Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Guided Practice 4
Page 33 Exercise 1 Answer
It is necessary to use Order of Operation to evaluate algebraic expression because the algebraic expression contains different operations so it is necessary to follow the Order of Operations to know which operations should
we evaluate first and there after.
If we do not use Order of Operation then the solution of the expression will be incorrect.
Result
It is necessary because we should know which operations to evaluate first.
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 33 Exercise 3 Answer
3t − 8 Evaluate
= 3(8) − 8 Substitute t = 8
= 24 − 8 Multiply
= 16 Subtract
Result
16
Page 33 Exercise 4 Answer
6w ÷ x + 9 Evaluate
= \(6\left(\frac{1}{2}\right) \div(3)+9\) Substitute w = \(\frac{1}{2}\) and x = 3
= 3 ÷ 3 + 9 Evaluate the parentheses
= 1 + 9 Divide
= 10 Add
Result
10
Page 33 Exercise 5 Answer
\(t^2\) − 12w ÷ x Evaluate
= \((8)^2-12\left(\frac{1}{2}\right) \div(3)\) Substitute t=8, w = \(\frac{1}{2}\) and x = 3
= 64 − 6 ÷ 3 Evaluate the parentheses
= 64 – 2 Divide
= 62 Subtract
Result
62
Page 33 Exercise 6 Answer
5x − 2w + t Evaluate
= \(5(3)-2\left(\frac{1}{2}\right)+(8)\) Substitute x = 3, w = \(\frac{1}{2}\) and t = 8
= 15 − 1 + 8 Evaluate the parentheses
= 14 + 8 Subtract
= 22 Add
Result
22
Page 33 Exercise 7 Answer
9x Evaluate
= 9(3) Substitute x = 3
= 27 Multiply
Result
27
Page 33 Exercise 8 Answer
3w + 6 ÷ 2x Evaluate
= 3(5) + 6 ÷ 2(3) Substitute w = 5 and x = 3
= 15 + 6 ÷ 6 Evaluate the parentheses
= 15 + 1 Divide
= 16 Add
Result
16
Page 33 Exercise 9 Answer
\(w^2\) + 2 + 48 ÷ 2x Evaluate
= \((5)^2\) + 2 + 48 ÷ 2(3) Substitute w = 5 and x = 3
= 25 + 2 + 48 ÷ 6 Evaluate the parentheses
= 25 + 2 + 8 Divide
= 35 Add
Result
35
Page 33 Exercise 10 Answer
\(3^3\) + 5y ÷ w + z Evaluate
= \((3)^3\) + 5(4) ÷ (5) + (8) Substitute x = 3, y = 4, w = 5 and z = 8
= 27 + 20 ÷ 5 + 8 Evaluate the parentheses
= 27 + 4 + 8 Divide
= 39 Add
Result
39
Page 33 Exercise 11 Answer
9y ÷ x + \(z^{2}\) − w Evaluate
= 9(4) ÷ (3) + \((8)^2\) − (5) Substitute y = 4, x = 3, z = 8 and w = 5
= 36 ÷ 3 + 64 − 5 Evaluate the parentheses
= 12 + 64 − 5 Divide
= 76 − 5 Add
= 71 Subtract
Result
71
Page 34 Exercise 12 Answer
\(x^{2}\) + 4w − 2y ÷ z Evaluate
= \((3)^2\) + 4(5) − 2(4) ÷ (8)
Substitute x = 3, w = 5, y = 4 and z = 8
= 9 + 20 − 8 ÷ 8 Evaluate the parentheses
= 9 + 20 − 1 Divide
= 29 − 1 Add
= 28 Subtract
Result
28
Page 34 Exercise 13 Answer
Weekly fee to rent a small car for a week = $250
Cost per mile = $0.30
a) Let m = number of miles Ms. White drives during the week
Expression for the amount she will pay for the car:
250 + 0.30m
b) Evaluate the expression if she drives 100 miles:
250 + 0.30m
=250 + 0.30(100) Substitute m = 100
= 250 + 30 Multiply
= $280
Result
a) 250 + 0.30m
b) $280
Page 34 Exercise 14 Answer
325 + 120d Evaluate
= 325 + 120(11) Substitute d = 11
= 325 + 1320 Multiply
= 1645 Add
Result
Mr. Black will have to pay $1645 for 11 − day rental
Page 34 Exercise 15 Answer
Small Car:
Cost for week = $250
Cost per day = $100
Cost for 2 days = 100 ⋅ 2 = $200
Cost for 3 days = 100 ⋅ 3 = $300
So, if we rent small car for 2 day then it will cost $200 which is less expensive to rent for the week.
Result
2 days
Page 34 Exercise 16 Answer
No, we cannot evaluate the expression 5 + 3n by adding 5 + 3 first and then multiplying by the value of n.
According to Charlene :
Example:
Let n = 2
5 + 3n
= 5 + 3(2) Substitute n = 2
= 8(2) Add
= 16 Multiply
We should multiply the value of n with 3 first and then add the value with 5
Example:
Let n = 2
5 + 3n
= 5 + 3(2) Substitute n = 2
= 5 + 6 Multiply
= 11 Add
Thus Charlene is not correct
Result
Charlene is not correct
Page 34 Exercise 17 Answer
\(\left(d \cdot 10^4\right)+\left(d \cdot 10^3\right)+\left(d \cdot 10^2\right)+\left(d \cdot 10^1\right)+\left(d \cdot 10^0\right)\) Evaluate
= \(\left(7 \cdot 10^4\right)+\left(7 \cdot 10^3\right)+\left(7 \cdot 10^2\right)+\left(7 \cdot 10^1\right)+\left(7 \cdot 10^0\right)\) Substitute d = 7
= (7 ⋅ 10000) + (7 ⋅ 1000) + (7 ⋅ 100) + (7 ⋅ 10) + (7 ⋅ 1) Evaluate the power
= 70000 + 7000 + 700 + 70 + 7 Multiply
= 77,777 Add
Result
77,777
Page 34 Exercise 18 Answer
\(a^{2}\) + 3b ÷ c − d Evaluate
= \((3)^2\) + 3(8) ÷ (6) − (1) Substitute a = 7, b = 8, c = 6 and d = 1
= 49 + 24 ÷ 6 − 1 Evaluate the parentheses
= 49 + 4 − 1 Divide
= 53 − 1 Add
= 52 Subtract
Result
A) 52
Page 34 Exercise 19 Answer
8b ÷ a − \(c^{2}\) + d Evaluate
= 8(5) ÷ (2) − \((3)^2\) + (9) Substitute b = 5, a = 2, c = 3 and d = 9
= 40 ÷ 2 − 9 + 9 Evaluate the parentheses
= 20 − 9 + 9 Divide
= 11 + 9 Subtract
= 20 Add
Result
C) 20