Chapter 2 of 8

All 8 chapters
  1. 1Multiplying and dividing in your head, readunderstood
  2. 2Short multiplication, readunderstood
  3. 3Long multiplication, readunderstood
  4. 4Short division, readunderstood
  5. 5Long division, readunderstood
  6. 6Order of operations, readunderstood
  7. 7Estimate, then check, readunderstood
  8. 8Choosing what to do, readunderstood

M3.2.2 Chapter 2

Short multiplication

How do I work out 4 × 326 on paper?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Multiply a 3 or 4 digit number by a 1 digit number
  • Use the grid method to show what each part means

A lorry makes 4 trips. Each trip carries 326 bricks. How many bricks is that? You could add 326 four times. Multiplying is quicker.

The grid method splits 326 into 300 + 20 + 6. Each part is multiplied by 4 in its own box. Then you add the boxes.

Draw it first

The grid method for 4 × 326

  1. A grid method table. The columns are 300, 20 and 6, and the row is 4. The boxes hold 1 200, 80 and 24. Under the grid are the words total 1 304 and not to scale.3002064not to scale

    1 Split 326 into 300, 20 and 6. Write them across the top. Write 4 down the side.

  2. A grid method table. The columns are 300, 20 and 6, and the row is 4. The boxes hold 1 200, 80 and 24. Under the grid are the words total 1 304 and not to scale.30020641 2008024not to scale

    2 Multiply each part by 4. 4 × 300 = 1 200, 4 × 20 = 80 and 4 × 6 = 24.

  3. A grid method table. The columns are 300, 20 and 6, and the row is 4. The boxes hold 1 200, 80 and 24. Under the grid are the words total 1 304 and not to scale.30020641 2008024total 1 304not to scale

    3 Add the three boxes. 1 200 + 80 + 24 = 1 304.

The written method is the grid method made short. Start with the ones. When a product has two digits, write the last digit and carry the rest to the next place.

The calculation 326 times 4 written in columns. The answer is 1 304. The carried 2 and 1 are written small above the answer.6234×403121
The small 2 and 1 are the carried digits.

Worked example

Work out 326 × 4 in columns.

  1. Ones: write 4 and carry 2, because 4 × 6 = 24.
  2. Tens: write 0 and carry 1, because 4 × 2 = 8 and 8 + 2 = 10.
  3. Hundreds: write 13, because 4 × 3 = 12 and 12 + 1 = 13.
  4. Read the answer from the left: 1 304.

Answer: 1 304

Worked example

Work out 2 748 × 6 in columns.

  1. Ones: write 8 and carry 4, because 8 × 6 = 48.
  2. Tens: write 8 and carry 2, because 4 × 6 = 24 and 24 + 4 = 28.
  3. Hundreds: write 4 and carry 4, because 7 × 6 = 42 and 42 + 2 = 44.
  4. Thousands: write 16, because 2 × 6 = 12 and 12 + 4 = 16.
  5. Read the answer from the left: 16 488.

Answer: 16 488

Worked example

Work out 4 308 × 5 with the grid method.

  1. Split 4 308 into 4 000 + 300 + 8. There are no tens, so there is no tens box.
  2. 5 × 4 000 = 20 000.
  3. 5 × 300 = 1 500.
  4. 5 × 8 = 40.
  5. Add the boxes. 20 000 + 1 500 + 40 = 21 540.

Answer: 21 540

See it three ways

With things

Make 4 piles of blocks. Each pile has 2 rods of ten and 3 single cubes. Push the piles together. Trade 10 cubes for 1 rod.

As a picture

Place value blocks showing 9 rods of ten and 2 single cubes, labelled 4 × 23 = 92.4 × 23 = 92

In symbols

4 × 20 = 80 and 4 × 3 = 12. 80 + 12 = 92.

Try it

Make 3 × 14 with sticks

You need: 42 short sticks: 3 bundles of ten tied with string, and 12 loose sticks, string.

  1. Make 3 groups. Put 1 bundle of ten and 4 single sticks in each group.
  2. Push the 3 groups together. Count the bundles and the single sticks.
  3. You will have 12 single sticks. Tie 10 of them into a new bundle.

What you will see: You have 4 bundles of ten and 2 single sticks. That is 42. So 3 × 14 = 42.

If you cannot try it, this is what happens.
Place value blocks showing 4 rods of ten and 2 single cubes, labelled 3 × 14 = 42.3 × 14 = 42

A wrong idea many people have

When you carry, add the carried number to the digit first, then multiply.

