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We will be multiplying decimals by 10, 100, and 1,000. When we multiply by 10, 100, and 1000 we shift all the digits to the left. One place left for 10, two places left for 100, and three places left for 1000. When we divide by 10, 100, and 1000 we do the opposite and shift all the digits to the right instead.

1.
Year 5: Week 2, Day 1

Decimals: Multiply and divide by 10, 100 and 1000

Each day covers one maths topic. It should take you about 1 hour or just a little more.

1. Start by reading through the Learning Reminders.

They come from our PowerPoint slides.

2. Tackle the questions on the Practice Sheet.

There might be a choice of either Mild (easier) or

Hot (harder)!

Check the answers.

3. Finding it tricky? That’s OK… have a go with a

grown-up at A Bit Stuck?

4. Have I mastered the topic? A few questions to

Check your understanding.

Fold the page to hide the answers!

© Hamilton Trust

Decimals: Multiply and divide by 10, 100 and 1000

Each day covers one maths topic. It should take you about 1 hour or just a little more.

1. Start by reading through the Learning Reminders.

They come from our PowerPoint slides.

2. Tackle the questions on the Practice Sheet.

There might be a choice of either Mild (easier) or

Hot (harder)!

Check the answers.

3. Finding it tricky? That’s OK… have a go with a

grown-up at A Bit Stuck?

4. Have I mastered the topic? A few questions to

Check your understanding.

Fold the page to hide the answers!

© Hamilton Trust

2.
Learning Reminders

© Hamilton Trust

© Hamilton Trust

3.
Learning Reminders

When we multiply by 10, 100 and 1000, the digits all move together, one, two, or three place value columns to the left.

When we divide by 10, 100 and 1000, the digits all move together, one, two, or three place value columns to the right.

© Hamilton Trust

When we multiply by 10, 100 and 1000, the digits all move together, one, two, or three place value columns to the left.

When we divide by 10, 100 and 1000, the digits all move together, one, two, or three place value columns to the right.

© Hamilton Trust

4.
Practice Sheet Mild

Multiplying and dividing by 10 and 100

1. 34.6 × 10 2. 34.6 × 100 3. 6.74 × 10 4. 6.74 × 100

5. 483 ÷ 10 6. 483 ÷ 100 7. 56.1 ÷ 10 8. 56.1 × 100

9. 83.4 × = 834 10. 83.4 ÷ = 8.34

© Hamilton Trust

11. 47.2 ÷ = 4.72 12. 47.2 × = 4720

© Hamilton Trust

Multiplying and dividing by 10 and 100

1. 34.6 × 10 2. 34.6 × 100 3. 6.74 × 10 4. 6.74 × 100

5. 483 ÷ 10 6. 483 ÷ 100 7. 56.1 ÷ 10 8. 56.1 × 100

9. 83.4 × = 834 10. 83.4 ÷ = 8.34

© Hamilton Trust

11. 47.2 ÷ = 4.72 12. 47.2 × = 4720

© Hamilton Trust

5.
Practice Sheet Hot

Multiplying and dividing by 10, 100 and 1000

1. 456.8 × 10 2. 4568 ÷ 10 3. 2.76 × 10 4. 843 ÷ 100

5. 47.3 × 100 6. 783 ÷ 100 7. 45.62 × 100 8. 783.4 ÷ 10

9. 45.74 × 1000 10. 3620 ÷ 1000

© Hamilton Trust

11. 348.2 × = 3482 12. 34,820 ÷ = 34.82

Challenge

Complete the following calculations.

78.43 × = 7843 78.43 × = 78,430 6450 ÷ = 64.5 6450 ÷ = 6.45

© Hamilton Trust

Multiplying and dividing by 10, 100 and 1000

1. 456.8 × 10 2. 4568 ÷ 10 3. 2.76 × 10 4. 843 ÷ 100

5. 47.3 × 100 6. 783 ÷ 100 7. 45.62 × 100 8. 783.4 ÷ 10

9. 45.74 × 1000 10. 3620 ÷ 1000

© Hamilton Trust

11. 348.2 × = 3482 12. 34,820 ÷ = 34.82

Challenge

Complete the following calculations.

