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Properties o f Addition

Properties o f Addition. Identity Property of Addition. a + 0 = a 17 + 0 = ? 17 -123 + 0 = ? -123. Commutative Property of Addition. Changing the order of the addends does not change their sum. a + b = b + a 23 + 17 = 17 + 23 50 + 2 = 2 + 50. NO SUCH THING!.

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Properties o f Addition

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  1. Properties of Addition

  2. Identity Property of Addition • a + 0 = a • 17 + 0 = ? • 17 • -123 + 0 = ? • -123

  3. Commutative Property of Addition • Changing the order of the addends does not change their sum. • a + b = b + a • 23 + 17 = 17 + 23 • 50 + 2 = 2 + 50

  4. NO SUCH THING! Commutative Property of Subtraction • a – b = b – a • 12 – 5 = 5 – 12

  5. Associative Property of Addition • Changing the grouping of the addends does not change their sum. • (a + b) + c = a + (b + c) • This property can be extremely useful. For example: • What is 23 + 125 + 7? • 23 + 7 = 30 … 30 + 125 = 155. • What is 99.5 + 17 + 0.5? • 117.

  6. Quick Check • Use mental math to find: 4.4 + 5.3 + 0.6 • 4.4 + 0.6 + 5.3 = 5 + 5.3 = 10.3 • Use mental math to find: 2.85 + 62.89 + 7.15 • 2.85 + 7.15 + 62.89 = 10 + 62.89 = 72.89

  7. Extension: Using Compensation • The sum of two numbers remains the same if you add a number to one addend and subtract the same number from the other addend. • 5 + 7 = 12 • (5 – 3) + (7 + 3) = 2 + 10 = 12 • (5 + 6) + (7 – 6) = 11 + 1 = 12 • Why is this useful?

  8. Compensation is useful when adding decimals • $4.96 + $3.79 • ($4.96 + $0.04) + ($3.79 - $0.04) • = $5.00 + $3.75 • = $8.75

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