Foundation and Higher · negative numbers

Negative numbers.
Four rules,
one number line.

two signs together?
sort them out first

when two signs sit next to each other —

+ −  and  − −

+ −  becomes  −

− −  becomes  +

rule 1 of 4

Adding a negative

1. + − becomes −: so this is 3 − 5.

2. Start at 3. Move 5 to the left.

✓ 3 + (−5) = −2

rule 2 of 4

Subtracting a negative

1. − − becomes +: so this is 2 + 4.

2. Start at 2. Move 4 to the right.

✓ 2 − (−4) = 6

rule 3 of 4

Starting below zero

1. Only one sign here: nothing to change.

2. Start at −2. Move 5 further left.

✓ −2 − 5 = −7, not −3 or 3

rule 4 of 4

Multiply and divide

1. Different signs give a negative answer.

2. Same signs give a positive answer.

✓ The same rule works for ÷

−3 × 4 = −12 different signs

−3 × −4 = 12 same signs

−12 ÷ 4 = −3

−12 ÷ −4 = 3

negative numbers —

+ −

becomes −

− −

becomes +

× and ÷

same signs +, different signs −

“Two negatives make a positive”
is only for × and ÷, and for − −.

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