78.43 × = 7843 78.43 × = 78,430 6450 ÷ = 64.5 6450 ÷ = 6.45

© Hamilton Trust

6.
Extra Practice for All

Complete any empty boxes on this diagram. Watch out - they might be answers or operations…

Create a similar diagram for a partner to solve.

© Hamilton Trust

Complete any empty boxes on this diagram. Watch out - they might be answers or operations…

Create a similar diagram for a partner to solve.

© Hamilton Trust

7.
Practice Sheets Answers

Multiplying and dividing by 10 and 100 (mild)

1. 34.6 × 10 = 346 2. 34.6 × 100 = 3460 3. 6.74 × 10 = 67.4

4. 6.74 × 100 = 674 5. 483 ÷ 10 = 48.3 6. 483 ÷ 100 = 4.83

7. 56.1 ÷ 10 = 5.61 8. 56.1 × 10 = 561 9. 83.4 × 10 = 834

10. 83.4 ÷ 10 = 8.34 11. 47.2 ÷ 10 = 4.72 12. 47.2 × 100 = 4720

Multiplying and dividing by 10, 100 and 1000 (hot)

1. 456.8 × 10 = 4568 2. 4568 ÷ 10 = 456.8 3. 2.76 × 10 = 27.6

4. 843 ÷ 100 = 8.43 5. 47.3 × 100 = 4730 6. 783 ÷ 100 = 7.83

7. 45.62 × 100 = 4562 8. 783.4 ÷ 10 = 78.34 9. 45.74 × 1000 = 45740

10. 3620 ÷ 1000 = 3.62 11. 348.2 × 10 = 3482 12. 34,820 ÷ 1000 = 34.82

Challenge

78.43 × 100 = 7843 78.43 × 1000 = 78,430

6450 ÷ 100 = 64.5 6450 ÷ 1000 = 6.45

© Hamilton Trust

Multiplying and dividing by 10 and 100 (mild)

1. 34.6 × 10 = 346 2. 34.6 × 100 = 3460 3. 6.74 × 10 = 67.4

4. 6.74 × 100 = 674 5. 483 ÷ 10 = 48.3 6. 483 ÷ 100 = 4.83

7. 56.1 ÷ 10 = 5.61 8. 56.1 × 10 = 561 9. 83.4 × 10 = 834

10. 83.4 ÷ 10 = 8.34 11. 47.2 ÷ 10 = 4.72 12. 47.2 × 100 = 4720

Multiplying and dividing by 10, 100 and 1000 (hot)

1. 456.8 × 10 = 4568 2. 4568 ÷ 10 = 456.8 3. 2.76 × 10 = 27.6

4. 843 ÷ 100 = 8.43 5. 47.3 × 100 = 4730 6. 783 ÷ 100 = 7.83

7. 45.62 × 100 = 4562 8. 783.4 ÷ 10 = 78.34 9. 45.74 × 1000 = 45740

10. 3620 ÷ 1000 = 3.62 11. 348.2 × 10 = 3482 12. 34,820 ÷ 1000 = 34.82

Challenge

78.43 × 100 = 7843 78.43 × 1000 = 78,430

6450 ÷ 100 = 64.5 6450 ÷ 1000 = 6.45

© Hamilton Trust

8.
Extra Practice for All Answers

Complete any empty boxes on this diagram. Watch out - they might be answers or operations…

27,300

÷ 100

÷ 10

273

x 100

0.0273

Create a similar diagram for a partner to solve.

© Hamilton Trust

Complete any empty boxes on this diagram. Watch out - they might be answers or operations…

27,300

÷ 100

÷ 10

273

x 100

0.0273

Create a similar diagram for a partner to solve.

© Hamilton Trust

9.
A Bit Stuck?

Left, left, right, right?

Work in pairs, but record numbers on your own place value grid

Things you will need:

• A place value grid

• A pencil

What to do:

• Look at the first group of fraction strips.

What number are they showing?

Write the number in your place value grid.

• Multiply this number by 100. 100s 10s 1s 0.1s 0.01s

Write the answer in your place value grid. 1 6 1

1 6 1

• Repeat this for each fraction picture.

• Choose three of these numbers to divide by 100.

Write the number and the answer in your place value grid.

654 127 243 438 364

S-t-r-e-t-c-h:

Multiply 0.25, 0.09 and 1.03 by 100.

Divide 408, 27 and 360 by 100.

Learning outcomes:

• I understand the value of each digit in a number with two decimal places.

