Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Homework And Practice 6
Page 41 Exercise 1 Answer
5(m − 2) Given
= 5(m) − 5(2) Using Distributive Property
= 5m − 10 Multiply
Result
5m − 10
Page 41 Exercise 2 Answer
24x + 18y Given
= 6(4x) + 6(3y) Using Distributive Property
= 6(4x + 3y) 6 is the common factor
Result
6(4x + 3y)
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Page 41 Exercise 3 Answer
\(2\left(9 p-\frac{1}{2}\right)\) Given
= \(2(9 p)-2\left(\frac{1}{2}\right)\) Using Distributive Property
= 18p − 1 Multiply
Result
18p − 1
Page 41 Exercise 4 Answer
8(2x − 3) Given
= 8(2x) − 8(3) using Distributive Property
= 16x − 24 Multiply
Result
8(2x − 3) and 16x − 24 are equivalent
Page 41 Exercise 5 Answer
5(3x − 9) Given
= 5(3x) − 5(9) Using Distributive Property
= 15x − 45 Multiply
Result
5(3x − 9) and 15x − 45 are equivalent
Page 41 Exercise 6 Answer
6(2x + 9) Given
= 6(2x) + 6(9) Using Distributive Property
= 12x + 54 Multiply
Result
6(2x + 9) and 12x + 54 are equivalent
Page 41 Exercise 7 Answer
3(6x − 7) Given
= 3(6x) − 3(7) Using Distributive Property
= 18x − 21 Multiply
Result
18x − 21
Page 41 Exercise 8 Answer
4(9x − 2) Given
= 4(9x) − 4(2) Using Distributive Property
= 36x − 8 Multiply
Result
36x − 8
Page 41 Exercise 9 Answer
6(8x + 1) Given
= 6(8x) + 6(1) Using Distributive Property
= 48x + 6 Multiply
Result
48x + 6
Page 41 Exercise 10 Answer
35x + 30 Given
= 5(7x) + 5(6) Using Distributive Property
= 5(7x + 6) Multiply
Result
5(7x + 6)
Page 41 Exercise 11 Answer
4(x + 7) Given
= 4(x) + 4(7) Using Distributive Property
= 4x + 28 Multiply
Result
4x + 28
Page 41 Exercise 12 Answer
5x − 15y Given
= 5(x) − 5(3y) Using Distributive Property
= 5(x − 3y) 5 is the common factor
Result
5(x − 3y)
Page 41 Exercise 13 Answer
\(6\left(3 y-\frac{1}{2}\right)\) Given
= \(6(3 y)-6\left(\frac{1}{2}\right)\) Using Distributive Property
= 18y − 3 Multiply
Result
18y − 3
Page 41 Exercise 14 Answer
1.6 + (2z + 0.4) Given
= (1.6 + 2z) + 0.4 Using Associative Property of Addition
Result
(1.6 + 2z) + 0.4
Page 41 Exercise 15 Answer
8w − 16 Given
= 8(w) − 8(2) Using Distributive Property
= 8(w − 2) 8 is the common factor
Result
8(w – 2)
Page 41 Exercise 16 Answer
2.2x + 2.2 Given
= 2.2(x) + 2.2(1) Using Distributive Property
= 2.2(x + 1) 2.2 is the common factor
Result
2.2(x + 1)
Page 41 Exercise 17 Answer
\(100\left(z^2-5.38\right)\) Given
= 100\((z)^2\) – 100(5.38) Using Distributive Property
100\(z^2\) − 538 Multiply
Result
100\(z^2\) − 538
Page 41 Exercise 18 Answer
\(8 \cdot\left(y^3 \cdot \frac{3}{4}\right)\) Evaluate
= \(8 \cdot \frac{3 y^3}{4}\) Evaluate inside parentheses
= 6\(y^3\)Multiply
Result
6\(y^3\)
Page 42 Exercise 19 Answer
Cost of 1 Pencil Pack = $1.50
Cost of 1 Notebook = $2
