T1_LO5 · lo-yr9-integers
Integers are whole numbers that can be positive, negative, or zero. They have no fractions or decimals. Use a number line to visualise addition and subtraction.
Steps — adding integers
Start at the first number on the number line.
If adding a positive, move right. If adding a negative, move left.
Steps — subtracting integers
Change subtraction to adding the opposite.
Then follow the addition rules.
Example: $7 - (-2) = 7 + 2 = 9$.
Key facts
Opposite of $-7$ is $7$.
$3, -5, 0$ are integers; $1/2$ and $-5.5$ are not.
$-3 + 5 = 2$ (start at $-3$, move 5 right)
$7 - (-2) = 7 + 2 = 9$
$(-3) + (-4) = -7$
On a number line, $-1 > -5$ because $-1$ is further right.
Thinking $-5$ is greater than $-1$. On the number line, $-1$ is to the right of $-5$, so $-1 > -5$.
What is the opposite of $-7$?
Calculate: $-3 + 5$.
Order from smallest: $-2, 0, 3$.
Example 1: temperature rise
A temperature is $-4^\circ$C. It rises by $10^\circ$C. What is the new temperature?$$ -4 + 10 = 6 $$Answer: $6^\circ$C.
Example 2: adding negatives
Calculate $(-3) + (-4)$.$$ (-3) + (-4) $$Start at $-3$, move 4 left: $-7$. Answer: $-7$.
Calculate: $5 + (-2)$.
Calculate: $-1 - 3$.
Calculate: $7 - (-2)$.
Example 3: multiply negatives
Calculate $(-3) \times 4$.$$ (-3) \times 4 $$Positive $\times$ negative = negative. Answer: $-12$.
Example 4: diving scenario
A diver at $-12$ m ascends 3 m then descends 5 m.$$ -12 + 3 - 5 = -14 $$Answer: final depth is $-14$ m.
Forgetting that two negatives make a positive. $(-3) \times (-4) = 12$, not $-12$. Think: subtracting a debt means gaining money.