How to teach operations with integers and rational numbers
Year 8 (ages 13 to 14)
This unit extends the four operations to negative numbers, and to signed fractions and decimals: adding, subtracting and multiplying integers, fractions and decimals that may be negative, using consistent sign rules.
How to teach it
- Review the integer addition/subtraction rules with a number line: adding a negative moves left, subtracting a negative moves right.
- Teach the multiplication sign rule explicitly: same signs give a positive result, different signs give a negative result.
- Extend the same sign rules to fractions and decimals once integer operations are secure, using a common denominator for fraction addition.
- Mix integer, fraction and decimal problems together so students practise identifying which sign rule applies each time.
- Have students predict the SIGN of an answer before calculating its value, as a quick self-check.
Worked example
Calculate: -7 + (4) -7 + 4 = -3 Calculate: (-1.5) x (2) -1.5 x 2 = -3
Common mistakes
- Forgetting that subtracting a negative number is the same as adding its positive.
- Applying the multiplication sign rule incorrectly, e.g. assuming two negatives always give a negative.
- Losing track of a negative sign partway through a multi-step calculation.
- Adding signed fractions without a common denominator, or forgetting to carry the sign through the simplification.
Frequently asked questions
How do you add or subtract two negative numbers?
Adding a negative is the same as subtracting its positive (5 + -3 = 5 - 3 = 2). Subtracting a negative is the same as adding its positive (5 - -3 = 5 + 3 = 8).
What is the rule for multiplying signed numbers?
Two numbers with the SAME sign multiply to a positive result; two numbers with DIFFERENT signs multiply to a negative result. (-4) x (-3) = 12, but (-4) x 3 = -12.
How do you add two fractions with negative numerators?
Treat the sign the same as with whole numbers: combine the numerators over the common denominator, then simplify. -3/8 + 5/8 = 2/8 = 1/4.
What year are the four operations with integers and rational numbers taught?
In the Australian Curriculum this is a Year 8 skill (AC9M8N04): using the four operations with integers and rational numbers, choosing efficient strategies.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.