Cost of 1 Marker = $2.50
Number of Pencil Packs ordered = 5
Number of Notebooks ordered = n
Number of Markers ordered = 5 sets
Algebraic Expression for the total cost of Ms. Thomas′s ordered:
Number of Pencil pack order × Cost of each pencil pack + Number of Notebooks order × Cost of each Notebook + Number of Markers order × Cost of each Marker
= 5 × 1.50 + n × 2 + 5 × 2.50
Result
5 × 1.50 + n × 2 + 5 × 2.50
Page 42 Exercise 20 Answer
5 × 1.50 + n × 2 + 5 × 2.50 Algebraic Expression
= 7.50 + 2n + 12.50 Multiply
= 7.50 + 12.50 + 2n Commutative Property of Addition
= 20 + 2n Add
= 2(10) + 2(n) Distributive Property
= 2(10 + n) 2 is the common factor
Result
2(10 + n)
Page 42 Exercise 21 Answer
2(10 + n) Evaluate
= 2(10 + 20) Substitute n = 20
= 2(30) Add
= $60 Multiply
Result
The total cost of Ms. Thomas′s Order if she ordered 20 Notebooks is $60
Page 42 Exercise 22 Answer
2l + 2w Evaluate
= 2(l) + 2(w) Using Distributive Property
=2(l + w) 2 is the common factor
Result
2l + 2w and 2(l + w) are equivalent expressions.
Page 42 Exercise 23 Answer
It is easier to use 2(l + w) than to use 2l + 2w because →
2l + 2w: We need to multiply length with 2 and then width with 2 and then add to get the solution.
2(l + w): We need to add length and width and then Multiply it with 2 to get the solution.
Example: Let length = 5 units and Width = 3 units
2l + 2w = 2 ⋅ 5 + 2 ⋅ 3 = 10 + 2 ⋅ 3 = 10 + 6 = 16 units
2(l + w) = 2(5 + 3) = 2(8) = 16 units
Result
Because it is less time consuming than the expression 2l+2w
Page 42 Exercise 24 Answer
\(4 \frac{1}{2}+\left(3 t+1 \frac{1}{2}\right)\)
= \(\left(4 \frac{1}{2}+3 t\right)+1 \frac{1}{2}\) Using Associative Property of Addition
= \(\left(4 \frac{1}{2}+1 \frac{1}{2}\right)+3 t\) Using Associative Property of Addition
\(4 \frac{1}{2}+\left(3 t+1 \frac{1}{2}\right)\)= \(\left(4 \frac{1}{2}+1 \frac{1}{2}\right)+3 t\) Using Associative Property of Addition
= 6 + 3t Adding
\(4 \frac{1}{2}+\left(3 t+1 \frac{1}{2}\right)\)= \(\left(4 \frac{1}{2}+1 \frac{1}{2}\right)+3 t\) Using Associative Property of Addition
= 6 + 3t Adding
= 3(2) + 3(t) Using Distributive Property
= 3(2 + t) 2 is the common factor
Result
\((4+3 t)+1 \frac{1}{2}\) \(\left(4+1 \frac{1}{2}\right)+3 t\)6 + 3t
3(2 + t)
Page 42 Exercise 25 Answer
8(x − 3)
= 8(x) − 8(3) Using Distributive Property
= 8x − 24
8(x − 24)
= 8(x) − 8(24) Using Distributive Property
= 8x − 192
9(x − 3) − (x – 3)
= 9(x) − 9(3) − x + 3 Using Distributive Property
= 9x − 27 − x + 3 Multiply
= 9x − x − 27 + 3 Using Commutative Property of Addition
= 8x − 24
(5 + 3)x − 24
= x(5) + x(3) − 24 Using Distributive Property
= 5x + 3x − 24 Multiply
= 8x − 24
Result
8x − 24 is equivalent to the following:
8(x − 3)
9(x − 3) − (x − 3)
(5 + 3)x − 24