Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 3 Review Test to finish your assignments.

Math in Focus Grade 7 Course 2 A Chapter 3 Review Test Answer Key

Concepts and Skills
Simplify each expression.
Question 1.
1.4w – 0.6w
1.4w – 0.6w = 0.8w.

Explanation:
1.4w – 0.6w
= 0.8w.

Question 2.
$$\frac{3}{4}$$m + $$\frac{4}{5}$$m
$$\frac{3}{4}$$m + $$\frac{4}{5}$$m = $$\frac{31}{20}$$m.

Explanation:
$$\frac{3}{4}$$m + $$\frac{4}{5}$$m
LCD of 4 n 5 = 20.
= [(3 × 5) + (4 × 4)]m ÷ 20
= (15 + 16)m ÷ 20
= 31m ÷ 20 or $$\frac{31}{20}$$m.

Question 3.
$$\frac{1}{6}$$y + $$\frac{1}{2}$$y + $$\frac{1}{3}$$y
$$\frac{1}{6}$$y + $$\frac{1}{2}$$y + $$\frac{1}{3}$$y = y.

Explanation:
$$\frac{1}{6}$$y + $$\frac{1}{2}$$y + $$\frac{1}{3}$$y = y.
LCD of 6 n 2 = 6.
= [(1 × 1) + (1 × 3)]y ÷ 6] +  $$\frac{1}{3}$$y
= [(1 + 3)y ÷ 6] + $$\frac{1}{3}$$y
= (4y ÷ 6) + $$\frac{1}{3}$$y
= $$\frac{2}{3}$$y+ $$\frac{1}{3}$$y
= (2 + 1)y ÷ 3
= 3y ÷ 3
= y.

Question 4.
1.8m – 0.2m – 7m
1.8m – 0.2m – 7m = -5.4m.

Explanation:
1.8m – 0.2m – 7m
= 1.6m – 7m
= -5.4m.

Question 5.
1.3a – 0.8b + 2.2b – a
1.3a – 0.8b + 2.2b – a = 0.3a + 1.4b.

Explanation:
1.3a – 0.8b + 2.2b – a
= 1.3a – a – 0.8b + 2.2b
= 0.3a – 0.8b + 2.2b
= 0.3a + 1.4b.

Question 6.
1 + $$\frac{1}{5}$$a + $$\frac{3}{5}$$b + $$\frac{4}{5}$$a
1 + $$\frac{1}{5}$$a + $$\frac{3}{5}$$b + $$\frac{4}{5}$$a = 1 + a + $$\frac{3}{5}$$b.

Explanation:
1 + $$\frac{1}{5}$$a + $$\frac{3}{5}$$b + $$\frac{4}{5}$$a
= 1 + $$\frac{1}{5}$$a + $$\frac{4}{5}$$a + $$\frac{3}{5}$$b
= 1 + [(1 + 4)a ÷ 5] + $$\frac{3}{5}$$b
= 1 + (5a ÷ 5) + $$\frac{3}{5}$$b
= 1 + a + $$\frac{3}{5}$$b.

Expand each expression. Then simplify when you can.
Question 7.
1.2(2p – 3)
1.2(2p – 3) = 2.4p – 3.6.

Explanation:
1.2(2p – 3)
= (1.2 × 2p) – (3 × 1.2)
= 2.4p – 3.6.

Question 8.
$$\frac{1}{3}$$(12p + 9q)
$$\frac{1}{3}$$(12p + 9q) = 4p + 3q.

Explanation:
$$\frac{1}{3}$$(12p + 9q)
= [12p × $$\frac{1}{3}$$] + [ 9q × $$\frac{1}{3}$$]
= 4p + 3q.

Question 9.
$$\frac{1}{5}$$$$\left(\frac{t}{3}+\frac{1}{2}\right)$$
$$\frac{1}{5}$$$$\left(\frac{t}{3}+\frac{1}{2}\right)$$ = $$\frac{t}{15}$$ + $$\frac{1}{10}$$.

Explanation:
$$\frac{1}{5}$$$$\left(\frac{t}{3}+\frac{1}{2}\right)$$
= [$$\frac{t}{3}$$ × $$\frac{1}{5}$$] + [$$\frac{1}{2}$$ × $$\frac{1}{5}$$]
= $$\frac{t}{15}$$ + $$\frac{1}{10}$$.

Question 10.
-4(-2q + 2.5)
-4(-2q + 2.5) = 8q – 10.

Explanation:
-4(-2q + 2.5)
= (-4 × -2q) + (2.5 × -4)
= 8q – 10.

Question 11.
–$$\frac{2}{3}$$(6x + 3)
–$$\frac{2}{3}$$(6x + 3) = 4x – 2.

Explanation:
–$$\frac{2}{3}$$(6x + 3)
= (6x × –$$\frac{2}{3}$$) + (3 × –$$\frac{2}{3}$$)
= (2x × 2) + (1 × -2)
= 4x – 2.

Question 12.
-0.5(2m – 4n)
-0.5(2m – 4n) = -m + 0.5n.

Explanation:
-0.5(2m – 4n)
= (2m × -0.5) – (1n × -0.5)
= -1m – (-0.5n)
= -m + 0.5n.

