Topic 1 Assessment: Rational Number Operations

Arianna runs up 4.5 flights of stairs. How far will Arianna have to run down to represent an additive inverse? Explain.

Answer explanation

Arianna will have to run down 4.5 flights of stairs to represent an additive inverse, as the additive inverse of a positive number is its negative counterpart.

Tags

CCSS.7.NS.A.1

Four out of nine dogs weigh less than 20 pounds. What is the decimal equivalent for the number of dogs weighing under 20 pounds?

• 0.2

• 0.24

• 0.4

• 0.49

Answer explanation

Four out of nine dogs is equivalent to 4/9, which simplifies to 0.4 when converted to a decimal. Therefore, the decimal equivalent for the number of dogs weighing under 20 pounds is 0.4.

Tags

CCSS.7.RP.A.1

CCSS.7.RP.A.2

CCSS.7.NS.A.2

CCSS.7.NS.A.3

Andy is scuba diving. He starts at sea level and then descends 10 feet in 2 1/2 minutes. Part A: How would you represent Andy’s descent as a unit rate? Express your answer as an integer.

Answer explanation

To represent Andy's descent as a unit rate, we divide the total descent of 10 feet by the time of 2 1/2 minutes. This gives us a unit rate of 4 feet per minute, expressed as an integer.

Tags

CCSS.7.RP.A.1

Andy is scuba diving. He starts at sea level and then descends 10 feet in 2 1/2 minutes. Part B: If he continues at this rate, where will Andy be in relation to sea level after 6 minutes?

Answer explanation

After 6 minutes, Andy will be 24 feet below sea level. He descends 10 feet in 2 1/2 minutes, so in 6 minutes, he descends 24 feet (10 feet * 6 minutes / 2.5 minutes).

Tags

CCSS.7.EE.B.3

If p < 0, q > 0, and p + q = r, which statement about r is true?

• |r| = |q|

• r > 0

• r < 0

• |r| > |q|

Answer explanation

Since p < 0 and q > 0, their sum (r) will be negative. Therefore, the statement 'r < 0' is true.

Tags

CCSS.7.EE.B.3

Javier had $305 in his bank account. His bank charges a fee of $7.50 each month that a balance is below $500. If he makes no other deposits or withdrawals, how much money is in Javier’s account at the end of three months?

Answer explanation

At the end of three months, Javier will have $282 in his account. He will incur a fee of $7.50 for each of the three months, resulting in a total deduction of $22.50 from his initial balance of $305.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.1

CCSS.7.NS.A.3

In the first round of a card game, Niki scored 20 points. Then, she lost 10 points on one turn and also lost 25 points on her final turn. Part A: Show the change in Niki’s score using the number line below.

Answer explanation

To show the change in Niki's score, start at 20, move left 10 to 10, then left 25 to -15 on the number line.

Tags

CCSS.7.NS.A.1

In the first round of a card game, Niki scored 20 points. Then, she lost 10 points on one turn and also lost 25 points on her final turn. Part B: What is Niki’s final score?

Answer explanation

Niki's final score is calculated by starting with 20 points, then subtracting 10 points and another 25 points. Therefore, her final score is 20 - 10 - 25 = -15 points.

Tags

CCSS.7.NS.A.1

A fish finder shows a large fish at 13 feet below the surface of the water and a smaller fish located 4 feet below the surface of the water. Select all the expressions that are equivalent to the distance between the fish.

• −13 + (−4)

• −13 − (−4)

• −13 − 4

• −4 + (−13)

• −4 − (−13)

Answer explanation

To find the distance between the fish, subtract their depths: -13 - (-4) = -13 + 4 = -9. Therefore, the expressions -13 - (-4) and -13 - 4 are equivalent to the distance between the fish.

Tags

CCSS.7.EE.B.3

CCSS.7.NS.A.1

CCSS.7.NS.A.3

A marathon is 26.2 miles long. There is a water station every 1 1/4 miles along the race route and at the finish line. How many water stations are needed for this marathon?

• 12

• 16

• 21

• 26

Answer explanation

To calculate the number of water stations, divide the total distance of the marathon (26.2 miles) by the distance between each station (1 1/4 miles). This gives 21 water stations needed.

Tags

CCSS.7.EE.B.3