Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Guided Practice
Page 15 Exercise 1 Answer
80 ÷ 8 × 5 + 4 = 90
We should insert parentheses around (80 ÷ 8) and (5 + 4).
(80 ÷ 8) × (5 + 4)
= 10 × 9 Solve within parentheses
= 90
Result
(80 ÷ 8) × (5 + 4) = 90
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 15 Exercise 2 Answer
(21 − 3) × (7 + 2) ÷ (12 − 4)
Using PEMDAS (parentheses, exponents, multiplications, division, addition, subtraction) for the order of operations:
First perform the operations within the parentheses.
Next, perform the multiplication.
Finally, perform the division.
Result
Last, we will perform division.
Page 15 Exercise 3 Answer
\(5^{2}\) + (6.7 − 3.1) Evaluate
= \(5^{2}\) + 3.6 Evaluate inside the parentheses
= 25 + 3.6 Evaluate the power
= 28.6 Add
Result
28.6
Page 15 Exercise 4 Answer
(8.2 + 5.3) ÷ 5 Evaluate
= 13.5 ÷ 5 Evaluate inside the parentheses
= 2.7 Divide
Result
2.7
Page 15 Exercise 5 Answer
[(7.3 + 3.6) − 4.7] + 1.8 − \(2^{2}\) Evaluate
= [10.9 − 4.7] + 1.8 − \(2^{2}\) Evaluate inside the parentheses
= 6.2 + 1.8 − \(2^{2}\) Evaluate inside the bracket
= 6.2 + 1.8 − 4 Evaluate the power
= 8 − 4 Add
= 4 Subtract
Result
4
Page 15 Exercise 6 Answer
\(\left[(11.2+8.8) \times \frac{1}{4}\right]-1.8\) Evaluate
= \(\left[20 \times \frac{1}{4}\right]-1.8\) Evaluate inside the parentheses
= 5 − 1.8 Evaluate inside the bracket
= 3.2 Subtract
Result
3.2
Page 15 Exercise 7 Answer
\(4^{2}\) − (3.1 + 6.4) + 4.5 Evaluate
= \(4^{2}\) − 9.5 + 4.5 Evaluate inside the parentheses
= 16 − 9.5 + 4.5 Evaluate the power
= 6.5 + 4.5 Subtract
= 11 Add
Result
11
Page 15 Exercise 8 Answer
\((8.7+3.3) \times\left(\frac{1}{2}\right)^2\) Evaluate
= \(12 \times\left(\frac{1}{2}\right)^2\) Evaluate inside the parentheses
= 12 x \(\frac{1}{4}\) Evaluate inside the parentheses
= 3 Multiply
Result
3
Page 15 Exercise 9 Answer
157.8 − (\(3^{2}\) + 6) × 3 Evaluate
= 157.8 − (9 + 6) × 3 Evaluate the power
= 157.8 − 15 × 3 Evaluate inside the parentheses
= 157.8 − 45 Multiply
= 112.8 Subtract
Result
112.8
Page 15 Exercise 10 Answer
4.3 + (8.4 − 5.1) Evaluate
= 4.3 + 3.3 Evaluate inside the parentheses
= 7.6 Add
Result
7.6
Page 15 Exercise 11 Answer
\(4^3-\left[(9.9 \div 3.3) \times \frac{1}{3}\right]\) Evaluate
= \(4^3-\left[3 \times \frac{1}{3}\right]\) Evaluate inside the parentheses
= \(4^{3}\) – 1 Evaluate inside the bracket
= 64 − 1 Evaluate the power
= 63 Subtract
Result
63
Page 15 Exercise 12 Answer
[\(2^{3}\) × (152 ÷ 8)] − 52 Evaluate
= [\(2^{3}\) × 19] − 52 Evaluate inside the parentheses
= [8 × 19] − 52 Evaluate the power
= 152 − 52 Evaluate inside the bracket
= 100 Subtract
Result
100
Page 16 Exercise 13 Answer
We should follow Order of Operations rule to find which part of the numerical expression to evaluate first.
Order of Operations:
1. → Evaluate inside the parentheses and brackets.
2. → Evaluate the powers.
3. → Divide and Multiply from left to right.
4. → Add and Subtract from left to right.
Evaluate the Expression:
(26 + 2.5) − [(8.3 × 3) + (\(1^{3}\) − 0.25)]
= (26 + 2.5) − [(8.3 × 3) + (1 − 0.25)] Evaluate the powers
= 28.5 − [24.9 + 0.75] Evaluate inside the parentheses
= 28.5 − 25.65 Evaluate inside the brackets
= 2.85
Result
2.85
Page 16 Exercise 14 Answer
Amount of plants an elk can eat in a day = 20 pounds
Number of days in a week = 7
Total number of elk = 18
18 × (20 × 7)
= 18 × 140
= 2520 pounds
Result
18 elk can eat 2520 pounds of plants in a week.
Page 16 Exercise 15 Answer
Cost of each hairbrush = $3.99
Number of hairbrushes Lillian bought = 4
She had a coupon of = $1 off
Amount paid by her mother = Half of the total bill
Expression : [(3.99 × 4) − 1] ÷ 2
[(3.99 × 4) − 1] ÷ 2
= [15.96 − 1] ÷ 2 Evaluate inside the parentheses
= 14.96 ÷ 2 Evaluate inside the bracket
= 7.48
Result
Lillian paid $7.48 towards the purchase of hairbrushes.
Page 16 Exercise 16 Answer
Frederick : In the expression solved by Frederick there is parentheses and bracket.
He follow Order of operation and evaluate the parentheses and bracket first.
So he is Correct.
Lana : In the expression solved by Lana there is no parentheses and bracket.
She also follow Order of operation and operate Add and Subtract from left to right. So she is also Correct.
Result
Frederick is correct as he evaluate parentheses and bracket first while Lana is correct as she solved the expression by Adding and Subtracting from left to right.
Page 16 Exercise 17 Answer
12.3 × [(2 × 1.7) + 6.6] − \(2^{3}\)
= 12.3 × [3.4 + 6.6] − \(2^{3}\) Evaluate inside the parentheses
= 12.3 × 10 − \(2^{3}\) Evaluate inside the bracket
= 12.3 × 10 − 8 Evaluate the power
= 123 − 8 Multiply
= 115
\(2^{4}\) ÷ [(3.2 × 0.8) + 1.44]
= \(2^{4}\) ÷ [2.56 + 1.44] Evaluate inside the parentheses
= \(2^{4}\) ÷ 4 Evaluate inside the bracket
= 16 ÷ 4 Evaluate the power
= 4
\(6.2+\left(3 \times \frac{1}{3}+4.8\right)\)= 6.2 + (1 + 4.8) Evaluate inside the parentheses
= 6.2 + 5.8 Evaluate inside the parentheses
= 12
[4 × (9.6 ÷ 3)] + 8.2
= [4 × 3.2] + 8.2 Evaluate inside the parentheses
= 12.8 + 8.2 Evaluate inside the bracket
= 21
Result
12.3 × [(2 × 1.7) + 6.6] − \(2^{3}\) = 115
\(2^{4}\) ÷ [(3.2 × 0.8) + 1.44] = 4
\(6.2+\left(3 \times \frac{1}{3}+4.8\right)=12\)[4 × (9.6 ÷ 3)] + 8.2 = 21