Operations with Rational Numbers GMAS review

John and Kamira are playing a game. John’s score (J) and Kamira’s score (K) after round 1 are shown on the number line.

The score recorded at the end of the first round is 2. What could this score represent?

• the sum of John’s score and Kamira’s score

• the difference between John’s score and Kamira’s score

• the absolute value of the difference of John’s score and Kamira’s score

• the sum of the absolute value of John’s score and the absolute value of Kamira’s score

Answer explanation

If the final score was 2, then the only answer choice that makes sense would be the sum between the two scores.

-5 + 7 = 2

What is the value of 4.2(46 – 65)?

• -798

• -79.8

• 79.8

• 798

Answer explanation

4.2(46 - 65)

PEMDAS

P - parentheses

46 - 65 = -10

4.2(-19) [DISTRIBUTIVE PROPERTY]

4.2 x -19 = -79.8

What is the product? –8(7 – 3.2)

• -59.2

• -30.4

• 30.4

• 52.8

Answer explanation

-8 (7 - 3.2) = PEMDAS

-8 (3.8) = -30.4

During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?

• $59 increase

• $59 decrease

• $691 increase

• $691 decrease

Answer explanation

4 withdraws (minus) of $40 each = 4 x -40 = -160

$156 PURCHSE (minus)

-160 - 156 = KCC

-160 + (-156) same sign add

= - 316

DEPOSITS (add) $375

-316 + 375 = different signs, subtract take sign of larger number

= 59

Last year at a track meet, runner A & B both ran each 4 laps in 1.5 mins. Runner A sets a goal for this year of changing his total time for the race -0.12 mins. with equal times for all four laps. Runner B sets a a goal for this year of changing his time on each lap by -0.025 mins.

Runner A's goal is to his time in each lap of the race by ______ mins.

• -0.48

• -0.12

• -0.03

• 0.3

• 0.12

Answer explanation

-0.12 divided by 4 laps = -0.03 on each lap

Last year at a track meet, runner A & B both ran each 4 laps in 1.5 mins. Runner A sets a goal for this year of changing his total time for the race -0.12 mins. with equal times for all four laps. Runner B sets a a goal for this year of changing his time on each lap by -0.025 mins.

Runner B's goal is to change his total time by ______ mins.

• -0.025

• -0.1

• -0.00625

• 0.025

• 0.1

Answer explanation

-0.025 x 4 laps = -0.1

Simplify.

(2)(18) ÷ (–2 + 5)(–1)

• -13

• -12

• 12

• 13

Answer explanation

(2)(18) ÷ (–2 + 5)(–1)

PEMDAS

P = (2)(18) ÷ (3)(–1)

E = NONE

M/D = 36 ÷ -3

D = -12

The overall change in temperature when the temperature goes from -12 degrees Celsius to 12 degrees Celsius is _____________.

• 0

• -24

• 12

• 24

Answer explanation

overall change = the absolute value of the difference

l-12 - 12l = l-24l = 24

The total profit made when a person buys an item for $3.25 and sells the item for $3.25?

• $0

• $-6.50

• $6.50

• $3.25

Which situation applies an additive inverse to find the total amount of money?

• Mrs. Bree spent $8, then found $8.

• Mrs. Bree spent $8, then gave $2 to a friend.

• Mrs. Kellie found $8, then found $8 more.

• Mrs. Kellie found $8, then kept $8 in her pocket.

Answer explanation

additive inverses are opposites that make $0. I found $8 (positive 8) and spent $8 (negative 8) 8 + (-8) = 0