Chapter 5 of 7

All 7 chapters
  1. 1Adding in your head, readunderstood
  2. 2Taking away in your head, readunderstood
  3. 3Column adding, readunderstood
  4. 4Column taking away, readunderstood
  5. 5Four digits and more, readunderstood
  6. 6Estimate and check, readunderstood
  7. 7Problems in two steps, readunderstood

M2.2.5 Chapter 5

Four digits and more

The ones column makes 14. Where do I put it?

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

  • Add and take away 4 digit numbers in columns
  • Add a list of three or four numbers

You can add and take away in columns. Four digit numbers use the same steps.

There is one more column on the left, the thousands. Start at the ones, as always.

Draw it first

Add 3 465 + 2 879 in columns

  1. A column sum, 3 465 plus 2 879, with each digit under its place and a line under the numbers. Step 1 says "Line up the digits". Step 2 writes 4 under the ones, a small 1 over the tens, and says "Ones: 5 + 9 = 14". Step 3 writes 4 under the tens, a small 1 over the hundreds, and says "Tens: 1 + 6 + 7 = 14". Step 4 writes 3 under the hundreds, a small 1 over the thousands, and 6 under the thousands. It says "Hundreds: 1 + 4 + 8 = 13" and "Thousands: 1 + 3 + 2 = 6". The answer is 6 344.56439782+Line up the digits

    1 Write the numbers so ones are under ones. Draw a line.

  2. A column sum, 3 465 plus 2 879, with each digit under its place and a line under the numbers. Step 1 says "Line up the digits". Step 2 writes 4 under the ones, a small 1 over the tens, and says "Ones: 5 + 9 = 14". Step 3 writes 4 under the tens, a small 1 over the hundreds, and says "Tens: 1 + 6 + 7 = 14". Step 4 writes 3 under the hundreds, a small 1 over the thousands, and 6 under the thousands. It says "Hundreds: 1 + 4 + 8 = 13" and "Thousands: 1 + 3 + 2 = 6". The answer is 6 344.56439782+41Ones: 5 + 9 = 14

    2 Ones: 5 + 9 = 14. Write 4. Carry the 1 to the tens.

  3. A column sum, 3 465 plus 2 879, with each digit under its place and a line under the numbers. Step 1 says "Line up the digits". Step 2 writes 4 under the ones, a small 1 over the tens, and says "Ones: 5 + 9 = 14". Step 3 writes 4 under the tens, a small 1 over the hundreds, and says "Tens: 1 + 6 + 7 = 14". Step 4 writes 3 under the hundreds, a small 1 over the thousands, and 6 under the thousands. It says "Hundreds: 1 + 4 + 8 = 13" and "Thousands: 1 + 3 + 2 = 6". The answer is 6 344.56439782+4141Tens: 1 + 6 + 7 = 14

    3 Tens: 1 + 6 + 7 = 14. Write 4. Carry the 1 to the hundreds.

  4. A column sum, 3 465 plus 2 879, with each digit under its place and a line under the numbers. Step 1 says "Line up the digits". Step 2 writes 4 under the ones, a small 1 over the tens, and says "Ones: 5 + 9 = 14". Step 3 writes 4 under the tens, a small 1 over the hundreds, and says "Tens: 1 + 6 + 7 = 14". Step 4 writes 3 under the hundreds, a small 1 over the thousands, and 6 under the thousands. It says "Hundreds: 1 + 4 + 8 = 13" and "Thousands: 1 + 3 + 2 = 6". The answer is 6 344.56439782+4141316Hundreds: 1 + 4 + 8 = 13Thousands: 1 + 3 + 2 = 6

    4 Hundreds: 1 + 4 + 8 = 13. Write 3, carry 1. Thousands: 1 + 3 + 2 = 6.

When a column makes 10 or more, you carry. Write the last digit under the column.

To carry is to move the other digit one column left. Write it small above that column.

See it three ways

With things

Put 5 beans and 9 beans in the ones box. You have 14. Swap 10 beans for 1 stick in the tens box.

