Grades 7 and 8 math: Integers, then rational numbers with decimals

If your child is working on Grades 7 and 8 math, the topic "Integers, then rational numbers with 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 Grades 7 and 8 children learn

• Add, subtract, multiply and divide integers using the number line and the sign rules
• Turn subtracting a negative into adding, and find the distance between two integers
• Work backwards from a sum and a product to find the integers
• Use the same rules for negative decimals, and see why integers and decimals that end (such as −0.6) are rational numbers

The key ideas

• Negative numbers sit left of zero on the number line: adding moves right and subtracting moves left, but subtracting a negative moves right, because 5 − (−3) = 5 + 3.
• Multiplying or dividing: same signs give a positive, different signs give a negative. With a string of factors, an even number of negatives gives a positive.
• The distance between two numbers is the larger minus the smaller.
• To find two integers from a sum and a product, list the factor pairs of the product and check which pair has the right sum.
• A rational number is any number that can be written as a fraction of two integers, so integers and decimals that end or repeat, such as −0.6 (which is −6/10), are all rational. The sign rules work the same way for them; line up the decimal points when adding.

Quick examples

• −14 + 9 − (−6) = 1
• (−6)(−4)(−2) = −48 (three negatives, so the answer is negative)
• The distance between −8 and 5 on a number line is 5 − (−8) = 13
• (−0.6)(2.5) − (−1.75) = −1.5 + 1.75 = 0.25 (the sign rules work for decimals too)

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 "Integers" 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

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