medium difficulty7 min

Integers and Their Arithmetic

Integers are numbers without fractional or decimal parts, including negative numbers, zero, and positive numbers.

In one line: Minus a minus becomes a plus, but only at that operation.

Understand it

Integer arithmetic depends strongly on signs. Adding a negative means moving left on the number line, subtracting a negative means adding the opposite, and multiplication or division of two same signs gives positive while different signs give negative.

Example

-7 + 3 = -4, -7 - (-3) = -4, (-6) × (-2) = 12, and (-15) ÷ 3 = -5.

Formula and rule

Same signs in multiplication or division give positive; different signs give negative.

Subtracting an integer means adding its additive inverse.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Simplify -12 + 7 - (-5).

1First change -(-5) to +5.
2Then -12 + 7 + 5 = 0.

Method you can reuse

Remove brackets carefully, replace subtraction by addition of the opposite integer, group positives and negatives, then subtract smaller total from larger total and keep the sign of the larger total.

Visual tip

A number line can show movement left for negative addition and movement right when subtracting a negative.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is -9 - (-4) equal to -5?

Think first, then show answer

Because subtracting -4 is the same as adding 4, so -9 - (-4) becomes -9 + 4, which equals -5.

Common wrong answer

For -12 + 7 - (-5), writing -10.

Why it loses marks: The second negative has been ignored.

Don't mix this up

A common mistake is writing -8 - (-5) as -13 instead of changing subtraction of a negative into addition.

Exam tip

In integer simplification, handle brackets and sign changes before doing the final arithmetic.