1. 1-3 Properties of Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 1-3 Properties of Numbers Warm Up Simplify. 1. 10 · 7 + 7 · 10 2. 15 · 9 + 61 3. (41 + 13) + (13 + 41) ‏ 4. 4(32) – 16(8) 140 196 108 0

3. 1-3 Properties of Numbers Problem of the Day Ms. Smith wants to buy each of her 113 students a colored marker. If the markers come in packs of 8, what is the least number of packs she could buy? 15

4. 1-3 Properties of Numbers Learn to apply properties of numbers and to find counterexamples.

5. 1-3 Properties of Numbers

6. 1-3 Properties of Numbers Vocabulary conjecture counterexample

7. 1-3 Properties of Numbers Equivalent expressions have the same value, no matter which numbers are substituted for the variables. Reading Math

8. 1-3 Properties of Numbers Use properties to determine whether the expressions are equivalent. Additional Example 1A: Identifying Equivalent Expressions 7 · x · 6 and 13x Use the Commutative Property. Use the Associative Property. 7 · x · 6 = 7 · 6 · x = (7 · 6) · x = 42x Follow the order of operations. The expressions 7 · x · 6 and 13x are not equivalent.

9. 1-3 Properties of Numbers Use properties to determine whether the expressions are equivalent. Additional Example 1B: Identifying Equivalent Expressions 5(y – 11) and 5y – 55 Use the Distributive Property. 5(y – 11) = 5(y) – 5(11) = 5y – 55 Follow the order of operations. The expressions 5(y – 11) and 5y – 55 are equivalent.

10. 1-3 Properties of Numbers Use properties to determine whether the expressions are equivalent. Check It Out: Additional Example 1A 2(z + 33) and 2z + 66 Use the Distributive Property. 2(z + 33) = 2(z) + 2(33) = 2z + 66 Follow the order of operations. The expressions 2(z + 33) and 2z + 66 are equivalent.

11. 1-3 Properties of Numbers Use properties to determine whether the expressions are equivalent. Check It Out: Additional Example 1B 4 · x · 3 and 7x Use the Commutative Property. Use the Associative Property. 4 · x · 3 = 4 · 3 · x = (4 · 3) · x = 12x Follow the order of operations. The expressions 4 · x · 3 and 7x are not equivalent.

12. 1-3 Properties of Numbers During the last three weeks, Jay worked 26 hours, 17 hours, and 24 hours. Use properties and mental math to answer the question. Additional Example 2A: Consumer Math Applications 26 + 17 + 24 Add to find the total. 50 + 17 = 67 Use the Commutative and Associative Properties to group numbers that are easy to add mentally. How many hours did Jay work in all? 26 + 24 + 17 (26 + 24) + 17 Jay worked 67 hours in all.

13. 1-3 Properties of Numbers Additional Example 2B: Consumer Math Applications 7(67) ‏ Multiply to find the total. 490 – 21 = 469 Rewrite 67 as 70 – 3 so you can use the Distributive Property to multiply mentally. Jay earns $7.00 per hour. How much money did he earn for the last three weeks? 7(70 – 3) ‏ Multiply from left to right. 7(70) – 7(3) Jay made $469 for the last three weeks. Subtract.

14. 1-3 Properties of Numbers During the last three weeks, Dosh studied 13 hours, 22 hours, and 17 hours. Use properties and mental math to answer the question. Check It Out: Additional Example 2A 13 + 22 + 17 Add to find the total. 30 + 22 = 52 Use the Commutative and Associative Properties to group umbers that are easy to add mentally. How many hours did Dosh study in all? 13 + 17 + 22 (13 + 17) + 22 Dosh studied 52 hours in all.

15. 1-3 Properties of Numbers Check It Out: Additional Example 2B 9(21) ‏ Multiply to find the total. 180 + 9 = 189 Rewrite 21 as 20 + 1 so you can use the Distributive Property to multiply mentally. Dosh tutors students and earns $9.00 per hour. How much money does he earn if he tutors students for 21 hours a week? 9(20 + 1) ‏ Multiply from left to right. 9(20) + 9(1) Dosh makes $189 if he tutors for 21 hours a week. Add.

16. 1-3 Properties of Numbers A conjecture is a statement that is believed to be true. A conjecture is based on reasoning and may be true or false. A counterexample is an example that disproves a conjecture, or shows that it is false. One counterexample is enough to disprove a conjecture.

17. 1-3 Properties of Numbers Find a counterexample to disprove the conjecture, “The product of two whole numbers is always greater than either number.” Additional Example 3: Using Counterexamples 2 · 1 Multiply. 2 · 1 = 2 The product 2 is not greater than either of the whole numbers being multiplied.

18. 1-3 Properties of Numbers Find a counterexample to disprove the conjecture, “The product of two whole numbers is never equal to either number.” Check It Out: Additional Example 3 9 · 1 Multiply. 9 · 1 = 9 The product 9 is equal to one of the whole numbers being multiplied.

19. 1-3 Properties of Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. 1-3 Properties of Numbers Lesson Quiz Use properties to determine whether the expressions are equivalent. 1. 3x – 12 and 3(x – 9) 2. 11 + y + 0 and y + 11 3. Alan and Su Ling collected canned goods for 4 days to donate to a food bank. The number of cans collected each day was: 35, 4, 21, and 19. Use properties and mental math to answer each question. a. How many cans did they collect in all? b. If each can contains 2 servings, how many servings of food did Alan and Su Ling collect? not equivalentequivalent 79 158 4. Find a counterexample to disprove the conjecture, “The quotient of two whole numbers is always less than either number.” 2  1 = 2; the quotient 2 is not less than either of the whole numbers.

21. 1-3 Properties of Numbers 1. Which of the following expresssions are equivalent? A. 2x – 4 = 2(x – 4) B. 2x – 4 = 2x – 2 + 2 C. 2x – 4 = 2x – 2 – 2 D. 2x – 4 = 2(x + 4) Lesson Quiz for Student Response Systems

22. 1-3 Properties of Numbers 2. Which of the following expresssions are equivalent? A. 3x + 4 = 2 + 2 + 3x B. 3x + 4 = 2 + 2 + 3 + x C. 3x + 4 = 3(x + 4) D. 3x + 4 = 3(x + 2) Lesson Quiz for Student Response Systems

23. 1-3 Properties of Numbers 3. Find a counterexample to disprove the conjecture, “Any number that is divisible by 2 is also divisible by 4.” A. 20  2 = 10 and 20  4 = 5 B. 18  2 = 9 and 18  4 = 4.5 C. 20  2 = 20 and 20  4 = 80 D. 18  2 = 36 and 18  4 = 72 Lesson Quiz for Student Response Systems