As a picture

Fourteen dots, labelled "14 ones", are equal to one rod of ten and four single squares, labelled "1 ten 4 ones".14 ones=1 ten 4 ones

In symbols

5 + 9 = 14. Write 4. Carry 1.

Taking away uses the same columns. Sometimes the top digit is too small.

Then you exchange. Take 1 from the column on the left. It becomes 10 in this column.

If that column is 0, go on to the next one. Look at 5 002 − 2 457.

A column take away, 5002 minus 2457, with the answer 2545. The 5 is crossed out and a small 4 is written above it. The two zeros are crossed out and each has a small 9 above it. A small 1 sits by the ones digit 2.20057542−19945452
Two zeros in a row: go back to the 5. Each zero becomes 9.

Worked example

Work out 5 002 − 2 457.

  1. In the ones, 2 is smaller than 7. The next two digits are 0.
  2. Go to the 5 thousands. Cross it out and write 4.
  3. Write 9 over the hundreds and 9 over the tens.
  4. Give the ones a ten. 2 becomes 12.
  5. Now take away. 12 − 7 = 5, 9 − 5 = 4, 9 − 4 = 5, 4 − 2 = 2.

Answer: 2 545

You can add a list of numbers in columns too. Line up all the numbers.

Add down each column, starting at the ones.

A column sum of four numbers: 245, 130, 78 and 302, lined up by place with a line under them. A small 1 sits over the tens and a small 1 over the hundreds. The answer is 755. The notes say "Ones: 5 + 0 + 8 + 2 = 15", "Tens: 1 + 4 + 3 + 7 = 15" and "Hundreds: 1 + 2 + 1 + 3 = 7".54203187203+11557Ones: 5 + 0 + 8 + 2 = 15Tens: 1 + 4 + 3 + 7 = 15Hundreds: 1 + 2 + 1 + 3 = 7
The ones make 15. Write 5 and carry 1.

Worked example

Work out 245 + 130 + 78 + 302.

  1. Ones: 5 + 0 + 8 + 2 = 15. Write 5. Carry 1.
  2. Tens: 1 + 4 + 3 + 7 + 0 = 15. Write 5. Carry 1.
  3. Hundreds: 1 + 2 + 1 + 0 + 3 = 7. Write 7.

Answer: 755

The ones can make 20 or more. Then you carry 2 or more.

Worked example

Work out 48 + 37 + 29 + 56.

  1. Ones: 8 + 7 + 9 + 6 = 30.
  2. Write 0. Carry 3 to the tens.
  3. Tens: 3 + 4 + 3 + 2 + 5 = 17. Write 17.

Answer: 170

Try it

Carry three tens with beans

You need: 30 beans or small stones, 3 sticks, a pencil and paper.

Be safe: Do not eat the beans.

  1. Draw two boxes on paper. Write "tens" over one and "ones" over the other.
  2. Put 8, 7, 9 and 6 beans in the ones box. Count them. You have 30.
  3. Take 10 beans out. Put 1 stick in the tens box. Do this 3 times.
  4. Look at the ones box.

What you will see: No beans are left in the ones box. There are 3 sticks in the tens box. So you write 0 and carry 3.

If you cannot try it, this is what happens.
Thirty beans, labelled "30 ones", are equal to three rods of ten, labelled "3 tens".30 ones=3 tens

A wrong idea many people have

I can write 14 under the ones column.

Why it feels right: 5 + 9 really is 14, so writing 14 seems right.

The test that breaks it: Try 15 + 9 that way. You write 14 and then 1, which reads 114. Count on from 15 by 9. You reach 24.

What is true: Each column holds one digit. 14 ones is 1 ten and 4 ones. Write 4 and carry 1. So 15 + 9 = 24.

Key words

carry
move the extra digit to the next column on the left.
exchange
take 1 from the column on the left. It becomes 10 in this column.

Back to your guess

The answer is B: Write 4 under the ones and carry the 1 to the tens.

