You can use the properties of operations to help you simplify numerical expressions more easily. Properties of Addition. Properties of Multiplication

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1 ? Name 1.1 ALGEBRA Properties Essential Question How can you use properties of operations to solve problems? Number and Operations 5.3.K MATHEMATICAL PROCESSES 5.1.C, 5.1.G You can use the properties of operations to help you simplify numerical expressions more easily. Properties of Addition Commutative Property of Addition If the order of addends changes, the sum stays the same. Associative Property of Addition If the grouping of addends changes, the sum stays the same. Identity Property of Addition The sum of any number and 0 is that number = (8 + 14) = (5 + 8) = 13 Properties of Multiplication Commutative Property of Multiplication If the order of factors changes, the product stays the same. Associative Property of Multiplication If the grouping of factors changes, the product stays the same. Identity Property of Multiplication The product of any number and 1 is that number. 4 9 = (3 6) = (11 3) = 4 Unlock the Problem The table shows the number of bones in several parts of the human body. What is the total number of bones in the ribs, the skull, and the spine? To find the sum of addends using mental math, you can use the Commutative and Associative Properties. Use properties to find Part Number of Bones Ankle 7 Ribs 24 Skull 28 Spine = 28 + _ + 26 = 28 + (24 + _ ) Use the Property to reorder the addends. Use the Property to group the addends. = 28 + _ Use mental math to add. = _ So, there are _ bones in the ribs, the skull, and the spine. Math Talk Mathematical Processes Explain why grouping 24 and 26 makes the problem easier to solve. Module 1 5

2 Distributive Property Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. 5 (7 + 9) = (5 7) + (5 9) The Distributive Property can also be used with multiplication and subtraction. For example, 2 (10 8) = (2 10) (2 8). Example Use the Distributive Property to find the product. One Way Use addition = 8 ( _ + 9) = (_ 50) + (8 _) = _ + _ = _ Another Way Use subtraction = 8 ( _ 1) Use a multiple of 10 to write 59 as a sum. Use the Distributive Property. Use mental math to multiply. Use mental math to add. Use a multiple of 10 to write 59 as a difference. = ( _ 60) (8 _ ) = _ _ = _ Share and Show Use the Distributive Property. Use mental math to multiply. Use mental math to subtract. Math Talk Mathematical Processes Explain how you could find the product by using mental math. 1. Use properties to find _ 25 Property of Multiplication 23 ( _ _ ) 23 Property of Multiplication Use properties to find the sum or product

3 Name Problem Solving Practice: Copy and Solve Use properties to find the sum or product Complete the equation, and tell which property you used (19 + 6) = (11 + _ ) = _ Show how you can use the Distributive Property to rewrite and find (32 6) + (32 4). Problem Solving 11. Multi-Step Three friends meals at a restaurant cost $13, $14, and $11. Use parentheses to write two different expressions and find how much the friends spent in all. Which property does your pair of expressions demonstrate? Fancy Guppy Prices 12. Multi-Step Jacob is designing an aquarium for a doctor s office. He plans to buy 6 red blond guppies, 1 blue neon guppy, and 1 yellow guppy. The table shows the price list for the guppies. How much will the guppies for the aquarium cost? Blue neon Red blond Sunrise Yellow $11 $22 $18 $ Sense or Nonsense? Julie wrote (15 6) 3 = 15 (6 3). Is Julie s equation sense or nonsense? Do you think the Associative Property works for subtraction? Explain. Module 1 Lesson 1 7

4 Daily Assessment Task Mathematical Processes Fill in the bubble completely to show your answer. 14. Connect In a flea circus, 12 fleas pull carts, 23 fleas ride on tiny bicycles, and 18 fleas sit on seesaws. You can add to find the total number of fleas. Which equation shows the Commutative Property of Addition? A = B = ( ) + 18 C = 12 + ( ) D = Use Symbols Complete the equation ( ) = (15 + ) + 27 A 40 C 10 B 25 D Multi-Step Nick read 24 pages in his book one day, 29 pages the next day, and 16 pages on the third day. Megan read 26 pages for three days in a row. Who read more pages? How many more? A B C D Megan read 9 more pages. Megan read 11 more pages. Nick read 9 more pages. Megan read 11 more pages. 8 TEXAS Test Prep 17. Canoes rent for $29 per day. Which expression can be used to find the cost in dollars of renting 6 canoes for a day? A (6 + 20) + (6 + 9) B (6 20) + (6 9) C (6 + 20) (6 + 9) D (6 20) (6 9)

5 Homework and Practice Name Number and Operations 5.3.K MATHEMATICAL PROCESSES 5.1.C, 5.1.G 1.1 Properties Use properties to find the sum or product Complete the equation, and tell which property you used = _ (70 + 8) = (16 + _ )+ 8 Problem Solving 6. Maggie s class bought three books at the book fair. The books cost $15, $9, and $12. Use parentheses to write two different expressions and find how much the class spent in all. Which property does the pair of expressions demonstrate? 7. Leo s basketball team makes 16 points in the first game, 22 points in the second game, and 18 points in the third game. Use the Associative Property of Addition to show two different ways Leo can group the addends to show the total number of points. Module 1 Lesson 1 9

6 Lesson Check TEXAS Test Prep Fill in the bubble completely to show your answer. 8. Which property is shown by the following equation? 44 + ( ) = ( ) Janel rakes leaves for $8 per lawn. Which expression can be used to find the amount she earns if she rakes 14 lawns? A B C D Commutative Property of Addition Associative Property of Addition Identity Property of Addition Distributive Property A (8 + 10) (8 + 4) B (8 + 10) + (8 + 4) C (8 10) (8 4) D (8 10) + (8 4) 10. Sara bought 7 tickets to the school play. Each ticket costs $11. To find the total cost in dollars, she added the product 7 1 to the product 7 10, for a total of $77. Which property did Sara use? A B C Commutative Property of Multiplication Associative Property of Multiplication Identity Property of Multiplication 11. There are 6 granola bars in each box. Which expression can be used to find the number of granola bars in a dozen boxes? A (6 + 10) (6 + 2) B (6 10) + (6 2) C (6 + 10) + (6 + 2) D (6 10) (6 2) D Distributive Property 12. Multi-Step Kara s garden has 4 sections. Each section has 7 rows of carrots and 9 rows of celery. How many rows are in the garden? A 64 B 56 C 20 D Multi-Step Max s school bought boxes of pencils. Each box holds 12 pencils. The fourth grade classes need 25 boxes. The fifth grade classes need 22 boxes. How many pencils are needed by both grades? A 300 B 264 C 564 D

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