We included HMH Into Math Grade 7 Answer Key PDF Module 4 Review to make students experts in learning maths.

Vocabulary

absolute value
opposite

For problems 1-3, choose the correct term from the box.

Question 1.
The number -4 is the ____ of 4.
The opposite of a negative sign is positive.
The number -4 is the opposite of 4.

Question 2.
The ____ of a number always represents the distance of that number from zero on a number line.
Answer: The absolute value of a number always represents the distance of that number from zero on a number line.

Question 3.
When subtracting two numbers, you add the ____ of the number being subtracted.
Answer: When subtracting two numbers, you add the smallest of the number being subtracted.

Question 4.
Which of the following statements is true?
A. The sum of two numbers is always positive.
B. The difference of two numbers is always negative.
C. The absolute value of a number is never negative.
D. The opposite of a number is always negative.
A. The sum of two numbers is always positive.
C. The absolute value of a number is never negative.
A and C statements are true.

Concepts and Skills

Question 5.
Use Tools Is the value of 5 – (-4) – 3 positive or negative? State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.
5 – (-4) – 3 = 5 + 4 – 3 = 6
So, 5 – (-4) – 3 is positive number.

Question 6.
The value of which expression is negative?
A. 1 + 2 – (-12)
B. 2 + 5 – 17
C. 4 – 5 – (-2)
D. 7 – 6 – (-5)
A. 1 + 2 – (-12) = 3 + 12 = 15
B. 2 + 5 – 17 = 7 – 17 = -10
C. 4 – 5 – (-2) = -1 + 2 = 1
D. 7 – 6 – (-5) = 1 + 5 = 6
Option B has a negative sign.

Question 7.
The temperature at 7:00 a.m. was 12 °C, and by 7:00 p.m. it had dropped to —10 °C. Which expression represents the change in temperature?
A. 12 + (-10)
B. 12 – 10
C. -10 + 12
D. -10 – 12
Given,
The temperature at 7:00 a.m. was 12 °C, and by 7:00 p.m. it had dropped to —10 °C.
12 – (-10) = 12 + 10 = 22 °C

Question 8.
The temperature at 4:00 p.m. was -6 °C, and then it fell by 7 °C. Which expression represents the new temperature?
A. -6 – 7
B. -7 – (-6)
C. 6 – (-7)
D. -6 + 7
Given,
The temperature at 4:00 p.m. was -6 °C, and then it fell by 7 °C.
-6 – (+7) = -6 – 7 = -13
Thus option A is the correct answer.

For Problems 9-25, find the value of each expression.

Question 9.
10 + (-6)
_________
Given expression
10 + (-6)
+ × – = –
10 – 6 = 4
10 + (-6) = 4

Question 10.
-3 + (-3)
_________
Given expression
-3 + (-3)
+ × – = –
-3 – 3 = -6
So, -3 + (-3) = -6

Question 11.
-8 + 2
_________
Given expression
-8 + 2 = -6
The greater number is having negative sign so the result will be negative.
Thus -8 + 2 = -6

Question 12.
-1 + (-7)
_________
Given expression
-1 + (-7)
+ × – = –
-1 – 7 = -8
When both the signs are the same then we have to add the numbers.
-(1 + 7) = -8

Question 13.
7 – (-9)
_________
Given expression
7 – (-9)
– × – = +
7 + 9 = 16
7 – (-9) = 16

Question 14.
-3 – 2
_________
Given expression
-3 – 2
When both the signs are the same then we have to add the numbers.
-(3 + 2) = -5

Question 15.
12 – (-9)
_________
Given expression
12 – (-9)
– × – = +
12 + 9 = 21
12 – (-9) = 21

Question 16.
12 – 18
_________
Given expression
12 – 18 = -6
The greater number is having negative sign so the result will be negative.
-18 + 12 = -6

Question 17.
3 – 8$$\frac{2}{3}$$
____________
Given expression
3 – 8$$\frac{2}{3}$$
Rewrite the expression by separating the parts
3 – 8 – $$\frac{2}{3}$$
3 – 8 = -5
-5 – $$\frac{2}{3}$$ = -5$$\frac{2}{3}$$

Question 18.
-2.7 – 1.8
Given expression
-2.7 – 1.8
When both the signs are the same then we have to add the numbers.
-(2.7 + 1.8) = -4.5
So, -2.7 – 1.8 = -4.5

Question 19.
5$$\frac{1}{5}$$ – (-2$$\frac{4}{15}$$)
Given expression
5$$\frac{1}{5}$$ – (-2$$\frac{4}{15}$$)
– × – = +
5$$\frac{1}{5}$$ – (-2$$\frac{4}{15}$$)
5$$\frac{1}{5}$$ + 2$$\frac{4}{15}$$
Solving the whole parts
5 + 2 = 7
Solving the fraction parts
$$\frac{1}{5}$$ + $$\frac{4}{15}$$ = $$\frac{7}{15}$$
7 + latex]\frac{7}{15}[/latex] = 7latex]\frac{7}{15}[/latex]

