2.2Addition and Subtraction of Integers

With negatives in play the number line runs both ways, so you can move left past $0$ .

Owe $\$2$ and borrow $\$3$ more and you owe $\$5$ . Have $\$5$ and owe $\$2$ and you are $\$3$ up.

Adding two negatives

(-a) + (-b) = -(a + b)

Adding a negative to a positive

a + (-b) = a - b

Subtracting a negative

a - (-b) = a + b

At noon it was $-5\,^{\circ}\text{C}$ . By midnight it had fallen a further $9\,^{\circ}\text{C}$ . Find the midnight temperature.

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Falling

9\,^{\circ}\text{C}

means subtracting:

(-5) + (-9)

Both moves go the same way down, so the falls add:

5 + 9 = 14

below zero.

Result is negative:

(-5) + (-9) = -14

The midnight temperature was

-14\,^{\circ}\text{C}

A submarine at $-120$ m rises $45$ m, then dives $30$ m. Find its final position relative to sea level.

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Start:

-120

Rise

45

-120 + 45 = -75

Dive

30

-75 + (-30) = -105

Final position:

-105

m, that is a depth of

105

m below sea level.

Ali's bank balance is $-\$85$ (overdrawn). He deposits $\$120$ . What is his new balance?

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(-85) + 120 = 120 - 85 = 35

His new balance is

\$35

A temperature rose by $11\,^{\circ}\text{C}$ to reach $-3\,^{\circ}\text{C}$ . Find where it started.

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A rise of

11

took it to

-3

, so go back down

11

from

-3

-3 - 11 = -14

It started at

-14\,^{\circ}\text{C}

Check:

-14 + 11 = -3

Now you try

A question on this, marked as you go, with the working shown. No account needed.

Practise this

Questions on Integers, Rational Numbers and Real Numbers, marked as you go, with the working shown.