Go through the **Spectrum Math Grade 6 Answer Key**** Chapter 5 Pretest** and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 5 Pretest Answers Key

**Check What You Know**

**Expressions and Equations**

**Write each power as a product of factors.**

Question 1.

a. 2^{4} ______

Answer:

The given value is 2^{4}, and it can be written as shown below.

= 2 x 2 x 2 x 2

= 16

Therefore the value of 2^{4} is 16.

b. 9^{2} ______

Answer:

The given value is 9^{2}, it can be written as shown below.

= 9 x 9

= 81

Therefore the value of 9^{2} is 81.

c. 5^{3} ______

Answer:

The given value is 5^{3}, it can be written as shown below.

= 5 x 5 x 5

= 125

Therefore the value of 5^{3} is 125.

**Use exponents to rewrite each expression.**

Question 3.

a. 4 × 4 × 4 × 4 = ______

Answer:

Given data is 4 x 4 x 4 x 4

= 4^{4}

= 256

Therefore the value of the Given Expression 4 x 4 x 4 x 4 is 256.

b. 2 × 2 × 2 = ____

Answer:

Given data is 2 x 2 x 2

= 2^{3}

= 8

Therefore the value of the Given Expression 2 x 2 x 2 is 8.

c. 6 × 6 × 6 × 6 × 6 = _______

Answer:

Given data is 6 x 6 x 6 x 6 x 6

= 6^{5}

= 7776

Therefore the value of the Given Expression 6 x 6 x 6 x 6 x 6 is 7776.

Question 4.

a. 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = ______

Answer:

Given data is 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3

= 3^{8}

=6561

Therefore the value of the Given Expression 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 is 6561.

b. 9 × 9 × 9 = ______

Answer:

Given data is 9 × 9 × 9

= 9^{3}

= 729

Therefore the value of the Given Expression 9 × 9 × 9 is 729.

c. 8 × 8 × 8 × 8 × 8 × 8 = _____

Answer:

Given data is 8 × 8 × 8 × 8 × 8 × 8

= 8^{6}

=262144

Therefore the value of the Given Expression 8 × 8 × 8 × 8 × 8 × 8 is 262144.

**Identify each of the following as an expression or an equation.**

Question 5.

a. 5 + x ____

Answer:

It is an Expression that contains one numerical value and it doesn’t contain any Equality(=) symbol.

b. 6 + 4 = 10 _____

Answer:

The given Example is an Equation which is having an Equality(=) Symbol indicating equality.

c. 75 × n _____

Answer:

It is an Expression that contains one numerical value and it doesn’t contain any Equality(=) symbol.

Question 6.

a. 9 – 4 = 5 ____

Answer:

The given Example is an Equation which is having an Equality(=) Symbol indicating equality.

b. 10 + x _____

Answer:

It is an Expression that contains one numerical value and it doesn’t contain any Equality(=) symbol.

c. 20 ÷ 5 _____

Answer:

It is an Expression that contains one numerical value and it doesn’t contain any Equality(=) symbol.

**For each term below, identify the coefficient (C) and the variable (V).**

Question 7.

a. 5y C ____ V ____

Answer:

Given the term is 5y.

Variable (V): y

Coefficient (C)= 5

b. 2x C ____ V ____

Answer:

Given term is 2x.

Variable (V): x

Coefficient (C)= 2

c. n C ____ V _____

Answer:

Given term is n.

Variable (V): n

Coefficient (C)= 1

Question 8.

a. 12z C ____ V ____

Answer:

The given term is 12z.

Variable (V) : z

Coefficient (C)= 12

b. 4m C ___ V ____

Answer:

Given term is 4m.

Variable (V) : m

Coefficient (C)= 4

c. 9d C ____ V ____

Answer:

The given term is 9d.

Variable (V) : d

Coefficient (C)= 9

**Write the expression for each statement.**

Question 9.

the product of 4 and the difference between 8 and 3 _____

Answer:

Given values are 4, 8 and 3

Therefore , The Expression is : 4 x ( 8-3 )

= 4 x 5

= 20.

Question 10.

4 increased by the product of 5 and 3 _____

Answer:

Given 4+(5×3)

= 4+15

= 19

Question 11.

the difference between 16 and the product of 4 and 2 _________

Answer:

Given product of 4 and 2 = 4 x 2

Now difference between 16 and product of 4×2 = 16-(4×2)

= 16-8

=8

Question 12.

the quotient of 25 and 5 increased by 3 _____

Answer:

The quotient of 25 and 5 = 5

The quotient of 25 and 5 increased by 3 = 5+3 = 8

Therefore, 25 and 5 increased by 3 is 8.

Question 13.

the product of 6 and 2 decreased by 1 _____

Answer:

Product of 6 and 2 = 6 x2 = 12

Now this decreased by 1 = 12-1

= 11

Question 14.

three times the quotient of 40 and 8 _____

Answer:

Quotient of 40 and 8 = 5

3 times quotient of 40 and 8 = 3 x 5

= 15

Question 15.

