Go through the Math in Focus Grade 7 Workbook Answer Key Cumulative Review Chapters 1-2 to finish your assignments.

## Math in Focus Grade 7 Course 2 A Cumulative Review Chapters 1-2 Answer Key

**Concepts and Skills**

**Write each number as \(\frac{m}{n}\) in simplest form, where m and n are integers with n ≠ 0. (Lesson 1.1)**

Question 1.

-0.87

Answer:

0.87 can be written in the \(\frac{m}{n}\) form as –\(\frac{87}{100}\)

Question 2.

12.8

Answer:

12.8 can be written in the \(\frac{m}{n}\) form as \(\frac{128}{10}\) or \(\frac{64}{5}\)

Question 3.

-1.9

Answer:

-1.9 can be written in the \(\frac{m}{n}\) form as \(\frac{-19}{10}\)

**Using long division, write each rational number as a terminating or a repeating decimal. Identify a pattern of repeating digits using bar notation. (Lesson 1.2)**

Question 4.

\(\frac{9}{5}\)

Answer: \(1 . \overline{8}\)

Question 5.

\(\frac{23}{16}\)

Answer: 1.4375 it is a terminating decimal

Question 6.

–\(\frac{51}{110}\)

Answer: \(0 . 46\overline{36}\)

**Use a calculator. Locate each irrational number to 2 decimal places on the number line using rational approximations. (Lesson 1.3)**

Question 7.

\(\sqrt{44}\)

Answer: 6.63

Question 8.

\(\sqrt{132}\)

Answer: 11.48

Question 9.

–\(\sqrt{162}\)

Answer: 12.72

Question 10.

Answer: 4.64

Question 11.

\(\frac{\pi}{7}\)

Answer: 0.44

Question 12.

π^{3}

Answer: 30.95

**Order the real numbers below from greatest to least using the symbol >. (Lesson 1.4)**

Question 13.

\(\sqrt{345}\), \(\frac{244}{7}\), , –\(\frac{86}{3}\), 33.9

Answer:\(\frac{244}{7}\) > 33.9> \(\sqrt{345}\)>>-\(\frac{86}{3}\)

**Round each number to the given number of significant digits. (Lesson 1.5)**

Question 14.

349,950 (to 4 significant digits)

Answer: 350000

Question 15.

0.09608 (to 3 significant digits)

Answer: 0.0961

**Evaluate each expression. (Lessons 2.1, 2.2)**

Question 16.

7 + (-12)

Answer:

7 – 12 = -5

Question 17.

-15 + (-20)

Answer:

-15 – 20 = -35

Question 18.

-8 + 6 – 4

Answer:

– 8 – 4 + 6

-12 + 6 = -6

Question 19.

11 – (-14)

Answer:

11 – (-14)

– × – = +

11 + 14 = 25

Question 20.

32 – (-17)

Answer:

32 – (-17)

– × – = +

32 + 17 = 39

Question 21.

-7 – 5 – (-6)

Answer:

-7 – 5 – (-6)

-7 – 5 + 6

-12 + 6 = -6

Question 22.

-250 + 480

Answer:

-250 + 480

480 – 250 = 230

The greatest value has a positive sign so put a positive sign to the obtained answer.

-250 + 480 = 230

Question 23.

-109 – (-121)

Answer:

-109 – (-121)

-109 + 121

The greatest value has a positive sign so put a positive sign to the obtained answer.

121 – 109 = 12

Question 24.

43 + (-95) – (-16)

Answer:

43 + (-95) – (-16)

43 – 95 + 16

43 + 16 – 95 = -36

**Evaluate each product or quotient. As needed, give your answer in simplest form. (Lessons 2.3, 2.5)**

Question 25.

-12.8

Answer:

– × + = –

12 × 8 = 96

Put negative sign to the obtained answer.

We get -96

Question 26.

\(\frac{2}{15} \cdot\left(-\frac{5}{8}\right)\)

Answer:

– × + = –

\(\frac{2}{15}\) × –\(\frac{5}{8}\) = –\(\frac{10}{120}\) = \(\frac{1}{12}\)

Question 27.

\(2 \frac{2}{5} \cdot\left(-1 \frac{1}{4}\right)\)

Answer:

– × + = –

2\(\frac{2}{5}\) × -1\(\frac{1}{4}\)

\(\frac{12}{5}\) × –\(\frac{5}{4}\)

= –\(\frac{60}{20}\)

= -3

Question 28.

-9 ÷ (-7)

Answer:

Cancel – by –

9 ÷ 7 = 1.28

Question 29.

\(-\frac{7}{16} \div\left(-\frac{21}{6}\right)\)

Answer:

Given,

\(\frac{7}{16}\) × –\(\frac{21}{6}\)

= \(\frac{7}{16}\) × –\(\frac{7}{2}\)

= –\(\frac{49}{32}\)

Question 30.

