How to teach the four operations with rational numbers
Year 7 (ages 12 to 13)
Fractions, decimals and percentages are different ways of writing the same kind of number. This unit builds fluency combining them with addition, multiplication and percentage-of calculations, converting between forms as needed.
How to teach it
- Establish fraction-to-decimal conversion (divide) as the go-to tool for combining fractions with decimals.
- Teach percentage-of as 'convert to a decimal or fraction, then multiply', rather than a separate rule to memorise.
- Practise mixed problems that combine two different forms (a fraction plus a decimal, a fraction times a decimal) so conversion becomes automatic.
- Check every answer's reasonableness with a quick estimate (e.g. 25% of 60 should be noticeably less than 60).
- Build up from single-step to two-step problems only once each individual conversion is secure.
Worked example
Calculate 1/4 + 0.35 (write as a decimal) 1/4 = 0.25 0.25 + 0.35 = 0.6
Common mistakes
- Adding a fraction and a decimal directly without converting either into the same form first.
- Multiplying by the percentage number itself (e.g. x25) instead of its decimal or fraction equivalent (x0.25).
- Forgetting to simplify or round appropriately after combining fractions and decimals.
- Losing track of which conversion was already done when a problem has multiple steps.
Frequently asked questions
How do you add a fraction and a decimal?
Convert the fraction to a decimal (or the decimal to a fraction) so both numbers are in the same form, then add as usual.
How do you find a percentage of a number?
Convert the percentage to a decimal or fraction (e.g. 25% = 0.25 = 1/4) and multiply it by the number. 25% of 60 is 0.25 x 60 = 15.
How do you multiply a fraction by a decimal?
Convert the fraction to a decimal first, then multiply the two decimals together as usual.
What year are the four operations with rational numbers taught?
In the Australian Curriculum this is a Year 7 skill (AC9M7N06): using the four operations with positive fractions, decimals and percentages, choosing efficient strategies.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.