1. Compute with Integers

2. Integers
Integers are whole numbers, both positive and negative, and 0.
Opposites are the same distance from 0.
–3 and +3 are opposites. +3 +7 -7 -3 -6 -5 -4 -2 -1 +4 +1 +2 +5 +6
negative integers
positive integers
opposites
sign –3

3. The symbol for absolute value is:
The absolute value of a number is its distance from 0 on a number line.
The symbol for absolute value is:
| |
|–5| = 5
is read “the absolute value of negative 5 is 5.”
|+5| = 5
is read “the absolute value of positive 5 is 5.” +3 +7 -7 -3 -6 -5 -4 -2 -1 +4 +1 +2 +5 +6

4. Adding Integers with the Same Sign
Add the absolute values of both integers.
–2 + (–3)
both –, so sum = –5
think: = 5 +3 +7 -7 -3 -6 -5 -4 -2 -1 +4 +1 +2 +5 +6
sum –3 –2
+2 + (+3)
both +, so sum = +5
Keep the sign of the addends.

5. Adding Integers with Different Signs
Find the difference of the absolute values of both integers.
–2 + (+3) +1
think: 3 > 2; 3 – 2 = 1; 3 is + +3 +7 -7 -3 -6 -5 -4 -2 -1 +4 +2 +5 +6
sum –2 –3
Use the sign of the addend with the greater absolute value.
+2 + (–3) –1
think: 3 > 2; 3 – 2 = 1; 3 is –

6. Subtracting Integers Addition and Subtraction are opposite operations.
+2 – (+3) –1
think: (opposite of +3) or +2 + (–3)
Think of subtracting as adding the opposite.
+2 – (–3) +5
think: (opposite of –3) or +2 + (+3)
–2 – (+3) –5
think: –2 + (opposite of +3) or –2 + (–3)
–2 – (–3) +1
think: –2 + (opposite of –3) or –2 + (+3)
+3 – (+2)
think: (opposite of +2) or +3 + (–2)
+3 – (–2)
think: (opposite of –2) or +3 + (+2)
–3 – (+2)
think: –3 + (opposite of +2) or –3 + (–2)
–3 – (–2)
think: –3 + (opposite of –2) or –3 + (+2)

7. The sign of the product follows these patterns:
Multiplying Integers
Multiply the numbers.
+2 × (+3) +6
think: 2 × 3 = 6; + × + = +
The sign of the product follows these patterns:
–2 × (–3)
+2 × (–3) –6
–2 × (+3)
× = + –
think: 2 × 3 = 6; – × – = +
think: 2 × 3 = 6; + × – = –
think: 2 × 3 = 6; – × + = –

8. The sign of the quotient follows these patterns:
Dividing Integers
Divide the numbers.
+6 ÷ (+3) +2
think: 6 ÷ 3 = 2; + ÷ + = +
The sign of the quotient follows these patterns:
–6 ÷ (–3)
+6 ÷ (–3) –2
–6 ÷ (+3)
÷ = + –
think: 6 ÷ 3 = 2; – ÷ – = +
think: 6 ÷ 3 = 2; + ÷ – = –
think: 6 ÷ 3 = 2; – ÷ + = –

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