 # To identify basic multiplication facts and properties.

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To identify basic multiplication facts and properties

MENTAL MATH Find each sum: 1. 2 + 2 + 2 + 2 2. 5 + 5 + 5 3. 8 + 8 + 8 +8 4. 9 + 9 + 9 5. 4 + 4 + 4 + 4 + 4 6. 7 + 7 + 7 + 7 + 7 7. 1 + 1 + 1 + 1 + 1 + 1 + 1

Multiplication Properties Commutative Property Associative Property Identity Property Zero 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.

Commutative Property The order of the numbers doesn’t change the result (answer to the problem) 6 x 4 = 4 x 6

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

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

Associative Property The grouping of the factors doesn’t change the answer. (4 x 2) x 3 = 24 4 x (2 x 3) = 24 (5 x 1) x 6 = 30 5 x (1 x 6) = 30

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!

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

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

Zero Property When any number is multiplied with zero, the answer is zero. If one factor is O, the product is O. Example: 98,756,432 X 0 = 0

Zero Property 7,547,598,375 X o = 0 758,375,937 X 0 = 0 0 X 75,879,705 = 0

Distributive Property Multiplying the sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the product. 9 X (20 - 3) = (9 X 20) – (9 X 3) 8 X (40 + 5) = (8 X 40) + (8 X 5) 8 X 45 = (8 X 40) + (8 X 5)

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) 195 X 5 = (200 X 5) – (5 X t)

Test Yourself 1. 9 X 3 = 3 X w 2. 3 X (4 X 2 ) = (n X 4) X 2 3. 234 X 1 = z 4. 56 X p = 11 X 56 5. 7,547,598,375 X c = 0 6. q X 8 = 8 X 4 7. 5 X (7 X 2) = (5 X 7) X n 8. 4 X 509 = (4 X 500) + (4 X m) 9. 6 X 310 = (6 X n) + (6 X 10) 10. (2 X z) X 5 = 2 X (8 X 5) 11. q X 2,567 = 2,567 12. 12. 195 X 5 = (200 X 5) – (5 X t) 13. z X 75,879,705 = 0 14. 98,765 X d = 98,765 15. 5 X 9 = r X 5 16. s X 205 = (5 X 200) + (5 X 5) 17. 4 X (p X 7) = (4 X 1) X 7 18. 758,375,937 X 0 = b Rewrite each equation with the correct answer, and write the name of the property.

Test Yourself Answers 1. 9 X 3 = 3 X 9 Commutative 2. 3 X (4 X 2) = (3 X 4) X 2 Associative 3. 234 X 1 = 234 Identity 4. 56 X 11 = 11 X 56 Commutative 5. 7,547,598,375 X 0 = 0 Zero 6. 4 X 8 = 8 X 4 Commutative 7. 5 X (7 X 2) = (5 X 7) X 2 Associative 8. 4 X 509 = (4 X 500) + (4 X 9) Distributive 9. 6 X 310 = (6 X 300) + (6 X 10) Distributive 10. (2 X 8) X 5 = 2 X (8 X 5) Associative 11. 1 X 2,567 = 2,567 Identity 12. 195 X 5 = (200 X 5) – (5 X 5) Distributive 13. 0 X 75,879,705 = 0 Zero 14. 98,765 X 1 = 98,765 Identity 15. 5 X 9 = 9 X 5 Commutative 16. 5 X 205 = (5 X 200) + (5 X 5) Distributive 17. 4 X (1 X 7) = (4 X 1) X 7 Associative 18. 758,375,937 X 0 = 0 Zero

How did you do? 18 correctExcellent 17 correctVery Good 16 - 15 correct Good 14 - 13 correct Passing 12 – 0 correct You need more practice.