Rational numbers: integers, fractions and decimals (Grade 8)

If your child is in Grade 8, the topic "Rational numbers: integers, fractions and decimals" is one of the ideas where confidence is most often won or lost. Here is what it means in plain words, a worked example you can follow together, and a few simple ways to help at home.

What Grade 8 children learn

• Add, subtract, multiply and divide positive and negative fractions and decimals
• Use the sign rules and the order of operations (BEDMAS) with negatives
• Switch between fractions and decimals when it makes the work easier

The key ideas

• A rational number is any number you can write as a fraction of two integers, so integers, fractions and decimals that end or repeat (such as 0.75) are all rational.
• Adding: same signs add and keep the sign; different signs subtract and the larger size wins. Subtracting a negative means adding a positive.
• Multiplying or dividing: same signs give a positive, different signs give a negative.
• Fractions: use a common denominator to add or subtract; to divide, multiply by the reciprocal.
• BEDMAS still applies, with brackets and exponents first.

Quick examples

• −2/3 + 3/4 = 1/12
• (−3/5) ÷ (9/10) = −2/3
• −6 + 2 × (4 − 7)² ÷ (−3) = −12
• 0.75 − 1 2/5 (one and two-fifths) = −0.65 (or −13/20)

A worked example

How to help at home

• Ask your child to explain the first step of the worked example in their own words before you show them anything.
• Work through the "Try it yourself" question together, and talk about why the answer makes sense.
• Spend a few minutes a day on the free Tutorizer "Rational numbers" practice. Short and regular beats long and rare.
• If a step feels shaky, go back to the key ideas above and use objects, drawings or a number line.

Try it yourself

Want a challenge?

Next steps