This handy **Spectrum Math Grade 7 Answer Key Chapter 1-7 Final Test** provides detailed answers for the workbook questions

## Spectrum Math Grade 7 Chapter 1-7 Final Test Answers Key

**Add, subtract, multiply, or divide.**

Question 1.

a. 3 + (-7) = _____________

Answer:

3 + (-7)

+ × – = –

3 – 7 = -4

So, 3 + (-7) = -4

b. 2\(\frac{1}{4}\) + 2\(\frac{2}{3}\) = _____________

Answer:

Given,

2\(\frac{1}{4}\) + 2\(\frac{2}{3}\)

2 + \(\frac{1}{4}\) + 2 + \(\frac{2}{3}\)

Add whole numbers

2 + 2 = 4

Add the fractions

\(\frac{1}{4}\) + \(\frac{2}{3}\)

LCD is 12.

\(\frac{3}{12}\) + \(\frac{8}{12}\) = \(\frac{11}{12}\)

4 + \(\frac{11}{12}\) = 4\(\frac{11}{12}\)

2\(\frac{1}{4}\) + 2\(\frac{2}{3}\) = 4\(\frac{11}{12}\)

c. (-5) + 8 = _____________

Answer:

Given,

(-5) + 8

+ × – = –

-5 + 8 = 3

Question 2.

a. (-8) + 12 = _____________

Answer:

(-8) + 12

+ × – = –

-8 + 12 = 4

b. 9 + (-11) = _____________

Answer:

9 + (-11)

+ × – = –

9 – 11 = -2

c. (-7) + 2 = _____________

Answer:

(-7) + 2

+ × – = –

-7 + 2 = -5

Question 3.

a. 5 – 8 = _____________

Answer:

5 – 8 = -3

The greatest number has a negative sign so the result will be negative.

b. 6 – 5 = _____________

Answer:

6 – 5 = 1

The greatest number has a positive sign so the result will be positive.

c. |-2| – 8 = _____________

Answer:

|-2| = 2

2 – 8 = -6

The greatest number has a negative sign so the result will be negative.

|-2| – 8 = -6

Question 4.

a. 3\(\frac{3}{10}\) – 2 \(\frac{4}{5}\) = ______________

Answer:

Given,

3\(\frac{3}{10}\) – 2 \(\frac{4}{5}\)

3 + \(\frac{3}{10}\) – 2 – \(\frac{4}{5}\)

3 – 2 = 1

\(\frac{3}{10}\) – \(\frac{4}{5}\)

LCD is 10

\(\frac{3}{10}\) – \(\frac{8}{10}\) = –\(\frac{5}{10}\) = –\(\frac{1}{2}\)

1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)

3\(\frac{3}{10}\) – 2 \(\frac{4}{5}\) = \(\frac{1}{2}\)

b. (-6) – 5 = _____________

Answer:

Given,

(-6) – 5

– × – = +

-6 – 5 = -11

c. 5 – 6 = _____________

Answer:

Given,

5 – 6

The greatest number has a negative sign so the result will be negative.

5 – 6 = -1

Question 5.

a. (23) × (-3) = _____________

Answer:

Given,

(23) × (-3)

+ × – = –

23 × -3 = -69

By multiplying 23 and -3 we get -69.

b. 45 × 8 = _______________

Answer:

Given,

45 × 8 = 360

By multiplying 45 and 8 we get 360.

c. (-18) × (-6) = ______________

Answer:

Given,

(-18) × (-6)

– × – = +

18 × 6 = 108

By multiplying 18 and 6 we get 108.

Question 6.

a. 71 × (-5) = ______________

Answer:

Given,

71 × (-5)

+ × – = –

71 × -5 = -355

b. (-83) × 7 = ______________

Answer:

Given,

(-83) × 7

+ × – = –

-83 × 7 = -581

By multiplying 83 and 7 we get -581.

c. \(\frac{4}{5}\) × \(\frac{1}{8}\) = _____________

Answer:

Given,

\(\frac{4}{5}\) × \(\frac{1}{8}\) = \(\frac{4×1}{5×8}\) = \(\frac{4}{40}\) = \(\frac{1}{10}\)

\(\frac{4}{5}\) × \(\frac{1}{8}\) = \(\frac{1}{10}\)

Question 7.

a. (-24) ÷ (-4) = ______________

Answer:

Given,

(-24) ÷ (-4)

– ÷ – = +

24 ÷ 4 = 6

By dividing 24 by 4 we get 6.

b. 45 ÷ (-9) = ______________

Answer:

45 ÷ (-9)

+ ÷ – = –

45 ÷ -9 = -5

By diving 45 by 9 we get 5.

