Multiplying fractions

What it looks like when your child can do it

• — Asked for 2/3 x 3/4, your child multiplies across to get 6/12 and simplifies it to 1/2.
• — Given one and two thirds times one and a half, your child first writes 5/3 x 3/2, then gets 15/6, which simplifies to 5/2, or 2 1/2.
• — Your child says 1/2 x 1/3 is smaller than both fractions, because it is half of a third.

How to teach it at the kitchen table

1. 01

   Picture half of a half

   Fold a paper in half, then fold that half in half again. The small piece is 1/4 of the sheet, so 1/2 x 1/2 = 1/4. Times a fraction means a part of.

2. 02

   Tops times tops, bottoms times bottoms

   For 2/3 x 4/5, multiply 2 x 4 = 8 for the top and 3 x 5 = 15 for the bottom. The answer is 8/15. There is no common bottom to find, which surprises many parents who remember adding fractions.

3. 03

   Turn mixed numbers into fractions first

   1 1/2 is 3/2: one whole is 2 halves, plus 1 more half makes 3 halves. Multiply the whole number by the bottom, add the top, and keep the bottom. A whole number like 2 can be written 2/1.

4. 04

   Simplify, then turn it back

   Divide the top and bottom by any number they share. If the top is bigger than the bottom, divide to make a mixed number again: 11/4 is 2 wholes and 3/4 left.

You will need: Paper to fold · Measuring cups

Try it together

1. Try 1

   Work out 3/4 x 2/5.

   Listen for  6/20, which simplifies to 3/10. Watch that your child multiplies straight across and does not hunt for a common bottom first.

2. Try 2

   Work out one and a half times 2/3.

   Listen for  1. As fractions it is 3/2 x 2/3 = 6/6, which is one whole. If the answer is anything else, check that one and a half became 3/2 before any multiplying.

3. Try 3

   A recipe needs 3/4 cup of sugar. You are making half the recipe. How much sugar do you need?

   Listen for  3/8 cup, because 1/2 x 3/4 = 3/8. Your child should expect less than 3/4 cup, since half of an amount is smaller.

4. Try 4

   A planter box is 4 feet long, 2 1/4 feet wide and 1 1/2 feet tall. What is its volume?

   Listen for  13 1/2 cubic feet. As fractions it is 4/1 x 9/4 x 3/2 = 108/8, which simplifies to 27/2. Watch for two and a quarter times 4 coming out as 8 1/4 instead of 9; that is the mixed number multiplied in pieces.

Watch for

• — Hunting for a common bottom number, the way you do when adding. Multiplying needs none.
• — Multiplying a mixed number in pieces, so two and a quarter times 4 comes out 8 1/4 instead of 9.

If it is not there yet

• — Go back to folding paper: half of a half, a third of a half, and name each small piece before writing any multiplication.
• — Practice turning mixed numbers into fractions on their own, with a measuring cup in hand: 1 1/2 cups is 3 half cups.

A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.

Where this skill comes up

• Grade 6 Math Practice Workbook · Lesson 8

  Converting Units with Ratio Reasoning

  Needs it because a unit conversion is a multiplication by a fraction whose value is one.

• Grade 6 Math Practice Workbook · Lesson 9

  Dividing a Fraction by a Fraction

  Needs it because dividing by a fraction is done by multiplying by its reciprocal.

• Grade 6 Math Practice Workbook · Lesson 26

  Volume When the Edges Are Fractions

  Needs it because the three edges are multiplied, and mixed numbers have to become fractions before that can happen.