Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Homework And Practice 9
Page 65 Exercise 1 Answer
4(3 ⋅ 8x) + 4(2 ⋅ 7x)
4(3 ⋅ 8x) → This part of expression represent the amount of time he runs for 3 days of the week.
4(2 ⋅ 7x) → This part of expression represent the amount of time he runs for 2 days of the week.
Result
4(3 ⋅ 8x) → For 3 days of the week
4(2 ⋅ 7x) → For 2 days of the week.
Page 65 Exercise 2 Answer
4(3 ⋅ 8x) + 4(2 ⋅ 7x)
Write Equivalent expressions using properties
→ By using Associative Properties of Multiplication, I can write this expression:
4(3 ⋅ 8x) + 4(2 ⋅ 7x) = 3(4 ⋅ 8x) + 2(4 ⋅ 7x)
Result
Associative Property of Multiplication: 3(4 ⋅ 8x) + 2(4 ⋅ 7x)
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 66 Exercise 3 Answer
5(6x + 25x + 10)
The part 6x and 25x represent the time each group member spent surveying volunteers.
Result
6x and 25x
Page 66 Exercise 4 Answer
5(6x + 25x + 10)
Since the total number of group members is 5. So, Josephine multiply the time taken by each member with 5.
She multiply the survey time in January with the number of volunteers.
She also multiply the survey time in May with the number of volunteers.
In her expression she also added the time taken in giving presentation by each member.
Hence, Josephine′s expression is accurate.
Result
Yes, Josephine′s expression is accurate
Page 66 Exercise 5 Answer
5(6x + 25x + 10)
Write Equivalent expressions using properties
→ By Combining like terms, I can write this expression:
5(6x + 25x + 10) = 5((6 + 25)x + 10) = 5(31x + 10)
→ By using the Distributive Properties, I can write this expression:
5(6x + 25x + 10) = 5(6x) + 5(25x) + 5(10) = 30x + 125x + 50
Result
Combining Like terms: 5(31x + 10)
Distributive Property: 30x + 125x + 50
Page 66 Exercise 6 Answer
If each members worked with 20 volunteers each then we can substitute the value of x and then combine the like terms to calculate the total time Josephine′s group spent on the research.
5(31x + 10)
= 5(31(20) + 10)
= 5(620 + 10)
= 5(630)
= 3150
Result
Total time Josephine′s group spent on research project is 3150 minutes