Why it feels right: In adding, you put the carried 1 with the next column before you do anything else.

The test that breaks it: Try 326 × 4 the wrong way in every column. After carrying 2, add it to the 2 to make 4. Then 4 × 4 = 16, so write 6 and carry 1. In the hundreds, (3 + 1) × 4 = 16. You end with 1 664. The grid method gives 1 304.

What is true: Multiply the digit first. Then add the carried number to the product.

Key words

grid method
splitting a number by place value and multiplying each part in its own box.
carry
to move the tens of a product to the next place on the left.

Back to your guess

The answer is C: Split 326 into 300, 20 and 6. Multiply each part by 4, then add. The answer is 1 304.

4 × 326 = 1 304. Each part is multiplied: 4 × 300 = 1 200, 4 × 20 = 80 and 4 × 6 = 24. Then you add them. The 12, 8 and 24 are right, but they are worth different amounts.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Use the grid method to work out 3 × 245.

    See the answer

    735

    Split 245 into 200, 40 and 5. 3 × 200 = 600, 3 × 40 = 120 and 3 × 5 = 15. 600 + 120 + 15 = 735.

  2. Build the answer to 4 × 23 with blocks.

    See the answer

    92

    4 × 23 is 8 tens and 12 ones. Trade 10 ones for 1 ten. That gives 9 tens and 2 ones, which is 92.

  3. What is 3 × 418?

    Tap your answer.

    1. Not this one. You may have written each product side by side: 12, 3 and 24. The digits are worth different amounts, so carry the tens. Go to M3.2.2. Try another.

    2. Not this one. You may have dropped the carried 2. 3 × 8 = 24, so 2 is carried. 3 × 1 = 3, and 3 + 2 = 5, not 3. Go to M3.2.2. Try another.

    3. Not this one. You may have added the carried 2 to the 1 first and then multiplied. Multiply first, then add the carry. Go to M3.2.2. Try another.

    4. Yes, that is right. Split 418 into 400, 10 and 8. 3 × 400 = 1 200, 3 × 10 = 30 and 3 × 8 = 24. 1 200 + 30 + 24 = 1 254.

    See the answer

    1 254

    Split 418 into 400, 10 and 8. 3 × 400 = 1 200, 3 × 10 = 30 and 3 × 8 = 24. 1 200 + 30 + 24 = 1 254.

    • If you chose A: You may have written each product side by side: 12, 3 and 24. The digits are worth different amounts, so carry the tens. Go to M3.2.2.
    • If you chose B: You may have dropped the carried 2. 3 × 8 = 24, so 2 is carried. 3 × 1 = 3, and 3 + 2 = 5, not 3. Go to M3.2.2.
    • If you chose C: You may have added the carried 2 to the 1 first and then multiplied. Multiply first, then add the carry. Go to M3.2.2.

  4. In the grid for 3 × 245, what goes in the box under the 40?

    A grid method table. The columns are 200, 40 and 5, and the row is 3. The boxes are empty. Under the grid is the label not to scale.2004053not to scale
    Tap your answer.

    1. Yes, that is right. The 4 in 245 is worth 40. 3 × 40 = 120.

    2. Not this one. You used the digit 4. But it is 4 tens, so its value is 40. 3 × 40 = 120. Go to M3.2.2. Try another.

    3. Not this one. You added 3 and 40. The grid multiplies each part by 3. Go to M3.2.2. Try another.

    4. Not this one. That is 3 × 200, the box under the 200. The box under the 40 is 3 × 40. Go to M3.2.2. Try another.

    See the answer

    120

    The 4 in 245 is worth 40. 3 × 40 = 120.

    • If you chose B: You used the digit 4. But it is 4 tens, so its value is 40. 3 × 40 = 120. Go to M3.2.2.
    • If you chose C: You added 3 and 40. The grid multiplies each part by 3. Go to M3.2.2.
    • If you chose D: That is 3 × 200, the box under the 200. The box under the 40 is 3 × 40. Go to M3.2.2.

  5. Which three numbers does the grid method add up for 4 × 326?

    Tap your answer.

    1. Not this one. These are 4 × 3, 4 × 2 and 4 × 6. The 3 is 300 and the 2 is 20, so the boxes are worth more. Go to M3.2.2. Try another.

    2. Yes, that is right. Split 326 into 300, 20 and 6. 4 × 300 = 1 200, 4 × 20 = 80 and 4 × 6 = 24.

    3. Not this one. These are the parts of 326 before they are multiplied. Each part must be multiplied by 4. Go to M3.2.2. Try another.