Answer:

–\(\frac{3}{4}\) × 2\(\frac{1}{4}\)

= –\(\frac{3}{4}\) × \(\frac{9}{4}\)

= – \(\frac{27}{16}\)

**Evaluate each expression. (Lessons 2.3, 2.4, 2.5, 2.6)**

Question 31.

-3 • 12 – (-6) + 2(-7) ÷ 7

Answer:

-3 • 12 – (-6) + 2(-7) ÷ 7

((-3) 12) – (-6) + ((2 * (-7)/7))

= -32

Question 32.

\(\frac{2}{3}\) • \(\frac{1}{6}\) + 1\(\frac{5}{9}\) + 2\(\left(-\frac{7}{18}\right)\)

Answer:

Given,

\(\frac{2}{3}\) • \(\frac{1}{6}\) + 1\(\frac{5}{9}\) + 2\(\left(-\frac{7}{18}\right)\)

\(\frac{2}{18}\) + \(\frac{14}{9}\) – \(\frac{43}{18}\)

– \(\frac{41}{18}\) + \(\frac{14}{9}\)

= – \(\frac{41}{18}\) + \(\frac{28}{18}\)

= –\(\frac{13}{18}\)

Question 33.

-4 • 5.2 – 0.5• (-7.8) + 2 • 1.3

Answer: -14.3

Question 34.

–\(\frac{1}{5}\) [-20 + 1.2(-3)] + 1\(\frac{2}{5}\)

Answer:

Given,

–\(\frac{1}{5}\) [-20 + 1.2(-3)] + 1\(\frac{2}{5}\)

–\(\frac{1}{5}\) [-20 – 3.6] + 1\(\frac{2}{5}\)

–\(\frac{1}{5}\) [-23.6] + 1\(\frac{2}{5}\)

4.72 + \(\frac{7}{5}\)

4.72 + 1.4

= 6.12

**Problem Solving**

**Solve. Show your work.**

Question 35.

An athlete completes a 400-meter dash in 46.3 seconds. What is his speed in meters per second correct to 3 significant digits? (Chapter 1)

Answer:

An athlete completes a 400-meter dash in 46.3 seconds.

400/46.3

8.639

8.64 m/s

Question 36.

The greatest and least temperatures ever recorded in Tim’s hometown are 101°F and -36°F. Find the difference between these two temperatures. (Chapter 2)

Answer:

Given,

The greatest and least temperatures ever recorded in Tim’s hometown are 101°F and -36°F.

101°F – (-36°F)

= 101°F + 36°F

= 137°F

Question 37.

On a math quiz consisting of 100 questions, the teacher gives 2 points for a correct answer, -1 point for an incorrect answer, and -2 points for not answering a question at all. (Chapter 2)

a) Emily answered 75 questions correctly, 18 incorrectly, and did not answer 7 questions. What is her score?

Answer:

75 × 2 = 150

18 × -1 = -18

7 × -2 = -14

150 -18 – 14

150 – 32 = 118

Thus the score of Emily is 118

b) Amy answered 30 questions correctly and 62 incorrectly. What is her score?

Answer:

30 × 2 = 60

62 × – 1 = -62

60 – 62 = -2

Amy score is -2

Question 38.

Justin dug a hole that was 9\(\frac{1}{2}\) inches deep. His sister Jean built a sand castle next to the hole that was 12\(\frac{3}{4}\) inches high. Show how you could use subtraction to find the vertical distance from the top of the castle to the bottom of the hole. (Chapter 2)

Answer:

Justin dug a hole that was 9\(\frac{1}{2}\) inches deep.

His sister Jean built a sand castle next to the hole that was 12\(\frac{3}{4}\) inches high.

12\(\frac{3}{4}\) – 9\(\frac{1}{2}\)

12 – 9 = 3

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

= 3\(\frac{1}{4}\) inches

Question 39.

Rick started his hike at an elevation of 8,975 feet. He descended at a constant rate of 8.5 feet per minute for 45 minutes. Find Rick’s elevation after 45 minutes. Give your answer to 4 significant digits. (Chapters 1, 2)

Answer:

Given,

Rick started his hike at an elevation of 8,975 feet.

He descended at a constant rate of 8.5 feet per minute for 45 minutes.

8.5 × 45 = 382.5 feet

8975 feet – 382.5 feet = 8592.5 feet

8593 feet

Question 40.

A car travels’at 68\(\frac{2}{3}\) miles per hour for 2\(\frac{1}{12}\) hours. Find the distance that the car has traveled correct to 3 significant digits. (Chapters 1, 2)

Answer: 68\(\frac{2}{3}\) × 2\(\frac{1}{12}\)

= 143 \(\frac{1}{18}\)

= 143.055

Question 41.

In a particular town, the temperature at midnight is -2°C. It rises at a steady rate for 12 hours to reach a temperature of 22°C at noon. (Chapter 2)

a) Find the difference between the temperature at noon and at midnight.

Answer: 24°C

b) Find the temperature at 7 A.M.

Answer: 12°C

c) Find the time when the temperature is 4°C.

Answer: 3 A.M.