Each column holds one digit. 14 ones is 1 ten and 4 ones. Write the 4. Carry the 1 to the tens.

Check yourself

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

  1. Work out 2 358 + 1 467 in columns.

    See the answer

    3 825

    Ones: 8 + 7 = 15, write 5, carry 1. Tens: 1 + 5 + 6 = 12, write 2, carry 1. Hundreds: 1 + 3 + 4 = 8. Thousands: 2 + 1 = 3.

  2. Work out 6 300 − 2 845 in columns.

    See the answer

    3 455

    In the ones, 0 is smaller than 5. Exchange along the zeros. The hundreds, now 2, need an exchange too. 10 − 5 = 5, 9 − 4 = 5, 12 − 8 = 4, 5 − 2 = 3. Check: 3 455 + 2 845 = 6 300.

  3. Add 54 + 38 + 27 + 66. The ones column makes 25. What do you do?

    Tap your answer.

    1. Yes, that is right. The ones make 4 + 8 + 7 + 6 = 25. That is 2 tens and 5 ones. The tens then make 5 + 3 + 2 + 6 + 2 = 18. The total is 185.

    2. Not this one. A column holds one digit. Write the last digit, 5, and carry the rest. Try another.

    3. Not this one. The digits are the wrong way round. 25 is 2 tens and 5 ones. The 5 stays. Try another.

    See the answer

    Write 5 and carry 2

    The ones make 4 + 8 + 7 + 6 = 25. That is 2 tens and 5 ones. The tens then make 5 + 3 + 2 + 6 + 2 = 18. The total is 185.

    • If you chose B: A column holds one digit. Write the last digit, 5, and carry the rest.
    • If you chose C: The digits are the wrong way round. 25 is 2 tens and 5 ones. The 5 stays.

  4. Work out 126 + 85 + 308 + 49.

    See the answer

    568

    Ones: 6 + 5 + 8 + 9 = 28, write 8, carry 2. Tens: 2 + 2 + 8 + 0 + 4 = 16, write 6, carry 1. Hundreds: 1 + 1 + 0 + 3 + 0 = 5.

  5. From an earlier chapter

    Ravi works out 403 − 167 and gets 364. He took the smaller digit from the bigger one each time. Is he right?

    Tap your answer.

    1. Not this one. In the ones, 3 is smaller than 7. You cannot take 7 from 3, so you must exchange. Go to M2.2.4. Try another.

    2. Yes, that is right. Exchange 1 hundred for 10 tens, then 1 ten for 10 ones. 13 − 7 = 6, 9 − 6 = 3, 3 − 1 = 2. Check: 236 + 167 = 403.

    3. Not this one. 570 is 403 + 167. A take away gives less than 403. Try another.

    See the answer

    No. The answer is 236.

    Exchange 1 hundred for 10 tens, then 1 ten for 10 ones. 13 − 7 = 6, 9 − 6 = 3, 3 − 1 = 2. Check: 236 + 167 = 403.

    • If you chose A: In the ones, 3 is smaller than 7. You cannot take 7 from 3, so you must exchange. Go to M2.2.4.
    • If you chose C: 570 is 403 + 167. A take away gives less than 403.

  6. Leila adds 4 763 + 1 859 in columns. What is the total?

    A column sum of 4763 plus 1859 with empty boxes for the answer.36749581+
    Tap your answer.

    1. Not this one. The hundreds made 16. Write 6 and carry 1 to the thousands. Thousands: 4 + 1 + 1 = 6. Try another.

    2. Yes, that is right. Ones: 3 + 9 = 12, write 2, carry 1. Tens: 6 + 5 + 1 = 12, write 2, carry 1. Hundreds: 7 + 8 + 1 = 16, write 6, carry 1. Thousands: 4 + 1 + 1 = 6.

