myLearning

Step 7: Fraction and decimal arithmetic

Long division by two-digit numbers

Step 7 · Fraction and decimal arithmetic topics

Divide numbers of up to four digits by two-digit numbers, estimating each digit of the answer from friendly numbers, and check by multiplying.

Estimating each digit

Dividing by a two-digit number is easier when you round it. To divide by 23, think of 20; to divide by 48, think of 50.

Example: Estimating

About how many times does 23 go into 100?

  1. Round 23 to 20.
  2. 20 × 5 = 100, so try 5.
  3. 23 × 5 = 115 is too big, so it is 4: 23 × 4 = 92.

Answer4 times

If a guess makes a product bigger than the number, try one less. If what is left over is as big as the divisor or bigger, try one more.

The steps of long division

Long division repeats four steps for each digit: divide, multiply, subtract, bring down.

Example: Long division

What is 952 ÷ 28?

  1. 95 ÷ 28 is about 3, since 30 × 3 = 90. 28 × 3 = 84, and 95 − 84 = 11.
  2. Bring down the 2: 112.
  3. 112 ÷ 28 is about 4. 28 × 4 = 112, and 112 − 112 = 0.

Answer34

StepIn 952 ÷ 28
Divide95 ÷ 28 is about 3
Multiply28 × 3 = 84
Subtract95 − 84 = 11
Bring down112, and start again

Example: With a remainder

What is 1,000 ÷ 32?

  1. 32 goes into 100 three times: 32 × 3 = 96, and 100 − 96 = 4.
  2. Bring down the 0: 40.
  3. 32 goes into 40 once: 40 − 32 = 8.

Answer31 remainder 8

Checking the answer

Multiply the answer by the divisor and add the remainder. You should get back the number you started with.

Example: Checking

Check that 1,000 ÷ 32 = 31 remainder 8.

  1. 31 × 32 = 992.
  2. 992 + 8 = 1,000.

AnswerIt is right.

An estimate catches big slips: 952 ÷ 28 is about 900 ÷ 30 = 30, so 34 is sensible, but 304 would not be.

Try it yourself

Work each one on paper first, then open the answer to check.

  1. What is 672 ÷ 21?

    Show answer

    32.

  2. What is 1,575 ÷ 45?

    Show answer

    35.

  3. What is 800 ÷ 25?

    Show answer

    32.

  4. What is 950 ÷ 32?

    Show answer

    29 remainder 22. 32 × 29 = 928.

  5. A hall has 540 seats in rows of 18. How many rows are there?

    Show answer

    30 rows.

What next?