Compute with Integers.

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Presentation transcript:

Compute with Integers

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

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

Adding Integers with the Same Sign Add the absolute values of both integers. –2 + (–3) both –, so sum = –5 think: 2 + 3 = 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.

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 –

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

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; – × + = –

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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