    3. Not this one. The ones made 12. Carry 1 ten. Tens: 6 + 5 + 1 = 12, not 11. Try another.

    See the answer

    6 622

    Ones: 3 + 9 = 12, write 2, carry 1. Tens: 6 + 5 + 1 = 12, write 2, carry 1. Hundreds: 7 + 8 + 1 = 16, write 6, carry 1. Thousands: 4 + 1 + 1 = 6.

    • If you chose A: The hundreds made 16. Write 6 and carry 1 to the thousands. Thousands: 4 + 1 + 1 = 6.
    • If you chose C: The ones made 12. Carry 1 ten. Tens: 6 + 5 + 1 = 12, not 11.

  7. Hana takes away 4 000 − 1 235 in columns. What is the answer?

    A column sum of 4000 take away 1235 with empty boxes for the answer.00045321−
    Tap your answer.

    1. Not this one. You took the smaller digit from the bigger one in each column. Add back: 1 235 + 3 235 = 4 470, not 4 000. Try another.

    2. Not this one. The 4 thousands gave 1 away. Only 3 are left. 3 − 1 = 2, not 3. Try another.

    3. Yes, that is right. Exchange along the zeros. The thousands are 3. The hundreds and tens are 9. The ones are 10. 10 − 5 = 5, 9 − 3 = 6, 9 − 2 = 7, 3 − 1 = 2. Check: 2 765 + 1 235 = 4 000.

    See the answer

    2 765

    Exchange along the zeros. The thousands are 3. The hundreds and tens are 9. The ones are 10. 10 − 5 = 5, 9 − 3 = 6, 9 − 2 = 7, 3 − 1 = 2. Check: 2 765 + 1 235 = 4 000.

    • If you chose A: You took the smaller digit from the bigger one in each column. Add back: 1 235 + 3 235 = 4 470, not 4 000.
    • If you chose B: The 4 thousands gave 1 away. Only 3 are left. 3 − 1 = 2, not 3.

  8. Mei adds 36 + 48 + 19 + 27 in columns. The ones make 30. What is the total?

    Tap your answer.

    1. Yes, that is right. Ones: 6 + 8 + 9 + 7 = 30. Write 0, carry 3. Tens: 3 + 4 + 1 + 2 + 3 = 13. The total is 130.

    2. Not this one. You carried only 1. The ones made 30, which is 3 tens. Carry 3. Tens: 3 + 4 + 1 + 2 + 3 = 13. Try another.

    3. Not this one. You forgot the 3 tens from the ones. Tens: 3 + 4 + 1 + 2 + 3 = 13. Try another.

    See the answer

    130

    Ones: 6 + 8 + 9 + 7 = 30. Write 0, carry 3. Tens: 3 + 4 + 1 + 2 + 3 = 13. The total is 130.

    • If you chose B: You carried only 1. The ones made 30, which is 3 tens. Carry 3. Tens: 3 + 4 + 1 + 2 + 3 = 13.
    • If you chose C: You forgot the 3 tens from the ones. Tens: 3 + 4 + 1 + 2 + 3 = 13.

  9. Look at 5 002 − 2 457. The hundreds digit is 0. What does it become after the exchange?

    Tap your answer.

    1. Not this one. The 0 gets 10 from the thousands. Then it gives 1 to the tens. That leaves 9, not 10. Try another.

    2. Yes, that is right. The 0 gets 10 from the thousands. Then it gives 1 to the tens. 10 − 1 = 9.

    3. Not this one. The 4 is in the thousands. It was 5 and gave 1 away. The hundreds 0 became 9. Try another.

    See the answer

    9

    The 0 gets 10 from the thousands. Then it gives 1 to the tens. 10 − 1 = 9.

    • If you chose A: The 0 gets 10 from the thousands. Then it gives 1 to the tens. That leaves 9, not 10.
    • If you chose C: The 4 is in the thousands. It was 5 and gave 1 away. The hundreds 0 became 9.

Keep it

Copy this into your exercise book.

Line up the digits. Start at the ones. When a column makes 10 or more, carry. Write the last digit. A list can carry 2 or more.

Draw: Write 3 465 + 2 879 in columns. Show each carry as a small 1.

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

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