Question 13.
3(a + 3) + 2a
3(a + 3) + 2a = 5a + 9.

Explanation:
3(a + 3) + 2a
= [(3 × a) + (3 × 3)] + 2a
= 3a + 9 + 2a
= 3a + 2a + 9
= 5a + 9.

Question 14.
4(2p – 3) – 3(p + 2)
4(2p – 3) – 3(p + 2) = 5p – 6.

Explanation:
4(2p – 3) – 3(p + 2)
= [(2p × 4) – (3 × 4)] – [(3 × p) + (2 × 3)]
= (8p – 12) – (3p + 6)
= 8p – 12 – 3p – 6
= 8p – 3p – 12 – 6
= 5p – 6.

Question 15.
2.5(m – 2) + 5.6m
2.5(m – 2) + 5.6m = 8.1m – 5.

Explanation:
2.5(m – 2) + 5.6m
= [(m × 2.5) – (2 × 2.5)] + 5.6m
= (2.5m – 5) + 5.6m
= 2.5m – 5 + 5.6m
= 2.5m + 5.6m – 5
= 8.1m – 5.

Question 16.
4(0.6n – 3) – 0.2(2n – 3)
4(0.6n – 3) – 0.2(2n – 3) = 2n – 12.6.

Explanation:
4(0.6n – 3) – 0.2(2n – 3)
= 2.4n – 12 – 0.4n + 0.6
= 2.4n – 0.4n – 12 – 0.6
= 2n – 12.6.

Factor each expression.
Question 17.
4t – 20s
4t – 20s = 4(t – 5s).

Explanation:
4t – 20s
= 4(t – 5s).

Question 18.
-6p – 21q
-6p – 21q = -3(2p + 7q).

Explanation:
-6p – 21q
= -3(2p + 7q).

Question 19.
8i + 12 + 4j
8i + 12 + 4j = 4(2i + 3 + j).

Explanation:
8i + 12 + 4j
= 4(2i + 3 + j)

Question 20.
6a + 10b – 20
6a + 10b – 20 = 2(3a + 5b – 10).

Explanation:
6a + 10b – 20
= 2(3a + 5b – 10).

Question 21.
-9m – 3n – 6
-9m – 3n – 6 = -3(3m + n + 2).

Explanation:
-9m – 3n – 6
= -3(3m + n + 2).

Question 22.
-15x – 6 – 12y
-15x – 6 – 12y = -3(5x + 2 + 4y).

Explanation:
-15x – 6 – 12y
= -3(5x + 2 + 4y).

Translate each verbal description into an algebraic expression. Then simplify when you can.
Question 23.
One-fourth x less than the sum of 7 and 2x.
$$\frac{x}{4}$$ – (7 + 2x) = – $$\frac{7}{4}$$x – 7.

Explanation:
One-fourth x less than the sum of 7 and 2x.
=> $$\frac{x}{4}$$ – (7 + 2x)
=> $$\frac{x}{4}$$ – 7 – 2x
=> $$\frac{x}{4}$$ – 2x – 7.
=> [(x – 8x) ÷ 4 ] – 7.
=> (-7x ÷ 4) – 7
=> – $$\frac{7}{4}$$x – 7.

Question 24.
4 times 5y divided by 18.
(4 × 5y ) ÷ 18 = $$\frac{10}{9}$$y.

Explanation:
4 times 5y divided by 18
=> (4 × 5y ) ÷ 18
=> 20y ÷ 18
=> 10y ÷ 9 or $$\frac{10}{9}$$y.

Question 25.
Five-ninths of (3p + 1) subtracted from one-third of (q + p).
[$$\frac{5}{9}$$ × (3p + 1) ] – [$$\frac{1}{3}$$ × (q + p)] = 2p – $$\frac{1}{3}$$q + $$\frac{5}{9}$$

Explanation:
Five-ninths of (3p + 1) subtracted from one-third of (q + p)
=> [$$\frac{5}{9}$$ × (3p + 1) ] – [$$\frac{1}{3}$$ × (q + p)]
=> $$\frac{15}{9}$$p + $$\frac{5}{9}$$ – $$\frac{1}{3}$$q + $$\frac{1}{3}$$p.
=> $$\frac{15}{9}$$p + $$\frac{1}{3}$$p – $$\frac{1}{3}$$q + $$\frac{5}{9}$$
= LCD of 9 n 3 = 9.
= [(15 + 3)p ÷ 9 ] – $$\frac{1}{3}$$q + $$\frac{5}{9}$$
= (18p ÷ 9) – $$\frac{1}{3}$$q + $$\frac{5}{9}$$
= (2p ÷ 1) – $$\frac{1}{3}$$q + $$\frac{5}{9}$$
= 2p – $$\frac{1}{3}$$q + $$\frac{5}{9}$$

Problem Solving
Question 26.
After 14 boys leave a concert, the ratio of boys to girls is 3 : 10. If there are p girls at the concert, write an algebraic expression for the number of boys at the beginning of the concert in terms of p.
=> $$\frac{b – 14}{p}$$ = $$\frac{3}{10}$$