Multiplying And Dividing Decimals Worksheet

Multiplying and dividing decimals at a glance

A decimal number has a part that is not whole. We write the whole number part, followed by a decimal point, then tenths, hundredths, thousandths, and so on. It is important that students can recognise the decimal place value of each column.

When multiplying decimals, we use powers of ten to convert our calculation into a whole-number multiplication so that the standard multiplication algorithms can be used. For example, to work out 0.31.52, we would multiply the first number by 10 and the second number by 100, to get 3152. Once the whole number answer has been worked out (456), we reverse the multiplication by powers of 10 to get the answer to the decimal multiplication – so in this example, we divide our answer by 1000, to give 0.456.

The method for decimal division depends on what is being divided. For an integer divisor with a decimal dividend, we use the standard algorithm for short or long division for two or three-digit numbers, placing the decimal point in the quotient directly above its position in the dividend. If the divisor is a decimal, we write the division as a fraction and use the concept of equivalent fractions to convert to a whole-number calculation.

Further multiplication and division problems include unit conversions, money calculations, and using decimals in standard form calculations.

Looking forward, students can then progress to additional number worksheets, for example a percentage worksheet or a rounding worksheet.

For more teaching and learning support on Number our GCSE maths lessons provide step by step support for all GCSE maths concepts.