Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Homework And Practice 7
Page 47 Exercise 1 Answer
n + n + n Given
= 1n + 1n + 1n Using Identity Property of Multiplication
= (1 + 1 + 1)n Using Distributive Property
= 3n Simplify
Result
3n
Page 47 Exercise 2 Answer
3n + 6 − n − 4 Given
= 3n − n + 6 − 4 Using Commutative Property of Addition
= 3n − 1n + 6 − 4 Using Identity Property of Multiplication
= (3 − 1)n + 6 − 4 Using Distributive Property
= 2n + 2 Simplify
Result
2n + 2
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Page 47 Exercise 3 Answer
\(1 \frac{1}{2} z^2+3 \frac{1}{2}+5 z-3+6 z-\frac{1}{2} z^2\) Given
= \(1 \frac{1}{2} z^2-\frac{1}{2} z^2+5 z+6 z+3 \frac{1}{2}-3\) Using Commutative Property of Addition
= \(\left(1 \frac{1}{2}-\frac{1}{2}\right) z^2+(5+6) z+\left(3 \frac{1}{2}-3\right)\) Using Distributive Property
= \(z^2+11 z+\frac{1}{2}\) Simplify
Result
\(z^2+11 z+\frac{1}{2}\)Page 47 Exercise 4 Answer
4y + 9y Given
= (4 + 9)y Using Distributive Property
= 13y Simplify
Result
13y
Page 47 Exercise 5 Answer
3z + \(\frac{3}{4}\) – 2z Given
= 3z – 2z + \(\frac{3}{4}\) Using Commutative Property of Addition
= (3 – 2)z + \(\frac{3}{4}\) Using Distributive Property
= z + \(\frac{3}{4}\) Simplify
Result
z + \(\frac{3}{4}\)
Page 47 Exercise 6 Answer
25 + 5w − 10 + w Given
= 5w + w + 25 − 10 Using Commutative Property of Addition
= 5w + 1w + 25 − 10 Using Identity Property of Multiplication
= (5 + 1)w + 25 − 10 Using Distributive Property
= 6w + 15 Simplify
Result
6w + 15
Page 47 Exercise 7 Answer
7.7w − 4.6w Given
= (7.7 − 4.6)w Using Distributive Property
= 3.1w Simplify
Result
3.1w
Page 47 Exercise 8 Answer
\(\frac{1}{2} x+\frac{1}{2}+\frac{1}{2} x+\frac{1}{2}\) Given
= \(\frac{1}{2} x+\frac{1}{2} x+\frac{1}{2}+\frac{1}{2}\) Using Commutative Property of Addition
= \(\left(\frac{1}{2}+\frac{1}{2}\right) x+\left(\frac{1}{2}+\frac{1}{2}\right)\) Using Distributive Property
= x + 1 Simplify
Result
x + 1
Page 47 Exercise 9 Answer
12\(y^2\) – 6\(y^2\) Given
= (12 – 6)\(y^2\) Using Distributive Property
= \(6y^2\)Simplify
Result
\(6y^2\)Page 47 Exercise 10 Answer
\(3 z^3+2 \frac{1}{4}-z^3\) Given
= \(3 z^3-z^3+2 \frac{1}{4}\) Using Commutative Property of Addition
= \(3 z^3-1 z^3+2 \frac{1}{4}\) Using Identity Property of Multiplication
= \((3-1) z^3+2 \frac{1}{4}\) Using Distributive Property
= \(2 z^3+2 \frac{1}{4}\) Simplify
Result
\(2 z^3+2 \frac{1}{4}\)
Page 47 Exercise 11 Answer
6.6m + 3m Given
=(6.6 + 3)m Using Distributive Property
= 9.6m Simplify
Result
9.6m
Page 47 Exercise 12 Answer
100n − 1 − 25n Given
= 100n − 25n − 1 Using Commutative Property of Addition
= (100 − 25)n − 1 Using Distributive Property
= 75n − 1 Simplify
Result
75n − 1
Page 47 Exercise 13 Answer
5x + \(\frac{1}{2}\) + 3y + \(\frac{1}{4}\) + 2x − 2y Given
