Multiplying by multiples of 10

What is this skill?

Multiplying by multiples of 10 means problems like 4 × 30, 7 × 50 or 6 × 90, where a one-digit number is multiplied by a number of tens. Third graders solve them by using a fact they know and thinking in tens: 4 × 30 is 4 groups of 3 tens, which is 12 tens, or 120. So 4 × 3 = 12, and 4 × 30 = 120.

The goal is for children to understand why the answer works, not only to learn the trick of "adding a zero." The zero is there because the answer is a number of tens. That understanding prevents mistakes later, such as with decimals, where adding a zero does not multiply by 10.

Why it matters

Multiplying by tens is a building block for multi-digit multiplication in fourth and fifth grade. To multiply 6 × 47, children split it into 6 × 40 and 6 × 7. Without a quick and confident 6 × 40 = 240, the method becomes hard to follow.

It is also a practical mental math skill for estimating: 8 packs of 29 stickers is about 8 × 30, which is 240. And it reinforces place value, because it shows what happens to a number when it is made ten times larger: every digit moves one place to the left.

Common mistakes

• Adding the zero without knowing the basic fact, or writing 4 × 30 as 4 × 3 = 12 and stopping there. Ask "Is it 12 ones or 12 tens?"
• Getting confused when the basic fact already ends in zero, as in 5 × 80 = 400. Children sometimes write 40 because they expect one zero. Saying "5 times 8 tens is 40 tens" makes it clear.
• Adding instead of multiplying, such as 4 × 30 = 34. Drawing 4 groups of 3 ten-rods shows the real total.
• Treating "add a zero" as a rule for every situation. It works for whole numbers times 10, but talking about it as "tens" protects against misusing it later.

How to help at home

• Use dimes: 6 groups of 3 dimes is 18 dimes, which is 180 cents. Money shows why the answer is in tens.
• Ask estimation questions: "Each box has 40 crayons and we have 7 boxes. About how many crayons?"
• Practice pairs: ask 3 × 4, then 3 × 40, then 30 × 4, and talk about what stays the same and what changes.
• Have your child explain the answer in tens: "6 times 9 tens is 54 tens, which is 540."
• Build it with base-ten rods if you have them, or bundles of ten straws: 3 groups of 4 bundles is 12 bundles, and counting the straws confirms 120.

Worked examples

These are real questions from the Tutorsaurus multiplying by multiples of 10 practice, with the answers worked out.

1. Example 1

   9 × 30 = ?

   Answer: 270. 9 × 3 = 27, then add a zero: 270.

2. Example 2

   2 × 40 = ?

   Answer: 80. 2 × 4 = 8, then add a zero: 80.

3. Example 3

   3 × 20 = ?

   Answer: 60. 3 × 2 = 6, then add a zero: 60.