Multiplying fractions: practice, examples and worksheets

Why you multiply straight across

Draw a square and split it into 4 equal columns. Shade 3 of them: that is 3/4. Now split the same square into 5 equal rows and shade 2 of them in a different color: that is 2/5. The part shaded twice is 3/4 of 2/5.

Count the small rectangles. The square is now cut into 4 × 5 = 20 equal pieces, which is why the denominators multiply. The overlap is 3 columns by 2 rows, so 3 × 2 = 6 pieces, which is why the numerators multiply. The answer is 6/20, which simplifies to 3/10.

This picture is called an area model, and it also explains the word "of". Three quarters of two fifths means 3/4 × 2/5. Whenever a question says "a fraction of" something, multiply.

Do you need a common denominator to multiply fractions?

No. Common denominators matter when you add or subtract, because you can only add pieces of the same size. Multiplying makes brand new pieces, as the area model shows, so the denominators can be different.

If your child finds a common denominator anyway, the answer still comes out right, just with bigger numbers. For 1/2 × 1/3, rewriting as 3/6 × 2/6 gives 6/36, which simplifies to 1/6. Multiplying straight across gives 1/6 at once.

Multiplying fractions with whole numbers

A whole number is a fraction over 1. So 4 × 2/3 is 4/1 × 2/3 = 8/3, which is 2 2/3 as a mixed number. You can also see it as four groups of 2/3: 2/3 + 2/3 + 2/3 + 2/3 = 8/3. Only the numerator gets multiplied, because the pieces are still thirds.

Finding a fraction of an amount is the same idea. For 3/5 of 20, find one fifth first (20 ÷ 5 = 4), then take three of them (4 × 3 = 12). Multiplying across gives the same thing: 3/5 × 20/1 = 60/5 = 12.

Multiplying fractions examples, from easy to harder

• 1/2 × 1/4 = 1/8. Half of a quarter is an eighth.
• 5 × 3/8 = 15/8, which is 1 7/8.
• 2/3 × 9/10 = 18/30 = 3/5. Or simplify first: 2 and 10 share a factor of 2, and 9 and 3 share a factor of 3, leaving 1/1 × 3/5 = 3/5.
• A rectangle 3/4 m long and 2/3 m wide has an area of 3/4 × 2/3 = 6/12 = 1/2 m².
• 1 1/2 × 2/3: change 1 1/2 to 3/2, then 3/2 × 2/3 = 6/6 = 1.

Simplifying first, sometimes called cross-cancelling, keeps the numbers small. You may divide any numerator and any denominator by the same number before you multiply.

Why the answer often gets smaller

Children are used to multiplying making things bigger, so 1/2 × 1/4 = 1/8 can feel wrong. Multiplying by a fraction less than 1 means taking part of something, so the answer is smaller than what you started with. Multiplying by a fraction greater than 1, like 3/2, makes it bigger.

This gives a quick check before any working. Ask: is the answer going to be more or less than the number I started with? If 3/4 × 2/5 came out bigger than 2/5, something went wrong.

How it's taught in school

In the US, the Common Core introduces multiplying a fraction by a whole number in grade 4 (standard 4.NF.B.4), treating 3 × 2/5 as 6 lots of 1/5. In grade 5, children multiply a fraction by a fraction (5.NF.B.4), find areas of rectangles with fractional sides, see multiplication as scaling (5.NF.B.5), and solve word problems with mixed numbers (5.NF.B.6).

In England, Year 5 pupils multiply proper fractions and mixed numbers by whole numbers, supported by diagrams. In Year 6 they multiply simple pairs of proper fractions and write the answer in its simplest form.

How parents can help

• Fold paper. Fold a sheet in half one way and in thirds the other, shade, and count the overlap: 1/2 × 1/3 = 1/6.
• Cook with fractions. Halving a recipe that needs 3/4 cup of milk means 1/2 × 3/4 = 3/8 cup.
• Ask for an estimate first: bigger or smaller than the starting number?
• Keep it short. Ten questions done carefully beat forty done in a rush.

Try the practice set below for fresh questions checked as you go, with hints and worked steps when you need them. For a paper copy, print a fresh worksheet with an answer key, showing answers only or answers with worked steps.