= \(5 x+2 x+3 y-2 y+\frac{1}{2}+\frac{1}{4}\) Using Commutative Property of Addition
= \((5+2) x+(3-2) y+\left(\frac{1}{2}+\frac{1}{4}\right)\) Using Distributive Property
= \(7 x+y+\frac{2+1}{4}\) Simplify
= 7x + y + \(\frac{3}{4}\) Simplify
Result
7x + y + \(\frac{3}{4}\)
Page 47 Exercise 14 Answer
\(p^2\)+ 2.3 + \(3p^2\) Given
= \(p^2\) + \(3p^2\) + 2.3 Using Commutative Property of Addition
= \(1p^2\) + \(3p^2\) + 2.3 Using Identity Property of Multiplication
= (1 + 3)\(p^2\) + 2.3 Using Distributive Property
= \(4p^2\) + 2.3 Simplify
Result
\(4p^2\) + 2.3
Page 47 Exercise 15 Answer
\(z^4+z^4+z^4+z^4\) Given
= \(1 z^4+1 z^4+1 z^4+1 z^4\) Using Identity Property of Multiplication
= \((1+1+1+1) z^4\) Using Distributive Property
= \(4z^4\) Simplify
Result
\(4z^4\)Page 48 Exercise 16 Answer
Cost of Small drink = $1.10
Cost of Medium drink = $1.25
Cost of Large drink = $1.50
Number of drinks ordered by Casey′s Family :
Small = 1 and Medium = m
Number of drinks ordered by Anika′s Family :
Medium = m and Large = 1
Algebraic Expression for Total cost of both orders:
Casey′s Family order + Anika′s Family order
= 1 × 1.10 + m × 1.25 + m × 1.25 + 1 × 1.50
= 1.10 + 1.25m + 1.25m + 1.50
Result
1.10 + 1.25m + 1.25m + 1.50
Page 48 Exercise 17 Answer
1.10 + 1.25m + 1.25m + 1.50 Given
= 1.25m + 1.25m + 1.50 + 1.10 Using Commutative Property of Addition
= (1.25 + 1.25)m + 1.50 + 1.10 Using Distributive Property
= 2.50m + 2.60 Simplify
Result
2.50m + 2.60
Page 48 Exercise 18 Answer
2.50m + 2.60 Given
= 2.50(3) + 2.60 Substitute m = 3
= 7.50 + 2.60 Multiply
= $10.10 Add
Result
The total cost of both order is $10.10
Page 48 Exercise 19 Answer
\(\frac{1}{2} y\) . 5 Given
= 5.\(\frac{1}{2} y\) Using Commutative Property of Multiplication
Result
Jan use Commutative Property of Multiplication
Page 48 Exercise 20 Answer
\(n^3\) < \(n^2\) Given
= \((0.5)^3\) < \((0.5)^2\) Substitute n = 0.5
= 0.125 < 0.25 Simplify
Result
\(n^3\) < \(n^2\) is true for 0 < n < 1
Page 48 Exercise 21 Answer
6x − x + 5 Given
= (6 − 1)x + 5 Using Distributive Properties
= 5x + 5 Simplify
Result
6x − x + 5 and 6 + 5 are not equivalent expressions.
Page 48 Exercise 22 Answer
\(\frac{b}{2}\) + \(\frac{b}{2}\) Given
= \(\left(\frac{1}{2}+\frac{1}{2}\right) b\) Using Distributive Property
= b Simplify
Result
b
Page 48 Exercise 23 Answer
\(\frac{1}{2} x+4 \frac{1}{2}+\frac{1}{2} x-\frac{1}{2}\)
= \(\frac{1}{2} x+\frac{1}{2} x+4 \frac{1}{2}-\frac{1}{2}\) Using Commutative Property of Addition
= \(\left(\frac{1}{2}+\frac{1}{2}\right) x+\left(4 \frac{1}{2}-\frac{1}{2}\right)\) Using Distributive Property
= x + 4
Result
Equivalent to: \(\frac{1}{2} x+4 \frac{1}{2}+\frac{1}{2} x+\frac{1}{2}\)
x + 4
Not Equivalent to: \(\frac{1}{2} x+4 \frac{1}{2}+\frac{1}{2} x+\frac{1}{2}\)
\(\frac{1}{2} x\) + 4
x + \(4 \frac{1}{2}\)
x − 4