Grade by Grade
B. Number · Operations: Numbers to 10 000, Decimal Tenths, Multiplying and Dividing

Mental Math: Multiplying by 10, 100 and 1000, Dividing by 10

B2.3 B2.5About 35 minutes
Learning goals
  • I can multiply whole numbers by 10, 100 and 1000 in my head.
  • I can divide whole numbers by 10 in my head.
  • I can use facts to multiply by multiples of 10 and 100, like 6 × 40.
  • I can explain what happens to the digits.

Words to know

place value
The value of a digit because of its place. In 3400, the 3 means 3 thousands.
multiple of 10
A number you say when counting by 10s: 10, 20, 30...
multiple of 100
A number you say when counting by 100s: 100, 200, 300...
shift
Move. When you multiply by 10, each digit shifts one place to the left.

Let's start with a story

The school library gets books in boxes of 10. 34 boxes arrive. How many books?

34 × 10 = 340. That was fast! Let's find out why it's so easy.

Multiplying by 10

Each place is worth 10 times the place to its right: 10 ones make a ten, 10 tens make a hundred, 10 hundreds make a thousand.

When you multiply by 10, every digit shifts one place to the left. A 0 fills the empty ones place.

34 × 10 → 3 tens 4 ones becomes 3 hundreds 4 tens = 340.

ThousandsHundredsTensOnes
3434
34 × 10 = 340340
34 × 100 = 34003400
Each time we multiply by 10, the digits shift one place to the left.

Multiplying by 100 and 1000

  • × 100 shifts each digit two places to the left. Two zeros fill the ones and tens: 34 × 100 = 3400.
  • × 1000 shifts each digit three places to the left: 7 × 1000 = 7000.

Why? Multiplying by 100 is like multiplying by 10 and then by 10 again.

Worked example

Example 1: Multiply by 10, 100 and 1000

Find 8 × 10, 8 × 100 and 8 × 1000.

  1. 8 × 10: 8 ones become 8 tens = 80.
  2. 8 × 100: 8 ones become 8 hundreds = 800.
  3. 8 × 1000: 8 ones become 8 thousands = 8000.

80, 800 and 8000

Dividing by 10

Dividing by 10 is the opposite: every digit shifts one place to the right.

  • 450 ÷ 10 = 45 (4 hundreds 5 tens become 4 tens 5 ones)
  • 3200 ÷ 10 = 320
  • 7000 ÷ 10 = 700

Check with the partner operation: 45 × 10 = 450. ✓

HundredsTensOnes4504545045÷ 10one place right
450 ÷ 10: the 4 hundreds become 4 tens and the 5 tens become 5 ones. Every digit slides one place to the right, so 450 ÷ 10 = 45.
Worked example

Example 2: Divide by 10

2600 hockey pucks are packed in boxes of 10. How many boxes?

  1. We need 2600 ÷ 10.
  2. Shift each digit one place to the right: 2 thousands 6 hundreds become 2 hundreds 6 tens.
  3. 2600 ÷ 10 = 260.
  4. Check: 260 × 10 = 2600. ✓

260 boxes

Using facts with tens and hundreds

Now combine a fact you know with tens or hundreds.

6 × 40: 40 is 4 tens. 6 × 4 tens = 24 tens = 240.

3 × 700: 700 is 7 hundreds. 3 × 7 hundreds = 21 hundreds = 2100.

Worked example

Example 3: A fact with hundreds

A bakery makes 500 bagels each day. How many in 9 days?

  1. We need 9 × 500.
  2. 500 is 5 hundreds. 9 × 5 = 45.
  3. So 9 × 5 hundreds = 45 hundreds = 4500.

4500 bagels

What about a number that doesn't end in 0?

What is 37 ÷ 10? The 3 tens become 3 ones, and the 7 ones become 7 tenths. So 37 ÷ 10 = 3.7. You'll learn more about tenths in the next lesson.

012345678910
37 ÷ 10 = 3.7. It is between 3 and 4, a little closer to 4.

Talk about place value

Don't just "add zeros". Say what happens to the place value: "The 4 tens became 4 hundreds." That way you'll never get confused, even with tenths.

Just for fun

What if your allowance were multiplied by 1000 every week? $5 would become $5000! (Sadly, grown-ups only seem to want to multiply chores.)

Hands-on activity

Place value slider

You need: a long strip of paper, a short strip of paper, a pencil.

  1. On the long strip, draw 4 boxes and label them Th, H, T, O (thousands, hundreds, tens, ones).
  2. On the short strip, write a 2-digit number, like 5 2, with each digit the same width as one box.
  3. Put your number under the T and O boxes. Read it: 52.
  4. Slide it one place left and write a 0 in the empty ones box. Read it: 520. You multiplied by 10!
  5. Slide it one more place left: 5200. That's × 100 from where you started.
  6. Now slide right to divide by 10.

Try it with 3 different numbers. Say each one out loud, like "52 times 100 is 5200."

Your turn

1

52 × 10 = ?

2

52 × 100 = ?

3

6 × 1000 = ?

4

830 ÷ 10 = ?

5

4000 ÷ 10 = ?

6

7 × 30 = ?

7

9 × 500 = ?

More practice: warm-up

1

8 × 10 = ?

2

3 × 100 = ?

3

2 × 1000 = ?

4

60 ÷ 10 = ?

5

15 × 10 = ?

More practice: on your own

1

67 × 100 = ?

2

4 × 800 = ?

3

9 × 60 = ?

4

1250 ÷ 10 = ?

5

A box holds 100 toothpicks. How many toothpicks are in 35 boxes?

Challenge

1

Find the missing number: □ × 100 = 7300

2

Find 5600 ÷ 10. Then divide your answer by 10 again. What do you notice?

3

What is 48 ÷ 10? Explain with place value.

Check your understanding

Quiz

1.

What is 74 × 100?

2.

What is 3600 ÷ 10?

3.

What is 8 × 1000?

4.

What is 6 × 70?

5.

When you multiply a whole number by 10, each digit...

6.

What is 29 × 10?

For parents and teachers

Big idea: The curriculum (B2.3) asks Grade 4 students to multiply whole numbers by 10, 100 and 1000 and divide whole numbers by 10 mentally, and to explain their strategies. The explanation is place value: each digit shifts places.

Common difficulties:

  • "Just add a zero" works for whole numbers but breaks later with decimals (3.7 × 10 is not 3.70). Encourage your child to talk about digits moving places instead.
  • Adding the wrong number of zeros (6 × 40 = 2400). Have your child say "6 times 4 tens is 24 tens."

How to help: Use money: ten-dollar and hundred-dollar amounts are great for this. "A bike costs $300. What would 4 bikes cost?" Count fingers in a room (10 per person).