• I am beginning to multiply numbers with two decimal places by 100 and divide 3-digit numbers by 100.

© Hamilton Trust

Left, left, right, right?

Work in pairs, but record numbers on your own place value grid

Things you will need:

• A place value grid

• A pencil

What to do:

• Look at the first group of fraction strips.

What number are they showing?

Write the number in your place value grid.

• Multiply this number by 100. 100s 10s 1s 0.1s 0.01s

Write the answer in your place value grid. 1 6 1

1 6 1

• Repeat this for each fraction picture.

• Choose three of these numbers to divide by 100.

Write the number and the answer in your place value grid.

654 127 243 438 364

S-t-r-e-t-c-h:

Multiply 0.25, 0.09 and 1.03 by 100.

Divide 408, 27 and 360 by 100.

Learning outcomes:

• I understand the value of each digit in a number with two decimal places.

• I am beginning to multiply numbers with two decimal places by 100 and divide 3-digit numbers by 100.

© Hamilton Trust

10.
A Bit Stuck?

Left, left, right, right?

© Hamilton Trust

Left, left, right, right?

© Hamilton Trust

11.
A Bit Stuck?

Left, left, right, right?

100s 10s 1s • 0.1s 0.01s

© Hamilton Trust

Left, left, right, right?

100s 10s 1s • 0.1s 0.01s

© Hamilton Trust

12.
Check your understanding

Questions

Divide 47,310 by 10 repeatedly until you get a number that is less than 100.

Write that number.

Fill the empty boxes:

0.15 = 1.5 10 5209 = x 100 ÷ 100 = 4.7 10.08 = ÷ 1000

Write the next two numbers in each sequence.

0.41 4.1 ____ ____

2.05 20.5 ____ ____

43,020 4302 ____ ____

True or false?

4030 ÷ 100 = 43 1.09 x 100 = 190 0.09 x 10 = 0.9 7000 ÷ 1000 = 0.7

Fold here to hide answers

Check your understanding

Answers

Divide 47,310 by 10 repeatedly until you get a number that is less than 100.

Write that number. 47.31

Each time the number is divided by 10, the digits move one place value column to the right:

47,310

4731

473.1

47.31

Fill the empty boxes:

0.15 = 1.5 ÷ 10 5209 = 52.09 x 100 470 ÷ 100 = 4.7 10.08 = 10,080 ÷ 1000

Write the next two numbers in each sequence.

0.41 4.1 41 410 (Multiplying by 10)

2.05 20.5 205 2050 (Multiplying by 10)

43,020 4302 430.2 43.02 (Dividing by 10)

True or false?

4030 ÷ 100 = 43 False – should be 40.3

1.09 x 100 = 190 False – should be 109

0.09 x 10 = 0.9 True

7000 ÷ 1000 = 0.7 False – should be 7

© Hamilton Trust

Questions

Divide 47,310 by 10 repeatedly until you get a number that is less than 100.

Write that number.

Fill the empty boxes:

0.15 = 1.5 10 5209 = x 100 ÷ 100 = 4.7 10.08 = ÷ 1000

Write the next two numbers in each sequence.

0.41 4.1 ____ ____

2.05 20.5 ____ ____

43,020 4302 ____ ____

True or false?

4030 ÷ 100 = 43 1.09 x 100 = 190 0.09 x 10 = 0.9 7000 ÷ 1000 = 0.7

Fold here to hide answers

Check your understanding

Answers

Divide 47,310 by 10 repeatedly until you get a number that is less than 100.

Write that number. 47.31

Each time the number is divided by 10, the digits move one place value column to the right:

47,310

4731

473.1

47.31

Fill the empty boxes:

0.15 = 1.5 ÷ 10 5209 = 52.09 x 100 470 ÷ 100 = 4.7 10.08 = 10,080 ÷ 1000

Write the next two numbers in each sequence.

0.41 4.1 41 410 (Multiplying by 10)

2.05 20.5 205 2050 (Multiplying by 10)

43,020 4302 430.2 43.02 (Dividing by 10)

True or false?

4030 ÷ 100 = 43 False – should be 40.3

1.09 x 100 = 190 False – should be 109

0.09 x 10 = 0.9 True

7000 ÷ 1000 = 0.7 False – should be 7

© Hamilton Trust