45 ÷ (-9) = -5

c. (-95) ÷ 5 = ______________

Answer:

Given,

(-95) ÷ 5

+ ÷ – = –

-95 ÷ 5 = -19

By dividing 95 and 5 we get 19.

(-95) ÷ 5 = -19.

Question 8.

a. (-22) ÷ (-1) = _____________

Answer:

Given,

(-22) ÷ (-1)

– ÷ – = +

-22 ÷ -1 = 22

By dividing 22 and 1 we get 22.

b. 42 ÷ (-7) = ______________

Answer:

Given,

42 ÷ (-7)

+ ÷ – = –

42 ÷ -7 = -6

By dividing 42 and 7 we get 6

42 ÷ (-7) = -6

c. (-81) ÷ 9 = _______________

Answer:

Given,

(-81) ÷ 9

+ ÷ – = –

81 ÷ 9 = 9

By dividing 81 and 9 we get 9.

-81 ÷ 9 = -9

**Use long division to change each rational number into a decimal. Then, circle to indicate if each is terminating (T) or repeating (R).**

Question 9.

a. \(\frac{3}{5}\) = _____________ T or R

Answer: 0.60

The given fraction is terminating (T).

b. \(\frac{7}{50}\) = ______________ T or R

Answer: 0.14

The given fraction is terminating (T).

c. \(\frac{1}{125}\) = ______________ T or R

Answer: 0.008

The given fraction is terminating (T).

**Solve each problem. Use 3.14 for π when needed.**

Question 10.

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?

Let s represent the number of students on each bus.

Equation: ___________________________

There were _____________ students on each bus.

Answer:

Given,

331 students went on a field trip.

Six buses were filled and 7 students traveled in cars.

Let s represent the number of students on each bus.

6s + 7 = 331

6s = 331 – 7

6s = 324

s = 324/6

s = 54

There are 54 students in each bus.

Question 11.

The length of a football field is 30 yards more than its width. If it is 100 yards long, how wide is the field?

Let w represent the width of the field.

Equation: ___________________________

The football field is _____________ yards wide.

Answer:

Given,

The length of a football field is 30 yards more than its width.

L = 100

L = 30 + W

100 = 30 + W

W = 100 – 30

W = 70 yards

Thus the width of the field is 70 yards.

The football field is 70 yards wide.

Question 12.

Julia has 3 red marbles, 4 blue marbles, 3 yellow marbles, and 6 black marbles. She takes one marble out of the bag at random.

The probability that it ¡s a black marble is _____________.

The probability that t is a yellow marble is _____________.

The probability that ¡t ¡s not o red marble is _____________.

Answer:

Given,

Julia has 3 red marbles, 4 blue marbles, 3 yellow marbles, and 6 black marbles.

She takes one marble out of the bag at random.

Total number of marbles = 3 + 4 + 3 + 6 = 16 marbles.

The probability that it is a black marble is 6/16

The probability that it is a yellow marble is 3/16

The probability that it is not o red marble is (4 + 3 + 6)/16 = 13/16

Question 13.

The municipal swimming pool is 50 meters long and 25 meters wide, and it is filled to a uniform depth of 3 meters. What is the volume of water in the pool?

The volume of the water is ____________ cubic meters.

Answer:

Given,

The municipal swimming pool is 50 meters long and 25 meters wide, and it is filled to a uniform depth of 3 meters.

1 cubic meter = 1000 liters

50 × 25 × 3 × 1000 = 3,750,000 liters

The volume of the water is 3750 cubic meters.

Question 14.

There are four hundred students at Thompson Middle School. If 54% of the students are female, what is the ratio of female students to male students?

The ratio of female to male students is _____________.

Answer:

Given,

There are four hundred students at Thompson Middle School.

54% = 54/100 = 0.54

0.54 × 400 = 216

400/216 = 1.85

The ratio of female to male students is 1:3

Question 15.

Ben is putting in a 7-foot diameter circular flower bed at his school. He wants to put plastic edging along the outside edge of the flower bed. How much edging will he need?

Ben will need _____________ feet of plastic edging.

Answer:

Given,

Ben is putting in a 7-foot diameter circular flower bed at his school.

He wants to put plastic edging along the outside edge of the flower bed.

C = πd

C = 3.14 × 7

C = 22

Ben will need 22 feet of plastic edging.

