Negative numbers Worked Solutions — GCSE Maths

Start on the number line

Start at −3. Adding a positive number means moving to the right.

Move $5$ to the right

Count 5 steps right: −3, −2, −1, 0, 1, 2.

State the answer

So the answer is $2$.

Adding a negative means subtracting

Adding −7 is the same as subtracting 7, so we move left from 4.

Count $7$ to the left

From 4 go left 7 steps, crossing zero: 4,3,2,1,0,−1,−2,−3.

State the answer

So the answer is −3.

Both numbers are negative

Adding −6 is subtracting 6, so we go further into the negatives.

Combine the amounts

The two negative amounts add to $8$, and the answer stays negative.

State the answer

So the answer is −8.

Adding a positive moves right

Start at −7. Adding a positive means moving to the right.

Move $10$ to the right

From −7, 7 steps reach 0, then 3 more reach 3.

State the answer

So the answer is $3$.

Adding a negative means subtracting

Adding −1 is subtracting 1, going further negative.

Combine the amounts

The negatives add to $10$, staying negative.

State the answer

So the answer is −10.