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## Multiplication Properties

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**Multiplication Properties**5th Grade**Multiplication Properties**• Associative Property • Commutative Property • Zero Property • Identity 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. • It makes understanding math easier.**Associative Property**• The grouping of the factors doesn’t change the answer (the parenthesis are moved). • (p X q) X r = p X (q X r) • (2 X 3) X 4 = 2 X (3 X 4)**Associative Property**• 3 X (4 X 2) = (n X 4) X 2 • 4 X (p X 7) = (4 X 1) X 7 • 5 X (7 X 2) = (5 X 7) X n • (2 X z) X 5 = 2 X (8 X 5) Is this Associative? • 5 X (n X 2) = (2 X 5) X 5 Watch out! Answers are on the next slide.**Associative Property**• 3 X (4 X 2) = (3 X 4) X 2 • 4 X (1 X 7) = (4 X 1) X 7 • 5 X (7 X 2) = (5 X 7) X 2 • (2 X 8) X 5 = 2 X (8 X 5) Is this Associative? No, it’s commutative. • 5 X (5 X 2) = (2 X 5) X 5**Commutative Property**• The order of the numbers doesn’t change the result (answer to the problem) • p X q = q X p • 4 X 5 = 5 X 4**Commutative Property**• 9 X 3 = 3 X w • 56 X p = 11 X 56 • q X 8 = 8 X 4 • 5 X 9 = r X 5 The answers are on the next slide.**Commutative Property**• 9 X 3 = 3 X 9 • 56 X 11 = 11 X 56 • 4 X 8 = 8 X 4 • 5 X 9 = 9 X 5**Zero Property**• When any number is multiplied with zero, the answer is zero. • 98,756,432 X 0 = 0**Zero Property**• 7,547,598,375 X c = 0 • 758,375,937 X 0 = b • z X 75,879,705 = 0**Identity Property**• Any number multiplied by 1 will give you the original number. • 23,487 X 1 = 23,487**Identity Property**• 234 X 1 = z • q X 2,567 = 2,567 • 98,765 X d = 98,765 Answers are on the next slide.**Identity Property**• 234 X 1 = 234 • 1 X 2,567 = 2,567 • 98,765 X 1 = 98,765**Distributive Property**• To multiply a sum by a number, you can multiply each addend by the number and then add the products. • 6 X 23 = 6 X (20+3) = (6X20)+(6X3)**Distributive Property**• 4 X 509 = (4 X 500) + (4 X m) • 6 X 310 = (6 X n) + (6 X 10) • s X 205 = (5 X 200) + (5 X 5) The answers are on the next slide.**Distributive Property**• 4 X 509 = (4 X 500) + (4 X 9) • 6 X 310 = (6 X 300) + (6 X 10) • 5 X 205 = (5 X 200) + (5 X 5)**9 X 3 = 3 X 9**3 X (4 X 2 ) = (3 X 4) X 2 234 X 1 = 234 56 X 11 = 11 X 56 7,547,598,375 X 0 = 0 4 X 8 = 8 X 4 5 X (7 X 2) = (5 X 7) X 2 4 X 509 = (4 X 500) + (4 X 9) 6 X 310 = (6 X 300) + (6X 10) (2 X 8) X 5 = 2 X (8 X 5) 1 X 2,567 = 2,567 12. 195 X 5 = (200 X 5) – (5 X 5) 0 X 75,879,705 = 0 98,765 X 1 = 98,765 5 X 9 = 9 X 5 5 X 205 = (5 X 200) + (5 X 5) 4 X (1 X 7) = (4 X 1) X 7 758,375,937 X 0 = 0 Test Yourself Rewrite each equation with the correct answer, and write the name of the property.**9 X 3 = 3 X 9 Commutative**3 X (4 X 2) = (3 X 4) X 2 Associative 234 X 1 = 234 Identity 56 X 11 = 11 X 56 Commutative 7,547,598,375 X 0 = 0 Zero 4 X 8 = 8 X 4 Commutative 5 X (7 X 2) = (5 X 7) X 2 Associative 4 X 509 = (4 X 500) + (4 X 9) Distributive 6 X 310 = (6 X 300) + (6 X 10) Distributive (2 X 8) X 5 = 2 X (8 X 5) Associative 1 X 2,567 = 2,567 Identity 195 X 5 = (200 X 5) – (5 X 5) Distributive 0 X 75,879,705 = 0 Zero 98,765 X 1 = 98,765 Identity 5 X 9 = 9 X 5 Commutative 5 X 205 = (5 X 200) + (5 X 5) Distributive 4 X (1 X 7) = (4 X 1) X 7 Associative 758,375,937 X 0 = 0 Zero Test Yourself Answers**How did you do?**• 18 correct Excellent • 17 correct Very Good • 16 - 15 correct Good • 14 - 13 correct Passing • 12 – 0 correct You need more practice.