Multiplying by a fraction

What it looks like when your child can do it

• — Asked for 3/4 of 12 cookies, your child splits them into 4 equal groups of 3 and takes 3 groups, which is 9 cookies.
• — Your child writes 3/4 of 20 as 3/4 x 20 and gets 15.
• — Your child expects 3/4 of 20 to be less than 20 and would notice if an answer came out bigger.

How to teach it at the kitchen table

1. 01

   Of means multiply

   3/4 of 20 is written 3/4 x 20. Say the word "of" out loud whenever a fraction sits beside a whole number, because that is what the times sign means there.

2. 02

   Share out, then take some

   Find 3/4 of 20 by cutting 20 into 4 equal groups of 5, then taking 3 of those groups: 3 x 5 = 15. Divide by the bottom, multiply by the top.

3. 03

   Or multiply first, then divide

   Multiply the whole number by the top, then divide by the bottom: 3 x 20 = 60, and 60 divided by 4 is 15. Both routes land on the same answer, so your child can use one to check the other.

4. 04

   Write a percent over 100

   30 percent means 30 out of every 100, so 30 percent of 70 is 30/100 x 70. That is 2100 divided by 100, which is 21. This is the exact move the grade 6 book builds on.

5. 05

   Make a sense check

   Half of 70 is 35, so 30 percent of 70 has to be less than 35. When the fraction is less than one, the answer is always smaller than the number you started with.

You will need: A handful of buttons, coins or dried beans · Paper and a pencil

Try it together

1. Try 1

   Lay out 18 coins or buttons. Ask your child for 2/3 of them.

   Listen for  12. Watch that your child makes 3 equal groups of 6 first, then takes 2 of the groups. Making 2 groups instead of 3, or taking 3 groups instead of 2, means the top and the bottom got swapped.

2. Try 2

   A road trip is 180 miles. You have driven 5/6 of it. How far is that?

   Listen for  150 miles. 180 divided by 6 is 30, and 5 x 30 = 150. Check it: 30 miles are left, which is the 1/6 not yet driven.

3. Try 3

   What is 25 percent of 44?

   Listen for  11. As a fraction it is 25/100 x 44, which is 1100 divided by 100. Also, 25 percent is a quarter, and a quarter of 44 is 11, so the two checks agree.

4. Try 4

   What is 40 percent of 65?

   Listen for  26. 40 x 65 = 2600, and 2600 divided by 100 is 26. If your child says 2600, the 100 was forgotten; for any percent under 100 the answer has to be less than 65.

Watch for

• — Multiplying by the top and forgetting to divide by the bottom, so 3/4 of 20 comes out 60 and 30 percent of 70 comes out 2100.

If it is not there yet

• — Go back to real objects, like 12 buttons or 20 dried beans. Make the equal groups by hand and take some before anything is written down.
• — Practice division facts, since finding a fraction of a number means dividing by the bottom of the fraction somewhere along the way.

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 7

  Percent: A Rate per Hundred

  Needs it because 30 percent of 40 is 30/100 times 40.