Multiplying and dividing integers; absolute value
Multiply and divide negative numbers with hops on the number line, find the pattern behind the signs, and measure distance from zero.
- UK: Year 7
- France: grade 7
- Germany: grade 5
- Iran: grade 7
- Afghanistan: grade 7
- Syria: grade 7
- Palestine: grade 7
- Ukraine: grade 6
- Russia: grade 6
Guide
Adding a negative number is a hop to the left: −3 + (−4) starts at −3 and hops 4 to the left.
Multiplying is repeated hops from zero: 3×(−2) is three hops of −2, so it lands on −6.
When a pattern goes down by one each time, the answers change by the same amount each time. Following the pattern past zero shows why a negative number times a negative number is positive.
Division undoes multiplication: (−12) ÷ 3 asks "3 times what makes −12?". The answer is −4, because 3×(−4) = −12.
The absolute value (modulus) of a number is its distance from zero, so it is never negative: |−7| = 7 and |7| = 7.