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Multiplication Properties

Multiplication Properties. Multiplication Properties. Commutative Property Associative Property Distributive Property. Why Should you Learn about the Properties of Multiplication?. It helps you solve problems without working them out. It helps with mental math.

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Multiplication Properties

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  1. Multiplication Properties

  2. Multiplication Properties • Commutative Property • Associative Property • Distributive Property

  3. Why Should you Learn about the Properties of Multiplication? • It helps you solve problems without working them out. • It helps with mental math. • It makes understanding math easier.

  4. Commutative Property • The order of the numbers doesn’t change the result (answer to the problem) • 3 X 4 = 4 X 3 12 = 12

  5. Commutative Property • 9 X 3 = 3 X • 56 X = 11 X 56 • X 8 = 8 X 4 • 5 X 9 = X 5 The answers are on the next slide.

  6. Commutative Property • 9 X 3 = 3 X 9 27 = 27 • 56 X 1 = 1 X 56 56 = 56 • 4 X 8 = 8 X 4 32 = 32 • 5 X 9 = 9 X 5 45 = 45

  7. Associative Property • The grouping of the factors doesn’t change the answer. • (4 X 2) X 3 = 4 X (2 X 3) 24 = 24

  8. Associative Property • 3 X (4 X 2) = ( X 4) X 2 • 4 X ( X 7) = (4 X 1) X 7 • 5 X (7 X 2) = (5 X 7) X • (2 X ) X 5 = 2 X (8 X 5) Is this Associative? • 5 X ( X 2) = (2 X 5) X 5 Watch out! Answers are on the next slide.

  9. Associative Property • 3 X (4 X 2) = (3 X 4) X 2 24 = 24 • 4 X (1 X 7) = (4 X 1) X 7 28 = 28 • 5 X (2 X 2) = (2 X 5) X 2 20 = 20 • (2 X 4) X 5 = 2 X (4 X 5) 40 = 40 Is this Associative? No, it’s commutative. • 5 X (5 X 2) = (2 X 5) X 5

  10. Distributive Property • Multiplying the answer by a number is the same as multiplying each number in the answer by a number and adding (or subtracting) the product. 9 X (10 - 3) = (9 X 10) – (9 X 3) 9 x (7) = (9 X 10) – (9 X 3) 9 x (7) = (90) – (27) 63 = 63

  11. Distributive Property • 2 X (10 + 2) = (2 X 10) + (2 X ) 2 X 12 = 20 + 24 = • 6 X (10 + 3) = (6 X ) + (6 X 3) 6 X 13 = + 18 78 = The answers are on the next slide.

  12. Distributive Property • 2 X (10 + 2) = (2 X 10) + (2 X 2) 2 X 12 = 20 + 4 24 = 24 • 6 X (10 + 3) = (6 X 10) + (6 X 3) 6 X 13 = 60 + 18 78 = 78

  13. Order of Operations • Please P Parentheses • Excuse E Exponents (not covered in 4th grade) • My Dear M/D Multiplication/Division • Aunt Sally A/S Addition/Subtraction • *Multiplication and Division are in the same step. In this case you would go from LEFT to RIGHT! • *Addition and Subtraction are in the same step. In this case you would go from LEFT to RIGHT!

  14. Examples Example: • 7 + 3 x 5 • 7 + 15 • 22 Example: • 7 x 3 – (4 x 3) +14 ÷ 2 • 7 x 3 – 12 +14 ÷ 2 • 21 – 12 + 14 ÷ 2 • 21 – 12 + 7 • 9 + 7 • 16

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