keep the bottom number, because the pieces are still fifths: 2 × 4/5 = 8/5.

Multiplying by a whole number takes copies of the fraction, and each copy adds pieces of the same size.

Only the top number counts pieces, so 2 × 4/5 multiplies the top: 2 × 4 = 8 pieces of 1/5.

8/5 is more than 1 whole: 5 of the pieces fill 1 bar, and the other 3 start a second.

To multiply a fraction by a whole number, multiply the top number and keep the bottom number.

Multiplying the bottom number by 2 as well, and writing 8/10.

8/10 is 8 pieces of a bar cut into 10, smaller pieces than these. The copies are still fifths, so the answer is 8/5.

8 × 3/10 = ___/10 — 24. 8 copies of 3/10 make 24 pieces of 1/10: 24/10.

3 × 2/5

Three friends each eat two-fifths of a pizza. How much pizza do they eat in all?

Two-fifths means we cut a pizza into five equal pieces and take two of them.

Each friend eats two-fifths, so together that's two-fifths plus two-fifths plus two-fifths.

Grade 4 · Three friends each eat 2/5 of a pizza

Adding the same fraction three times is the same as three times two-fifths.

To multiply, we multiply the top numbers: three times two equals six.

The bottom number, the denominator, stays the same. The pieces are still fifths.

So three times two-fifths equals six-fifths.

Six-fifths is bigger than one whole. Five-fifths makes one whole, with one-fifth left over.

Three times two-fifths is one and one-fifth pizzas. Great 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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Standards

CCSS.4.NF.B.4

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

CCSS.4.NF.B.4b

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number

Grade 4

Quoted from the Common Core State Standards.

Where this sits

Comes after

Understand a Fraction as a Multiple of a Unit Fraction

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 4

This is one rung of 71 in Grade 4 mathematics, in the order they build on each other.

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