Unit 1 Lesson 4 Homework !
!
!
1. What property tells us that 6 ! + 0 = 6 ! ? 2. What is the additive inverse of !? 7
A. Additive identity property − 9
3. W
hat i
s t
he a
dditive i
nverse of –0.053? B. Inverse property of addition 0.053 4. What is the additive inverse of –a? C. Commutative property of addition a D. Associative property of addition In Exercises 5 and 6, choose the property that justifies the step. Next to each step, there should be a drop-­‐down menu from which students choose from the following: Additive Identity Property Additive Inverse Property Commutative Property of Addition Associative Property of Addition 𝟓
𝟐
𝟏
5. 𝟒 𝟖 + 𝟑 𝟑 + 𝟔 𝟑
!
!
!
4 ! + 3 ! + 6 ! Associative Property of Addition 5
4 + 10
8
14
6. (3.8 – 4.5) – 3.8 5
8
(3.8 + (-­‐4.5)) + (-­‐3.8) (-­‐4.5 + 3.8) + (-­‐3.8) Commutative Property of Addition -­‐4.5 + (3.8 + (-­‐3.8)) Associative Property of Addition -­‐4.5 + 0 Additive Inverse Property -­‐4.5 Additive Identity Property 7. Find the error(s) in Marcus’s calculation. Calculate the correct value. 5 + 4 – (-­‐5) 5 + (-­‐5) – 4 0 –4 4 –0 4 Find the error Calculate the correct value Here is a correct Marcus switched the order of 4 and –5 in 4 – (–5), calculation: and he switched the order of 4 and 0 in 0 – 4. 5 + 4 – (–5) = 5 + 4 + 5 = 14 Switching the order is incorrect because subtraction is not commutative. 8. Find the error(s) in Lucy’s calculation. Calculate the correct value. 12 – (12 + 17) (12 – 12) + 17 0 + 17 17 Find the error Calculate the correct value Here is a correct Lucy tried to apply the associative property to calculation: group 12 – 12 together. However, the associative 12 – (12 + 17) = 12 – 29 property works only with addition. = 12 + (–29) = –17 9. Find the error(s) in Jack’s calculation. Calculate the correct value. 20 – 12.5 + 7.5 20 – (12.5 + 7.5) 20 – 20 0 Find the error Calculate the correct value Here is a correct Jack tried to apply the associative property to calculation: group 12.5 + 7.5 together. However, the associative 20 – 12.5 + 7.5 = 20 + (–12.5) + 7.5 = 7.5 + 7.5 property only works with addition. = 15 In Exercises 10–12, simplify the expression. !
!
!
!
10. 3 ! + 1 ! + 2 ! − ! = 7 11. 16 – 9 – 7 + 20 – 9 = 11 !
12. (-­‐0.09 + 0.73) + (-­‐1 + 0.27) = -­‐0.09 or − !"" 13. Circle all equivalent expressions. 5 – 12 + 8 – 3 3 – 8 + 12 – 5 8 – 12 + 5 – 3