Question 20.
46.33 – (-15.07)
Given expression
46.33 – (-15.07)
– × – = +
46.33 – (-15.07) = 46.33 + 15.07 = 61.4

Question 21.
-7$$\frac{3}{4}$$ + 2$$\frac{1}{8}$$
Given expression
-7$$\frac{3}{4}$$ + 2$$\frac{1}{8}$$
Solving the whole parts
-7 + 2 = -5
–$$\frac{3}{4}$$ + $$\frac{1}{8}$$
LCD of 4 and 8 is 8
–$$\frac{6}{8}$$ + $$\frac{1}{8}$$ = –$$\frac{5}{8}$$
Combine the whole and fraction parts
-5 –$$\frac{5}{8}$$ = -5$$\frac{5}{8}$$

Question 22.
-13$$\frac{4}{7}$$ – (-6$$\frac{10}{21}$$) + $$\frac{1}{3}$$
Given expression
-13$$\frac{4}{7}$$ – (-6$$\frac{10}{21}$$) + $$\frac{1}{3}$$
-13$$\frac{4}{7}$$ + 6$$\frac{10}{21}$$ + $$\frac{1}{3}$$
-13 + 6 = -7
–$$\frac{4}{7}$$ + $$\frac{10}{21}$$
LCD of 7 and 21 is 21
–$$\frac{12}{7}$$ + $$\frac{10}{21}$$ = –$$\frac{2}{21}$$
-7 – $$\frac{2}{21}$$ = -7$$\frac{2}{21}$$
-7$$\frac{2}{21}$$ + $$\frac{1}{3}$$
-7 – $$\frac{2}{21}$$ + $$\frac{1}{3}$$
– $$\frac{2}{21}$$ + $$\frac{7}{21}$$ = $$\frac{5}{21}$$
-7 + $$\frac{5}{21}$$ = -6$$\frac{16}{21}$$

Question 23.
15.47 — (—17.09) + 3.7
Given expression
15.47 — (—17.09) + 3.7
– × – = +
15.47 + 17.09 + 3.7 = 36.26

Question 24.
3$$\frac{1}{2}$$ – 5.3 + (-5$$\frac{1}{10}$$)
Given expression
3$$\frac{1}{2}$$ – 5.3 + (-5$$\frac{1}{10}$$)
3$$\frac{1}{2}$$ – 5$$\frac{1}{10}$$ – 5.3
3 + $$\frac{1}{2}$$ – 5 – $$\frac{1}{10}$$ – 5.3
Solving the whole parts
3 – 5 = -2
Solving the fraction parts
$$\frac{1}{2}$$ – $$\frac{1}{10}$$
LCD = 10
$$\frac{5}{10}$$ – $$\frac{1}{10}$$ = $$\frac{4}{10}$$ = $$\frac{2}{5}$$
-2 + $$\frac{2}{5}$$ = -1$$\frac{3}{5}$$
-1$$\frac{3}{5}$$ – 5.3
-1$$\frac{3}{5}$$ = -8/5 = -1.6
-1.6 – 5.3 = -6.9

Question 25.
-8.45 – 3$$\frac{1}{10}$$ + 6.73
Given expression
-8.45 – 3$$\frac{1}{10}$$ + 6.73
-8.45 + 6.73 – 3$$\frac{1}{10}$$
The greater number is having negative sign so the result will be negative.
-1.72 – 3$$\frac{1}{10}$$
3$$\frac{1}{10}$$ = 31/10 = 3.1
-1.72 – 3.1 = -4.82
When both the signs are the same then we have to add the numbers.
-(1.72 + 3.1) = -4.82

Question 26.
Which is greater: -999 + 1 or -999 + (-1)? Explain.
-999 + 1
The greater number is having negative sign so the result will be negative.
-999 + 1 = -998
-999 + (-1)
+ × – = –
When both the signs are the same then we have to add the numbers.
– × – = +
-999 – 1 = -1000

Question 27.
Samantha owes $25.50, and borrows another$20.00. She pays back $15.25 of her debt and then earns$45.00. Later, Samantha pays back $22.50 of her debt. How much does she still have to pay back? Show your work. Answer: Given, Samantha owes$25.50, and borrows another $20.00. She pays back$15.25 of her debt and then earns $45.00. Later, Samantha pays back$22.50 of her debt.
45 + 25.5 + 20 – 22.5 – 15.25
70.5 + 20 – 22.5 – 15.25
90.5 – 22.5 – 15.25
68 – 15.25
52.75

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