Operations with Decimals

Operations with Decimals

Operations with decimals

How do I add or subtract decimals without a calculator?

• If the numbers involve decimals, the column methods for addition and subtraction can be used

  • Line the place value columns up carefully

  • Make sure the decimal points are all in the same column

    •  Writing zeros (often called place value holders) can help keep everything in line

  • e.g.  2.145 + 13.02 would be written as

How do I multiply decimals without a calculator?

• The standard methods for multiplication can be easily adapted for use with decimal numbers

  • E.g. column method, lattice method and grid method

• You can make a problem easier by converting to integer values then undoing the action to the answer

  • Multiply each value by a power of 10 to make it an integer

  • Perform the easier multiplication

  • Undo the initial action by dividing by the same powers of 10

  • E.g. 2.5 x 4.01

    • Multiply 2.5 by 10 to give 25 and 4.01 by 100 to give 401

    • 25 x 401 = 10 025

    • Divide the answer by 10 and 100 to undo the initial changes

    • So the answer is 10.025

• An alternative method is to ignore the decimal point whilst multiplying

  • then put it back in the correct place for the final answer using estimation

  • E.g. 1.3 × 2.3

    • Ignoring the decimals this is 13 × 23, which works out to 299

    • 1.3 × 2.3 is approximately 1.5 × 2, which is 3

    • So we know the answer should be close to 3, rather than 0.3 or 30

    • So the answer is 2.99

How do I divide a decimal without a calculator?

• Use a similar approach to when multiplying decimals

• Make a problem easier by converting to integer values then undoing the action to the answer

  • Write the division as a fraction

  • Multiply each value by a power of 10 to make it an integer

  • Perform the easier division

  • Undo the initial action

    • divide by the same power of 10 the numerator was multiplied by

    • multiply by the same power of 10 the denominator was multiplied by

  • E.g. 37.5 ÷ 0.25

    • $37.5÷0.25 \to \frac{37.5}{0.25}$

    • $\frac{37.5\times 10}{0.25\times 100}=\frac{375}{25}$

    • equation$\frac{375}{25}=15$

    • Undo the initial actions $\frac{15\times 100}{10}$

    • So the answer is 150

• Alternatively, ignore the decimal point whilst carrying out the division

  • then put it back in the correct place for the final answer using estimation

  • E.g. 4.68 ÷ 6

    • 4.68 ÷ 6 is approximately 5 ÷ 6, which is between 1 and 0.5

    • So we know the answer should be 0.78, rather than 7.8 or 0.078