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

## Math in Focus Grade 7 Course 2 A Chapter 3 Answer Key Algebraic Expressions

### Math in Focus Grade 7 Chapter 3 Quick Check Answer Key

**Consider the algebraic expression 3x + 4. State the following.**

Question 1.

How many terms are there?

Answer:

Two terms are there.

Explanation:

Algebraic expression : 3x + 4

Question 2.

State the coefficient of the algebraic term.

Answer:

3 is coefficient of the algebraic term.

Explanation:

A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables.

In the term 3x + 4, 3 is the coefficient.

Question 3.

What is the constant term?

Answer:

4 is the constant term in 3x + 4.

Explanation:

A constant term is a term in an algebraic expression that does not contain any variables and therefore is constant.

Question 4.

Write the operation symbol.

Answer:

Addition (+) is the operation symbol in 3x + 4.

Explanation:

The symbol indicating a math operation is an operator symbol.

Question 5.

Complete the table.

Answer:

Explanation:

When x = 0:

7x = 7 × 0 = 0.

5x – 2 = 5(0) – 2 = 0 – 2 = – 2.

When x = 2:

x + 9 = 2 + 9 = 11.

7x = 7 × 2 = 14.

5x – 2 = 5(2) – 2 = 10 – 2 = 8.

When x = -1:

x + 9 = -1 + 9 = 8.

7x = 7 × -1 = -7.

5x – 2 = 5(-1) – 2 = -5 – 2 = -7.

When x = 7:

x + 9 = 7 + 9 = 16.

7x = 7 × 7 = 49.

5x – 2 = 5(7) – 2 = 35 – 2 = 33.

**State whether each expression can be simplified. Explain your reasoning.
**Question 6.

2k – 3 + k

Answer:

2k – 3 + k = 3(k – 1).

Explanation:

2k – 3 + k

= 3k – 3

= 3(k – 1)

Question 7.

7x + 3 – 3y

Answer:

7x + 3 – 3y = 7x + 3(1 – y).

Explanation:

7x + 3 – 3y

= 7x + 3(1 – 1y)

= 7x + 3(1 – y)

Question 8.

6u + 5w – 1

Answer:

6u + 5w – 1 cannot be simplified further as there is no common terms.

Explanation:

6u + 5w – 1

= 6u + 5w – 1.

Question 9.

4g – 3g – g

Answer:

4g – 3g – g = 0.

Explanation:

4g – 3g – g

= g(4 – 3 – 1)

= g(1 – 1)

= g (0)

= 0.

**Simplify each expression.
**Question 10.

4t + 1 + 6

Answer:

4t + 1 + 6 = 4t + 7.

Explanation:

4t + 1 + 6

= 4t + 7.

Question 11.

5p – 5p

Answer:

5p – 5p = 0.

Explanation:

5p – 5p

= 5p(1 – 1)

= 5p(0)

= 0.

Question 12.

4y + 5y + 3

Answer:

4y + 5y + 3 = 7y + 3.

Explanation:

4y + 5y + 3

= y(4 + 3) + 3

= y(7) + 3

= 7y + 3.

Question 13.

4m – 3m – 3

Answer:

4m – 3m – 3 = m – 3.

Explanation:

4m – 3m – 3

= m(4 – 3) – 3

= m(1) – 3

= m – 3.

**Expand each expression.
**Question 14.

4(h + 2)

Answer:

4(h + 2) = 4h + 8.

Explanation:

4(h + 2)

= 4h + 8.

Question 15.

5(4 + 5c)

Answer:

5(4 + 5c) = 20 + 25c.

Explanation:

5(4 + 5c)

= 20 + 25c.

Question 16.

3(4x – 11)

Answer:

3(4x – 11) = 12x – 33.

Explanation:

3(4x – 11)

= 12x – 33.

Question 17.

7(3 – 5p)

Answer:

7(3 – 5p) = 21 – 35p.

Explanation:

7(3 – 5p)

= 21 – 35p.

**Factor each expression.
**Question 18.

6m + 3

Answer:

6m + 3 = 3(2m + 1).

Explanation:

6m + 3

= 3(2m + 1)

Question 19.

4v + 14

Answer:

4v + 14 = 2(2v + 7).

Explanation:

4v + 14

= 2(2v + 7)

Question 20.

10p – 2

Answer:

10p – 2 = 2(5p – 1).

Explanation:

10p – 2

= 2(5p – 1)

Question 21.

6 – 18c

Answer:

6 – 18c = 6(1 – 3c).

Explanation:

6 – 18c

= 6(1 – 3c).

**Choose an equivalent expression.
**Question 22.

6y – 3 is equivalent to

a) 3(3y – 1)

b) 3(2y – 1)

c) 3(2y – 3)

d) 6(3y – 1)

Answer:

6y – 3 is equivalent to 3(2y – 1).

b) 3(2y – 1).

Explanation:

a. 3(3y – 1) = 9y – 3.

b. 3(2y – 1) = 6y – 3.

c. 3(2y – 3) = 6y – 9.

d. 6(3y – 1) = 18y – 6.

**x is an unknown number. Write an expression for each of the following.
**Question 23.

7 more than the number

Answer:

Expression = x + 7.

Explanation:

x is an unknown number.

7 more than the number

=> x + 7.

Question 24.

Product of 8 and the number

Answer:

Expression = 8x.

Explanation:

Product of 8 and the number.

=> 8 × x= 8x.

Question 25.

5 less than twice the number

Answer:

Expression = 2x – 5.

Explanation:

5 less than twice the number.

=> 2x – 5.

Question 26.

3 more than half the number

Answer:

Expression = 3 + (x ÷ 2).

Explanation:

3 more than half the number.

=> 3 + (x ÷ 2)