Skip to main content
Common Core Math5th GradeFractions

5.NF.4: Multiply Fractions

Also written as 5.NF.B.4 and CCSS.MATH.CONTENT.5.NF.B.4 · Cluster: Apply and extend previous understandings of multiplication and division.

Make a 5.NF.4 WorksheetAll 26 5th Grade Math Standards

The Official Wording

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

Common Core State Standards, Grade 5, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026

What 5.NF.4 Means in Plain English

Fifth graders multiply a fraction by a whole number and by another fraction. 2/3 × 4 means two of the three equal parts of 4, or 8/3. For 2/3 × 4/5 they multiply tops and bottoms to get 8/15, and a 3-by-5 grid shows why.

Part b turns the product into area: a rectangle 2/3 yard by 5/6 yard, tiled with small squares, has an area of 5/9 square yard. 4th graders multiplied fractions only by whole numbers (4.NF.4). Next come scaling (5.NF.5), word problems (5.NF.6) and dividing fractions in 6th grade (6.NS.1).

5.NF.4 I Can Statements

  • I can multiply a fraction by a whole number and explain the product.
  • I can multiply two fractions and show the product on a grid.
  • I can find the area of a rectangle with fraction side lengths.

5.NF.4 Worked Example

One garden bed, measured two ways: tiled with small squares (part b) and multiplied straight across (part a). Both must agree.

Problem

A raised garden bed is 2/3 yard wide and 5/6 yard long. What is its area in square yards?

A garden bed 2/3 yard by 5/6 yard
  1. Area is length times width, so the problem is 2/3 × 5/6. Read it as 2/3 of 5/6: take 5/6 of a yard, cut it into 3 equal parts, keep 2.Area = 2/3 × 5/6
  2. Tile it. Draw one square yard and cut it into sixths both ways: 36 small squares, each 1/6 yard on a side and 1/36 square yard in area.1 square yard = 36 squares of 1/36
  3. The bed covers 4 sixths across (that is 2/3) and 5 sixths down. Count the squares: 4 rows of 5.4 × 5 = 20 squares, so 20/36 square yard
  4. Now multiply the fractions directly: numerators together, denominators together. The grid and the rule must give the same number.2/3 × 5/6 = (2 × 5)/(3 × 6) = 10/18
  5. Simplify both. 20/36 and 10/18 are the same fraction, 5/9.20/36 = 10/18 = 5/9
Answer5/9 square yard

Check it: Estimate: both sides are a bit under 1 yard, so the area must be under 1 square yard, and 5/9 is a little over half. Or follow part a as a sequence: 2 × 5/6 = 10/6, then divide by 3 to get 10/18 = 5/9.

Common Mistakes with 5.NF.4

Finding a common denominator first

2/3 × 4/5 = 10/15 × 12/15 = 120/15

Try this: Say it plainly: multiplying needs no common denominator. On a 3-by-5 grid, 2 rows and 4 columns overlap in 8 of 15 squares.

Multiplying the whole number into the bottom too

2/3 × 4 = 8/12

Try this: Write the whole number as a fraction first, 4 = 4/1, so only the top gets the 4: 2/3 × 4/1 = 8/3.

Reading the tiles as wholes

“The bed covers 20 squares, so the area is 20 square yards”

Try this: Label one tile before counting: each small square is 1/6 by 1/6, which is 1/36 of a square yard, so 20 tiles make 20/36.

Where 5.NF.4 Fits

Comes Before4.NF.4Multiply a fraction by a whole number, like 3 × 2/5.3.MD.7Find the area of a rectangle by tiling and by multiplying side lengths.
Alongside5.NF.5Predict whether a product is bigger or smaller than a factor.5.NF.6Use fraction multiplication in real-world problems.
Comes Next5.NF.7Divide a unit fraction by a whole number and a whole number by a unit fraction.6.NS.1Divide a fraction by a fraction.

Practice 5.NF.4

Math Worksheet GeneratorFree ToolFraction times fraction and fraction times whole number, with an answer key in simplest terms.Multiply fractionsSimplest formAnswer key
Make a Worksheet
Graph Paper GeneratorFree ToolGrid paper for the area models: students outline a unit square, shade 2 of 3 rows and 4 of 5 columns, and count the overlap.Large squaresLetterPrint
Make Graph Paper

Quick Check

  1. 2/3 × 4
  2. 3/4 × 2/5
  3. A rug is 1/2 yard by 3/4 yard. What is its area?

5.NF.4: Other Names

5.NF.45.NF.B.4CCSS.MATH.CONTENT.5.NF.B.4

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.