**Write yes or no to tell if each set of ratios is proportional.**

Question 16.

a. \(\frac{5}{4}\), \(\frac{35}{28}\)

Answer:

\(\frac{5}{4}\) = \(\frac{35}{28}\)

\(\frac{35}{28}\) × \(\frac{7}{7}\) = \(\frac{5}{4}\)

The ratio is proportional.

b. \(\frac{4}{3}\), \(\frac{24}{30}\)

Answer:

\(\frac{4}{3}\), \(\frac{24}{30}\)

\(\frac{24}{30}\) = \(\frac{4}{5}\)

\(\frac{4}{3}\) ≠ \(\frac{4}{5}\)

The ratio is not proportional.

c. \(\frac{6}{5}\), \(\frac{24}{20}\)

Answer:

\(\frac{6}{5}\), \(\frac{24}{20}\)

\(\frac{24}{20}\) = \(\frac{6}{5}\)

\(\frac{6}{5}\) = \(\frac{6}{5}\)

The ratio is proportional.

d. \(\frac{11}{3}\), \(\frac{33}{9}\)

Answer:

\(\frac{11}{3}\), \(\frac{33}{9}\)

\(\frac{33}{9}\) = \(\frac{11}{3}\)

\(\frac{11}{3}\) = \(\frac{11}{3}\)

The ratio is proportional.

**Find the constant of proportionality for the set of values.**

Question 17.

k = _____________

Answer:

The corresponding angles and sides will have the same ratio in similar triangles.

(20 × 20) + (21 × 21) = AC²

AC² = 400 + 441 = 841

AC = √841

AC = 29

DE/AC = 43.5/21 = 1.5

FE = 1.5 × BC

FE = 1.5 × 20 = 30

DF = 1.5 × AB

DF = 1.5 × 21 = 31.5

DE² = DF² + FE²

= 31.5² + 30²

= 992.25 + 900

= 1892.25

DE = √1892.25

DE = 43.5

**These similar triangles are drawn to scale. Find the missing side lengths.**

Question 18.

a.

AC = _____________ cm

DF = _____________ cm

FE = _____________ cm

Answer:

b.

ST = _____________ ft.

TU = _____________ ft.

VX = _____________ ft.

Answer:

The corresponding angles and sides will have the same ratio in similar triangles.

VX² = 20² + 15²

VX² = 400 + 300

VX = √700

VX = 26.45 ft

SU/VX = 30/26.45

SU/VX = 1.13 ft

TU = 1.13 × 15

TU = 16.95 ft

ST = 20 × 1.13

ST = 22.6 ft

**Find the area of each figure and the area and circumference of each circle. Use 3.14 for π. Round answers to the nearest hundredth.**

Question 19.

a.

circumference: ______________ cm

area: ____________ sq. cm

Answer:

Given,

r = 8 cm

We know that,

C = 2πr

C = 2 × 3.14 × 8

C = 50.26 cm

A = πr²

A = 3.14 × 8²

A = 201.06 sq. cm

b.

____________ in.

____________ sq. in

Answer:

Given,

d = 12 in.

r = d/2

r = 12/2 = 6 in.

We know that,

C = 2πr

C = 2 × 3.14 × 6

C = 37.7 in.

A = πr²

A = 3.14 × 6²

A = 3.14 × 36

A = 113.1 sq. in.

c.

____________ yd

____________ sq. yd.

Answer:

Given,

r = 18 yd.

We know that,

C = 2πr

C = 2 × 3.14 × 18

C = 113.09 yd

A = πr²

A = 3.14 × 18²

A = 1017.88 sq. yd

Question 20.

a.

A = ____________ in.^{2}

Answer:

a = 15 in.

b = 36 in.

A = ab/2

A = (15)(36)/2

A = 270 sq. in

b.

A = ____________ m^{2}

Answer:

Given,

b = 1.8 m

h = 1.2 m

A = bh

A = 1.8 × 1.2

A = 1.16 sq. m

c.

A = ____________ ft^{2}

Answer:

Given,

b = 16 ft

h = 12 ft

A = 1/2 × bh

A = 1/2 × 16 × 12

A = 96 sq. ft

**Answer the questions about the angles below. ∠M = 55°, ∠X = 35°**

Question 21.

∠Y = ______________

Answer:

∠X = 35°

∠X + ∠Y = 180°

35° + ∠Y = 180°

∠Y = 180° – 35°

∠Y = 145°

Question 22.

