Adding and Subtracting Rational Numbers

Rational Numbers, Opposites, and Absolute Values

100

A worker in a silver mine descends 36 feet. Use an integer to represent the change in the​ worker's position.

-36

200

Which of these situations can be represented by the opposite of −77​? You walk down 77 flights of stairs. You climb up 77 flights of stairs. The temperature drops 77°F. You spend $7 on a book.

You climb up 77 flights of stairs.

300

Two submarines are underwater. The number −4,451 represents Submarine​ A's position​ (in feet) relative to the surface. The number −4,979 represents Submarine​ B's position​ (in feet) relative to the surface. Which submarine is closer to the​ surface?

Submarine A

400

Which of these situations can be represented by the opposite of 66​? Select all that apply. A book was 66 pages shorter than you expected. Andrew spent $66. The temperature was 66°F. Jennifer sold 66 apples.

The book was 66 pages shorter than you expected Andrew spent $66 Jennifer sold 66 apples

500

In a recent​ year, the number of DVDs shipped to an online retailer was 84,000 less than the previous year. Use an integer to describe the change in the number of DVDs shipped.

-84,000

Adding Integers

100

Complete the statement below. Then use a number line to find the sum 4+​(−3​). 4+​(−3​) is​ ___ units from 4​, in the​ ___ direction.

3; negative; 1

200

Which pairs of integers are additive inverses? Select all that apply. 4, 4; 4, −4; 6, −6; 6, −4

4, -4; 6, -6

300

Suppose a deep sea diver dives from the surface to 83 feet below the surface. He then dives down 11 more feet. The diver's depth is represented by the sum −83+(−11). Find and interpret the sum to describe the diver's present depth.

-94; 94 feet below the surface

400

From the following list, select all pairs that are additive inverses. 8, 8; −8, 8; 9, −9; −8, −8; −9, −9

-8, 8; 9,-9

500

A car backs up 17 feet, followed by 11 more feet. The​ car's position can be represented by the sum −17+(−11). Find the sum. Use pencil and paper. Represent the situation with a drawing

-28

Adding Rational Numbers

100

Find the sum. (7/11)+(−1/11)

6/11

200

Find the value of the expression 6.9+(−2.6).

4.3

300

Add. −9.3+(−6.5)

-15.8

400

In her garden Pam plants the seed 4 1/2 in. below the ground. After one month the tomato plant has grown a total of 9 3/4 in. How many inches is the plant above the ground?

5 1/4

500

Simplify the expression. (2/3)+(1/9)

7/9

Subtracting Integers

100

Use a number line model to find −3−6. Solve the expression

-9

200

Find the value of the expression. 9−​(-3)

12

300

Find −7−​(−9​).

2

400

13 - (-5) - 1

17

500

Write an addition expression equivalent to 2−​(−6​). Then find 2−​(−6​).

2+6; 8

Subtracting Rational Numbers

100

Decide if each expression describes a difference that is positive, negative, or zero. 3.7 −9.9; 3.7−(−9.9)

Negative; Positive

200

Find 1.6 - 7.8

-6.2

300

Find (−1/3)−(-5/6)

1/2

400

Subtract. 10.0−(−2.5)

12.5

500

The freezing point of Chemical A is −127.27°C. The freezing point of Chemical B is −89.1°C. Which chemical has a higher freezing​ point? How much higher is​ it?

Chemical B has a higher freezing point by 38.17 degrees