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Division tips

Gain confidence and improve speed by practicing new division methods.

Tips and tricks for calculations involving division.

Division

- General tips to get the ball rolling.

Cancel out zeros.

Simplify division by striking out common zeros

Example: 180÷90

Worked answer:

18÷9=2

Ignore the decimals

Example: 7.5÷2.5

Multiplying both numbers by ten is equivalent to removing or 'ignoring' the decimals.

Worked answer:

75÷25=3

Double the decimal.

When dividing by a decimal check whether multiplication will make the decimal a whole number.

Double the number and the decimal.

Example: 10÷2.5

Worked answer:

10×2=20

2.5×2=5

20÷5=4

Denominator X - rise of the numerator

  • Rounding-off the denominator to a multiple of ten, simplifies division.
  • Multiply the numerator by the same number.

Example: 8÷5

Worked answer:

8×2=16

5×2=10

16÷10=1.6

- Dividing individual numbers - 4, 5, 25, and 125.

Divide by four

Divide twice by 2.

Example: 88÷4

Worked answer:

88×2=44

44÷2=22

Divide by five

Double the number, and then divide by ten.

Example: 885÷5

Worked answer:

885×2=1,770

1,770÷10=177

Divide by twenty five

First divide by ten and then multiply by four. Divide the result by ten.

Example: 98÷25

Worked answer:

98÷10=9.8

9.8×4=39.2

39.2÷10=3.92

Divide by one hundred and twenty five

Remove any zeros and then multiply by 8

Example: 1750÷125

Worked answer:

175×8=1,400

These calculations require a prior ballpark estimate. Since 10 times 125 is close to the answer, remove both zeros from 1,400 for a final result of 14.

Checking division

  1. Re-arrange the division equation to make a multiplication equation.
  2. Calculate a digit sum for each factor.
  3. Multiply the digit sums and make a new digit sum from the product.
  4. Calculate the digit sum of the product in the multiplication equation.

If step 3 and step 4 are equal then the division equation is probably correct. If step 3 and step 4 are not equal then the answer is definitely wrong.

Note: The digits sums must have only one digit. If the digit sum is two digits, then add the digits again. For example, the digit sum of 89 is 17. Add the digits again to arrive at 8.

Example: 464÷58=8

Step 1

58x8=464

Step 2

Digit sum for 58: 5+8=13, 1+3=4

Digit sum for 8: 8

Step 3

4×8=32

Digit sum for 32: 3+2=5

Step 4

Digit sum for 464: 4+6+4=14, 4+1=5

The digits sums in steps 3 and 4 are the same. Therefore, 464÷58=8, is probably correct.