LumenšŸŖ™ 0

Adding and subtracting integers

šŸ“– LearnšŸŽ¬ Guided Practiceāœļø Practice

Integers

Adding and subtracting integers

Once numbers go below zero, adding can make things smaller and subtracting can make them bigger. A number line keeps it straight.

Subtract ā†’ count back-6-5-4-3-2-10123= āˆ’5Add ā†’ count forward-6-5-4-3-2-10123= āˆ’2

Integers and the number line

The integers are the whole numbers and their negatives: ā€¦ āˆ’3, āˆ’2, āˆ’1, 0, 1, 2, 3 ā€¦ On a number line, numbers get bigger as you move RIGHT and smaller as you move LEFT. So āˆ’5 is less than āˆ’2, even though 5 is bigger than 2.

Adding

Adding a POSITIVE number moves you right. Adding a NEGATIVE number moves you left. 5 + 3 = 8 ā€” move 3 right. 5 + (āˆ’3) = 2 ā€” move 3 left. āˆ’4 + 6 = 2 ā€” start at āˆ’4, move 6 right. So adding a negative is the same as subtracting: 5 + (āˆ’3) is the same as 5 āˆ’ 3.

Subtracting

Subtracting a POSITIVE number moves you left. Subtracting a NEGATIVE number moves you RIGHT. 5 āˆ’ 3 = 2 ā€” move 3 left. 5 āˆ’ (āˆ’3) = 8 ā€” move 3 right, so it is the same as 5 + 3. āˆ’2 āˆ’ 5 = āˆ’7 ā€” start at āˆ’2, move 5 left. The rule worth remembering: two minus signs next to each other make a plus.

Which is bigger?

With negatives, the number that looks bigger may be smaller. āˆ’8 is LESS than āˆ’3, because āˆ’8 is further left on the line. A quick check: the further a negative number is from zero, the smaller it is.

Worked examples

5 + (āˆ’3)

  1. Adding a negative moves you LEFT.
  2. Start at 5 and move 3 left.

Answer: 2 ā€” the same as 5 āˆ’ 3

āˆ’4 + 6

  1. Adding a positive moves you RIGHT.
  2. Start at āˆ’4 and move 6 right.

Answer: 2

5 āˆ’ (āˆ’3)

  1. Subtracting a negative moves you RIGHT.
  2. Two minus signs together make a plus.
  3. So it is 5 + 3.

Answer: 8

āˆ’2 āˆ’ 5

  1. Subtracting a positive moves you LEFT.
  2. Start at āˆ’2 and move 5 left.

Answer: āˆ’7

Which is bigger, āˆ’8 or āˆ’3?

  1. āˆ’8 is further LEFT on the number line.
  2. Further left means smaller.

Answer: āˆ’3 is bigger

What must you add to āˆ’8 to get 7?

  1. From āˆ’8 to 0 is 8 steps right.
  2. From 0 to 7 is another 7.
  3. 8 + 7 = 15.

Answer: 15

Where you see this in real life

  • A temperature of āˆ’8 Ā°C is colder than āˆ’3 Ā°C, even though 8 is more than 3. Rising by 5 Ā°C from āˆ’8 Ā°C takes you to āˆ’3 Ā°C.
  • A bank balance of āˆ’Ā£20 means you owe Ā£20. Paying in Ā£30 gives āˆ’20 + 30 = Ā£10.

Key words

Integer
a whole number, positive, negative or zero
Negative number
a number less than zero
Number line
a line showing numbers in order, smaller to the left
Positive number
a number greater than zero
Difference
the result of a subtraction
šŸŽ¬ Try Guided Practice ā†’Skip to Practice ā†’