∠Z = _______________

Answer:

∠X = 35°

∠Y = 145°

∠Z + ∠Y = 180°

145° + ∠Z = 180°

∠Z = 180° – 145°

∠Z = 35°

Question 23.

∠W = _______________

Answer:

∠Z = 35°

∠W + ∠Z = 180°

∠W + 35° = 180°

∠W = 180° – 35° = 145°

Question 24.

∠N = _______________

Answer:

∠M = 55°

∠M + ∠N = 90°

55° + ∠N = 90°

∠N = 90° – 55°

∠N = 35°

**Find the volume of each figure. Round to the nearest hundredth.**

Question 25.

a.

V = ___________ m^{3}

Answer:

Given,

l = 3m

b = 8 m

h = 2.5 m

We know that,

V = lbh

V = 3 × 8 × 2.5

V = 60 cu. m

b.

V = _____________ in.^{3}

Answer:

Given,

l = 11 in.

w = 16 in.

h = 8 in.

We know that,

V = lbh

V = 11 × 16 × 8

V = 1408 cu. in

c.

V = ______________ ft.^{3}

Answer:

s = 18 ft

l = 15 ft

V = a² h/3

V = 18² (15)/3

V = 18 × 18 × 5

V = 1620 cu. ft

**Create a free diagram using the situation described below and use it to answer the questions.**

Question 26.

Tracy decides to visit the concession stand while she is at the movies. She wants a drink, popcorn, and candy. She can choose between a cola, juice, and water to drink. She can top her popcorn with butter or have it plain. Finally, she has a choice of chocolate mints, red licorice, or caramels for her candy. Make a tree diagram that shows all possible combinations.

Answer:

Question 27.

What is the total number of possible outcomes?

Answer:

From the above tree diagram we can say that the total number of possible outcomes are 18.

Question 28.

What is probability of having red licorice?

Answer:

Total number of possible outcomes is 18.

Red licorice = 6/18 = 1/3

Question 29.

What is the probability of having buttered popcorn and caramels?

Answer:

The probability of having buttered popcorn and caramels

= 3/18 = 1/6

**Complete the items below.**

Sample quiz scores are collected from two classes.

Question 30.

Create a graphic display for both sets of quiz scores.

Answer:

Question 31.

Find the measures of center and the range for both sets of quiz scores.

median: ______________

mode: ______________

mean: ______________

range: ______________

median: ______________

mode: ______________

mean: ______________

range: ______________

Answer:

Quiz Score Class 1:

Given data,

8, 9, 12, 13, 16, 17, 18, 22, 23

Mean = (8 + 9 + 12 + 13 + 16 + 17 + 18 + 22 + 23)/9

Mean = 15.33

8, 9, 12, 13, 16, 17, 18, 22, 23

Median = 16

Mode = 8, 9, 12, 13, 16, 17, 18, 22, 23

Range = 23 – 8

Range = 15

Quiz Score Class 2:

Given data,

10, 11, 14, 15, 17, 20, 21, 22, 23

Mean = (10 + 11 + 14 + 15 + 17 + 20 + 21 + 22 + 23)/9

Mean = 17

Median = 17

Mode = 10, 11, 14, 15, 17, 20, 21, 22, 23

Range = 23 – 10 = 13

Question 32.

If there are 30 students in Class 1, what is the best prediction for the number of students who scored a 10 or less on the quiz?

Answer: 9 students scored 10 or less on the quiz

Question 33.

If there are 25 students in Class 2, what is the best prediction for the number of students who scored more than 20 on the quiz?

Answer: 10 students scored more than 20 on the quiz

Question 34.

Tell one way the two data sets are alike and different.

alike: _____________

different: ______________

Answer:

The number of observations in two data sets are alike.

The mean, median, mode and range are different in two data sets.

**Tell which property is used in each equation (commutative, associative, or identity).**

Question 35.

a. 5 + 3 = 3 + 5 _____________

Answer:

Commutative Property of Addition

The commutative property of addition says that changing the order of addends does not change the sum.

b. 0 + 8 = 8 _______________

Answer:

Identity Property of Addition

The sum of 0 and any number is that number.

Question 36.

a. (2 + 1) + 5 = 2 + (1 + 5) _______________

Answer:

Associative Property of Addition

Associative Property of Addition states that changing the grouping of addends does not change the sum.

b. -5 + 5 = 0 _______________

Answer:

The inverse property of addition states that adding a number and its opposite, called the additive inverse, will produce a sum of zero.