    4. Not this one. The 6 must be multiplied by 4 too. 4 × 6 = 24. Go to M3.2.2. Try another.

    See the answer

    1 200, 80 and 24

    Split 326 into 300, 20 and 6. 4 × 300 = 1 200, 4 × 20 = 80 and 4 × 6 = 24.

    • If you chose A: These are 4 × 3, 4 × 2 and 4 × 6. The 3 is 300 and the 2 is 20, so the boxes are worth more. Go to M3.2.2.
    • If you chose C: These are the parts of 326 before they are multiplied. Each part must be multiplied by 4. Go to M3.2.2.
    • If you chose D: The 6 must be multiplied by 4 too. 4 × 6 = 24. Go to M3.2.2.

  6. The calculation is 2 748 × 6. The first step is 8 × 6 = 48. What do you write?

    The calculation 2 748 times 6 written in columns, with the answer not yet worked out.84726×
    Tap your answer.

    1. Not this one. The 4 is 4 tens. It is worth 40, so it must be added to the next product. Go to M3.2.2. Try another.

    2. Not this one. Each place holds one digit. Write the 8 and carry the 4 tens to the next place. Go to M3.2.2. Try another.

    3. Not this one. The digit you write is the ones digit, 8. The 4 is 4 tens, and it is carried. Go to M3.2.2. Try another.

    4. Yes, that is right. 48 is 4 tens and 8 ones. You write the 8 in the ones place and carry the 4 tens to the tens place.

    See the answer

    Write 8 and carry 4.

    48 is 4 tens and 8 ones. You write the 8 in the ones place and carry the 4 tens to the tens place.

    • If you chose A: The 4 is 4 tens. It is worth 40, so it must be added to the next product. Go to M3.2.2.
    • If you chose B: Each place holds one digit. Write the 8 and carry the 4 tens to the next place. Go to M3.2.2.
    • If you chose C: The digit you write is the ones digit, 8. The 4 is 4 tens, and it is carried. Go to M3.2.2.

  7. What is 1 523 × 4?

    Tap your answer.

    1. Not this one. You may have dropped the carried 1 from 3 × 4 = 12. Then 2 × 4 + 1 = 9, not 8. Go to M3.2.2. Try another.

    2. Not this one. You may have dropped the carry of 2 from 5 × 4 = 20. Then 1 × 4 + 2 = 6, not 4. Go to M3.2.2. Try another.

    3. Yes, that is right. Ones: 3 × 4 = 12, write 2 and carry 1. Tens: 2 × 4 = 8 and 8 + 1 = 9. Hundreds: 5 × 4 = 20, write 0 and carry 2. Thousands: 1 × 4 = 4 and 4 + 2 = 6.

    4. Not this one. You may have written each product side by side: 4, 20, 8 and 12. Carry the tens instead. Go to M3.2.2. Try another.

    See the answer

    6 092

    Ones: 3 × 4 = 12, write 2 and carry 1. Tens: 2 × 4 = 8 and 8 + 1 = 9. Hundreds: 5 × 4 = 20, write 0 and carry 2. Thousands: 1 × 4 = 4 and 4 + 2 = 6.

    • If you chose A: You may have dropped the carried 1 from 3 × 4 = 12. Then 2 × 4 + 1 = 9, not 8. Go to M3.2.2.
    • If you chose B: You may have dropped the carry of 2 from 5 × 4 = 20. Then 1 × 4 + 2 = 6, not 4. Go to M3.2.2.
    • If you chose D: You may have written each product side by side: 4, 20, 8 and 12. Carry the tens instead. Go to M3.2.2.

  8. Use the grid method to work out 7 × 3 062.

    See the answer

    21 434

    Split 3 062 into 3 000, 60 and 2. There is no hundreds box. 7 × 3 000 = 21 000, 7 × 60 = 420 and 7 × 2 = 14. 21 000 + 420 + 14 = 21 434.

  9. From an earlier chapter

    Work out 400 × 30.

    See the answer

    12 000

    Work out 4 × 3 = 12. Then put back the three zeros, two from 400 and one from 30. 400 × 30 = 12 000.

Keep it

Copy this into your exercise book.

Grid method: split into hundreds, tens and ones, multiply each part, add the boxes. In columns: start at the ones. Multiply, add the carry, write the last digit, carry the rest.

Draw: Draw a grid for 4 × 326 with 300, 20 and 6 on top and 4 at the side. Write each product in its box and add them.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (792 KB). It opens on any phone.