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TCAP Coach Lesson

TCAP Coach Lesson. Lesson 3: Properties of Addition and Multiplication Pages: 21-25. Getting the Idea. The properties of addition and multiplication can make computation easier and faster.

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TCAP Coach Lesson

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  1. TCAP Coach Lesson Lesson 3: Properties of Addition and Multiplication Pages: 21-25

  2. Getting the Idea • The properties of addition and multiplication can make computation easier and faster. • The Commutative Property of Addition states that changing the order of the addends does not change the sum. • The Commutative Property of Multiplication states that changing the order of the factors does not change the product.

  3. Example 1 • What is the value of x? 9.8+4.7 = X +9.8 • Strategy: Use the Commutative Property of Addition. Changing the order of the addends does not change the sum. 9.8+4.7 = 4.7+9.8 14.5 = 14.5 Solution: The value of x is 4.7

  4. Example 2 • What is the value of y? 3.95 X y = 2.3 X 3.95 • Strategy: Use the Commutative Property of Multiplication. Changing the order of the factors does not changes the product. 3.95 X 2.3 = 2.3 X 3.95 9.085 = 9.085 • Solution: The value of y is 2.3

  5. Associative Properties • The Associative Property of Addition states that changing the grouping of the addends does not change the sum. • The Associative property of Multiplication states that changing the grouping of the factors does not change the product. • When you use associative properties, try to find a grouping of numbers that makes the computation easier to do mentally.

  6. Example 3 • 14.3+(12.7+13.27)=[ ] • Strategy: Use the Associative Property of Addition Step 1: Use the Associative Property to regroup the addends. 14.3+(12.7+13.47) = (14.3+12.7) +13.47 Step 2: Add inside the parentheses first. (14.3+12.7)+13.47 27 +13.47 Step 3: Find the final sum. 27+13.47=40.47 • Solution: 14.3+(12.7+13.47)=40.47

  7. Example 4 • (32x6)x15= [ ] • Strategy: Use the Associative Property of Multiplication Step 1: Use the associative property of multiplication to regroup the factors. (32x6)x15 = 32x(6x15) Step 2: Multiply inside the parentheses first. 32x(6x15) 32x90 Step 3: Find the final product. 32x90=2,880 • Solution: (32x6)x15=2,880

  8. Distributive Property • The Distributive Property of Multiplication over Addition states that to multiply a sum by a number, you can multiply each addend by the number and add the products. • For any numbers a,b,and c, a(b+c)= (axb)+(axc)

  9. Example 5 • 76x47= [ ] • Strategy: Use the Distributive Property of Multiplication over Addition Step 1: Write one factor as the sum of two numbers. 47=40+7 76x47=76x(40x7)+(76x7) Step 2: Multiply each set of factors. (76x40)+(76x7) 3,040 + 532 Step 3: Add the products. 3,040+532=3,572 • Solution: 76x47=3,572

  10. Distributive Property • The Distributive Property of Multiplication over Subtraction states that to multiply a difference by a number, you can multiply each of the two numbers by that number and then find the difference in the products. • For any numbers a, b, and c • a(b-c) = ab-ac

  11. Example 6 • 83X58= [ ] • Strategy: Use the Distributive Property of Multiplication over Subtraction. Step1: Write one factor as the difference of two numbers. 58=60-2 83 X 58 = 83 x (60-2) - (83x2) Step 2: Multiply each set of factors (83x60) – (83x2) 4,980 - 166 Step 3: Subtract the products. 4,980-166= 4,814 • Solution: 83x58= 4,814

  12. Other Properties to help you Multiply • The Identity Property of Addition states that when one addend is 0, the sum is equal to the other addend. Ex. 3.82+0=3.82 • The Identity Property of Multiplication states that when one factor is 1, the product is equal to the other factor. Ex. 4.25x1=4.25 • The Zero Property of Multiplication states that when one factor is 0, the product is equal to 0. Ex. 5.73x0=0

  13. Lesson Practice • You are now to complete the Lesson Practice. • Questions 1-8 • Page 25

  14. Exit Ticket • Define: • Commutative Property of Addition • Associative Property of Multiplication • Distributive Property of Multiplication over Addition

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