Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 3 Lesson 3.2 Subtracting Algebraic Terms to finish your assignments.

## Math in Focus Grade 7 Course 2 A Chapter 3 Lesson 3.2 Answer Key Subtracting Algebraic Terms

### Math in Focus Grade 7 Chapter 3 Lesson 3.2 Guided Practice Answer Key

**Copy and complete to simplify each expression.**

Question 1.

0.7y – 0.4y

0.7y – 0.4y =

Answer:

Explanation:

0.7y – 0.4y

= 0.3y.

Question 2.

1.1a – 0.2a

1.1a – 0.2a =

Answer:

Explanation:

1.1a – 0.2a

=0.9a

Question 3.

1.2y – y

1.2y – y =

Answer:

1.2y – y = 0.2y.

Explanation:

1.2y – y

= 0.2y.

**Copy and complete to simplify each expression.
**Question 4.

\(\frac{4}{9}\)x – \(\frac{1}{3}\)x

The LCD of \(\frac{4}{9}\) and \(\frac{1}{3}\) is .

So, x is divided into x sections.

\(\frac{4}{9}\)x – \(\frac{1}{3}\)x =

Answer:

\(\frac{4}{9}\)x – \(\frac{1}{3}\)x = \(\frac{1}{9}\)x.

Explanation:

The LCD of \(\frac{4}{9}\) and \(\frac{1}{3}\) is 9.

So, x is divided into 9 x sections.

\(\frac{4}{9}\)x – \(\frac{1}{3}\)x

= [4 – (1 × 3)]x ÷ 9

= (4 – 3)x ÷ 9

= x ÷ 9 or \(\frac{1}{9}\)x

Question 5.

\(\frac{3}{4}\)p – \(\frac{1}{6}\)p

\(\frac{3}{4}\)p – \(\frac{1}{6}\)p =

=

Rewrite the coefficients as fractions with denominator .

Answer:

\(\frac{3}{4}\)p – \(\frac{1}{6}\)p = \(\frac{7}{12}\)p.

Explanation:

\(\frac{3}{4}\)p – \(\frac{1}{6}\)p

LCD of 4 n 6 = 12.

= [(3 × 3) – (1 × 2)]p ÷ 12

= (9 – 2)p ÷ 12

= 7p ÷ 12 or \(\frac{7}{12}\)p

### Math in Focus Course 2A Practice 3.2 Answer Key

**Simplify each expression with decimal coefficients.
**Question 1.

0.8y – 0.7y

Answer:

0.8y – 0.7y = 0.1y.

Explanation:

0.8y – 0.7y = 0.1y.

Question 2.

0.9x – 0.6x

Answer:

0.9x – 0.6x = 0.3x.

Explanation:

0.9x – 0.6x = 0.3x.

Question 3.

1.7p – 0.4p

Answer:

1.7p – 0.4p = 1.3p.

Explanation:

1.7p – 0.4p = 1.3p.

Question 4.

1.9h – 0.9h

Answer:

1.9h – 0.9h = 1.0h.

Explanation:

1.9h – 0.9h = 1.0h.

Question 5.

1.3m – 0.5m

Answer:

1.3m – 0.5m = 0.8m.

Explanation:

1.3m – 0.5m = 0.8m.

Question 6.

1.6n – 0.8n

Answer:

1.6n – 0.8n = 0.8n.

Explanation:

1.6n – 0.8n = 0.8n.

**Simplify each expression with fractional coefficients.
**Question 7.

\(\frac{5}{6}\)x – \(\frac{1}{6}\)x

Answer:

\(\frac{5}{6}\)x – \(\frac{1}{6}\)x = \(\frac{2}{3}\)x

Explanation:

\(\frac{5}{6}\)x – \(\frac{1}{6}\)x

= (5 – 1)x ÷ 6

= 4x ÷ 6

= 2x ÷ 3 or \(\frac{2}{3}\)x

Question 8.

\(\frac{7}{8}\)x – \(\frac{5}{8}\)x

Answer:

\(\frac{7}{8}\)x – \(\frac{5}{8}\)x = \(\frac{1}{4}\)x.

Explanation:

\(\frac{7}{8}\)x – \(\frac{5}{8}\)x

= (7 – 5)x ÷ 8

= 2x ÷ 8

= x ÷ 4 or \(\frac{1}{4}\)x

Question 9.

\(\frac{9}{5}\)x – \(\frac{1}{5}\)x

Answer:

\(\frac{9}{5}\)x – \(\frac{1}{5}\)x = \(\frac{8}{5}\)x.

Explanation:

\(\frac{9}{5}\)x – \(\frac{1}{5}\)x

= (9 – 1)x ÷ 5

= 8x ÷ 5 or \(\frac{8}{5}\)x.

Question 10.

\(\frac{8}{3}\)p – \(\frac{1}{3}\)p

Answer:

\(\frac{8}{3}\)p – \(\frac{1}{3}\)p = \(\frac{7}{3}\)p.

Explanation:

\(\frac{8}{3}\)p – \(\frac{1}{3}\)p

= (8 – 1)p ÷ 3

= 7p ÷ 3 or \(\frac{7}{3}\)p.

**Simplify each expression with fractional coefficients by rewriting the fractions.
**Question 11.

\(\frac{1}{4}\)a – \(\frac{1}{8}\)a

Answer:

\(\frac{1}{4}\)a – \(\frac{1}{8}\)a = \(\frac{1}{8}\)a.

Explanation:

\(\frac{1}{4}\)a – \(\frac{1}{8}\)a

= LCD of 4 n 8 = 8.