7 decreased by the product of 4 and 2 _____

Answer:

Product of 4 and 2 = 8

7 decreased by product of 4 and 2 = 8 – 7 = 1

**Solve each equation.**

Question 16.

a. x – 4 = 4 ____

Answer:

Given Equation is x- 4 = 4

x – 4 – 4 = 0

x – 8 = 0

x = 8

Therefore the value of x is 8

b. x + 3 = 5 ____

Answer:

Given Equation is x + 3 = 5

x + 3 – 5= 0

x – 2 = 0

x = 2

Therefore the value of x is 2

c. n – 2 = 0 _____

Answer:

Given Equation is n – 2 = 0

n – 2 = 0

n = 2

Therefore the value of n is 2

Question 17.

a. b + 8 = 19 ____

Answer:

Given Equation is b + 8 = 19

b + 8 – 19 = 0

b – 11= 0

b = 11

Therefore the value of b is 11.

b. n + 5 = 5 _____

Answer:

Given Equation is n + 5 = 5

n + 5 – 5 = 0

n = 0

Therefore the value of n is 0.

c. y + 3 = 3 _____

Answer:

Given Equation is y + 3 =3

y + 3 – 3 = 0

y = 0

Therefore the value of y is 0

Question 18.

a. a + 4 = 11 ____

Answer:

Given Equation is a + 4 = 11

a + 4-11= 0

a – 7 = 0

a = 7

Therefore the value of a is 7.

b. n – 8 = 8 ____

Answer:

Given Equation is n – 8 = 8

n- 8 -8 = 0

n – 16 = 0

n = 16

Therefore the value of n is 16.

c. y – 5 = 5 _____

Answer:

Given Equation is y – 5 = 5

y – 5 – 5 = 0

y – 10 = 0

y = 10

Therefore the value of y is 10.

Question 19.

a. \(\frac{a}{4}\) = 4 ____

Answer:

To Evaluate the given value, Try to undo the division by 4, and multiply by 4.

\(\frac{a}{4}\) × \(\frac{4}{1}\) = 4 × 4

a = 16

Therefore the value of a is 16.

b. a × 4 = 4 ____

Answer:

To Evaluate the given a value, Try to perform the undo multiplication by 4, and divide by 4.

\(\frac{a4}{4}\) = \(\frac{4}{4}\)

a = 16

Therefore the value of a is 16.

c. \(\frac{m}{5}\) = 5 ______

Answer:

To Evaluate the given m value, Try to perform the undo division by 5, and multiply by 5.

\(\frac{m}{5}\) × \(\frac{5}{1}\) = 5 × 5

m = 25

Therefore the value of m is 25

Question 20.

a. y × 20 = 30 ____

Answer:

To Evaluate the given y value, Try to perform the undo multiplication by 20, and divide by 20.

\(\frac{y.20}{20}\) = \(\frac{30}{20}\)

y = 1.5

Therefore the value of y is 1.5

b. \(\frac{x}{12}\) = 3 _____

Answer:

Given x / 12 = 3

\(\frac{x}{12}\) = 3

To Evaluate the given x value, Try to perform the undo division by 12, and multiply by 12.

\(\frac{x}{12}\) × \(\frac{12}{1}\) = 3 × 12

x = 36

Therefore the value of x is 36

c. b × 7 = 21 _____

Answer:

To Evaluate the given a value, Try to perform the undo multiplication by 7, and divide by 7.

\(\frac{b7}{7}\) = \(\frac{21}{7}\)

b = 3

Therefore the value of b is 3.

Question 21.

a. \(\frac{x}{5}\) = 20 _____

Answer:

Given x / 5 = 20

\(\frac{x}{5}\) = 20

To Evaluate the given x value, Try to perform the undo division by 2, and multiply by 2.

\(\frac{x}{5}\) × \(\frac{5}{1}\) = 20 × 5

x = 100

Therefore the value of x is 100.

b. n × 5 = 25 _____

Answer:

To Evaluate the given n value, Try to perform the undo multiplication by 5, and divide by 5.

\(\frac{n5}{4}\) = \(\frac{25}{5}\)

n = 5

Therefore the value of n is 5.

c. \(\frac{x}{9}\) = 1 _____

Answer:

Given x / 9 = 1

\(\frac{x}{9}\) = 1

To Evaluate the given x value, Try to perform the undo division by 9, and multiply by 9.

\(\frac{x}{9}\) × \(\frac{ 9}{1}\) = 1 × 9

x = 9

Therefore the value of x is 9.

**Solve the problems.**

Question 22.

Eva spent $48 on a shirt and a pair of pants. The pants cost twice as much as the shirt. How much did each item cost?

Let s stand for the cost of the shirt.

Equation: ______ s = _______

The shirt cost ______. The pants cost _____

Answer:

The total amount of money spent on both the shirts and pants = 48

Let us assume the Cost of the Shirt = s

Given Cost of pants is two times of shirts = 2s

Hence the Equation is: s + 2s = 48

3s = 48

s= 16

Therefore the cost of shirts spent = 16

Cost of pants spent by Eva: 2s =2 x 16 = 32

Question 23.

In Ben’s office, there are 5 more women than men. There are 23 women. How many men are there? What is the unknown number? _____

Equation: _____ n = ______

There are _____ men in the office.

Answer:

Let the unknown number be x

Number of Women in Ben’s office = 23

Number of men = 5 more than women

Hence the Equation is: 23+5

x = 23 + 5

= 28

Therefore there are 28 men in the office.