= (2 – 1)a ÷ 8

= a ÷ 8 or \(\frac{1}{8}\)a

Question 12.

\(\frac{5}{6}\)m – \(\frac{2}{3}\)m

Answer:

\(\frac{5}{6}\)m – \(\frac{2}{3}\)m = \(\frac{1}{6}\)m

Explanation:

\(\frac{5}{6}\)m – \(\frac{2}{3}\)m

= LCD of 6 n 3 = 6.

= [5 – (2 × 2)]m ÷ 6

= (5 – 4)m ÷ 6

= m ÷ 6 or \(\frac{1}{6}\)m

Question 13.

\(\frac{5}{3}\)b – \(\frac{1}{6}\)b

Answer:

\(\frac{5}{3}\)b – \(\frac{1}{6}\)b = \(\frac{1}{2}\)b.

Explanation:

\(\frac{5}{3}\)b – \(\frac{1}{6}\)b

= LCD of 3 n 6 = 6.

= [(5× 2) – 1]b ÷ 6

= (10 – 1)b ÷ 6

= 9b ÷ 6

= 3b ÷ 6

= b ÷ 2 or \(\frac{1}{2}\)b.

Question 14.

\(\frac{7}{4}\)x – \(\frac{1}{8}\)x

Answer:

\(\frac{7}{4}\)x – \(\frac{1}{8}\)x = \(\frac{13}{8}\)x.

Explanation:

\(\frac{7}{4}\)x – \(\frac{1}{8}\)x

LCD of 4 n 8 = 8.

= [(7 × 2) – 1]x ÷ 8

= (14 – 1)x ÷ 8

= 13x ÷ 8 or \(\frac{13}{8}\)x.

Question 15.

\(\frac{4}{5}\)p – \(\frac{1}{3}\)p

Answer:

\(\frac{4}{5}\)p – \(\frac{1}{3}\)p = \(\frac{2}{3}\)p.

Explanation:

\(\frac{4}{5}\)p – \(\frac{1}{3}\)p

LCD of 5 n 3 = 15.

= [(4 × 3) – (1 × 5)]p ÷ 15

= (15 – 5)p ÷ 15

= 10p ÷ 15

= 2p ÷ 3 or \(\frac{2}{3}\)p.

Question 16.

\(\frac{3}{4}\)r – \(\frac{2}{3}\)r

Answer:

\(\frac{3}{4}\)r – \(\frac{2}{3}\)r = \(\frac{1}{12}\)r.

Explanation:

\(\frac{3}{4}\)r – \(\frac{2}{3}\)r

LCD of 4 n 3 = 12.

= [(3 × 3) – (2 × 4)]r ÷ 12

= (9 – 8)r ÷ 12

= r ÷ 12 or \(\frac{1}{12}\)r.

Question 17.

\(\frac{11}{7}\)k – \(\frac{1}{2}\)k

Answer:

\(\frac{11}{7}\)k – \(\frac{1}{2}\)k = \(\frac{15}{14}\)k.

Explanation:

\(\frac{11}{7}\)k – \(\frac{1}{2}\)k

LCD of 7 n 2 = 14.

= [(11 × 2) – (1 × 7)]k ÷ 14

= (22 – 7)k ÷ 14

= 15k ÷ 14 or \(\frac{15}{14}\)k.

Question 18.

\(\frac{7}{4}\)d – \(\frac{3}{5}\)d

Answer:

\(\frac{7}{4}\)d – \(\frac{3}{5}\)d = \(\frac{23}{20}\)d.

Explanation:

\(\frac{7}{4}\)d – \(\frac{3}{5}\)d

LCD of 4 n 5 = 20.

= [(7 × 5) – (3 × 4)]d ÷ 20

= (35 – 12)d ÷ 20

= 23d ÷ 20 or \(\frac{23}{20}\)d.

**Solve. Show your work.
**Question 19.

Math Journal Matthew simplified the algebraic expression \(\frac{3}{2}\)x – \(\frac{1}{3}\)x as shown below.

\(\frac{3}{2}\)x – \(\frac{1}{4}\)x = \(\frac{18}{12}\)x – \(\frac{4}{12}\)x

= \(\frac{14}{12}\)x

Is Matthew’s simplification correct? Why or why not?

Answer:

Matthew’s simplification is incorrect because \(\frac{3}{2}\)x – \(\frac{1}{4}\)x is not equal to \(\frac{18}{12}\)x – \(\frac{4}{12}\)x.

Explanation:

\(\frac{3}{2}\)x – \(\frac{1}{4}\)x

LCD of 2 n 4 = 4.

= [(3 × 2) – (1 × 1)]x ÷ 4

= (6 – 1)x ÷ 4

= 5x ÷ 4 or \(\frac{5}{4}\)x.

\(\frac{18}{12}\)x – \(\frac{4}{12}\)x

= (18 – 4)x ÷ 12

= 14x ÷ 12

= 7x ÷ 6 or \(\frac{7}{6}\)x.

\(\frac{14}{12}\)x = \(\frac{7}{6}\)x

Question 20.

Rectangle A, shown below, is larger than rectangle B. Write and simplify an algebraic expression that represents the difference in the areas of the two rectangles.

Answer:

Difference in the Area of rectangle A and Area of rectangle B = 11.7 square cm.

Explanation:

Area of rectangle A = Length × Width

= 4.5cm × 3cm

= 13.5 square cm.

Area of rectangle B = Length × Width

= 0.9cm × 2cm

= 1.8 square cm.

Difference in the Area of rectangle A and Area of rectangle B:

= 13.5 square cm – 1.8 square cm

= 11.7 square cm.