Exercises: Solve real-world and mathematical problems involving the four operations with rational numbers - Common Core Math - Grade 7

A

Recall / Warm-Up

1.

What is the value of $(-6) \times (-4)$ ?

A.

$-24$

B.

$24$

C.

$-10$

D.

$10$

2.

Which decimal is equal to $\frac{1}{4}$ ?

A.

$0.14$

B.

$0.4$

C.

$0.25$

D.

$4.0$

3.

Evaluate: $-\frac{3}{4} \div 3$ . Express as a fraction in simplest form.

B

Fluency Practice

1.

A hiker's elevation decreases by $2.5$ meters per minute for $8$ minutes. What is the total change in elevation? Include the sign in your answer.

2.

A recipe uses $\frac{3}{4}$ cup of flour per batch. How many cups of flour are needed for $2\frac{1}{2}$ batches? Express as a mixed number.

3.

A $45.50$ loss is shared equally among $5$ investors. What is each investor's share of the loss? Express as a decimal.

4.

The temperature changes from $-3.5^\circ$ F to $11^\circ$ F. What is the temperature change in degrees Fahrenheit?

5.

A room's temperature drops $1.25^\circ$ F every hour. Which expression BEST represents the total temperature change after $6$ hours using a single operation?

A.

$(-1.25) + (-1.25) + (-1.25) + (-1.25) + (-1.25) + (-1.25)$

B.

$(-1.25) \times 6$

C.

$1.25 \times 6$

D.

$(-1.25) \div 6$

C

Varied Practice

1.

A climber's elevation changes from $1{,}250$ meters above sea level to $840$ meters above sea level. Which expression gives the signed change in elevation?

A.

$1{,}250 - 840 = 410$

B.

$840 - 1{,}250 = -410$

C.

$1{,}250 + 840 = 2{,}090$

D.

$840 \div 1{,}250 = 0.672$

2.

A boat starts at position $-8$ km (8 km south of a port). It travels north at $\frac{3}{2}$ km per hour for $6$ hours.

After 6 hours, the boat's position is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ km.

Then the boat travels south at $2$ km per hour for $\frac{3}{4}$ hour.

The boat's final position is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ km.

position after step 1:

final position:

3.

The temperature changes from $12^\circ$ F to $4^\circ$ F. The signed change is $4 - 12 = -8^\circ$ F. A student is asked 'How far did the temperature fall?' Which answer is correct?

A.

$-8^\circ$ F, because the temperature fell by a signed value of $-8$ .

B.

$8^\circ$ F, because the question asks for a distance (magnitude of change), which is always non-negative.

C.

$4^\circ$ F, because that is the final temperature.

D.

$12^\circ$ F, because that is the starting temperature.

4.

An investor's account undergoes three changes: a loss of $240$ , then a gain of $185$ , then a loss of $75$ . What is the total net change in the account?

D

Word Problems

1.

A credit card account starts with a balance of $-245$ (meaning the cardholder owes $245$ ).

1.

The account holder makes a payment of $120$ . What is the new balance?

2.

The cardholder then makes purchases totaling $67.50$ . Purchases are charges (they add to the debt). What is the final balance? Is the account still in debt?

2.

The high temperatures over five days were: $-3.2^\circ$ C, $1.5^\circ$ C, $-0.8^\circ$ C, $4.1^\circ$ C, $-2.6^\circ$ C.

What was the average daily high temperature over these five days? Express as a decimal.

3.

A scuba diver is at a depth of $-18$ meters below the surface.

The diver descends an additional $7.5$ meters. What is her new depth in meters (include the sign)?

4.

An elevator starts at the $10$ th floor and descends at a constant rate of $4.5$ floors per minute until it reaches floor $-8$ (8 floors below ground level).

How many minutes does the elevator travel?

E

Error Analysis

1.

A credit card account has a balance of $-125$ .

Purchases of $67.50$ are charged to the account. A student shows this work:

Step 1: (already completed) Balance after payment = $-125$
Step 2: Final balance = $-125 + 67.50 = -57.50$

What error did the student make in Step 2?

A.

The student treated the purchases as a positive addition (a gain) instead of a negative addition (an increase in debt). Purchases should be added as $-67.50$ , giving $-125 + (-67.50) = -192.50$ .

B.

The student used the wrong operation — purchases should be multiplied, not added.

C.

The student computed $-125 + 67.50$ incorrectly — the correct value of $-125 + 67.50$ is $-192.50$ , not $-57.50$ .

D.

The student used the wrong intermediate result — Step 1 should have given $+125$ , not $-125$ .

2.

A submarine descends from a depth of $-60$ meters to a depth of $-95$ meters.

A student is asked "How far did the submarine descend?"

The student writes:
Change = $-95 - (-60) = -95 + 60 = -35$

The student reports: 'The submarine descended $-35$ meters.'

Did the student compute the change correctly? What error, if any, is in the student's final answer?

A.

The computation is wrong — the change should be $-60 - (-95) = 35$ , not $-35$ .

B.

The computation is correct ( $-35$ is the signed change), but 'how far' asks for a distance, which should be reported as $35$ meters (positive), not $-35$ meters.

C.

The computation and the reported answer are both correct — a descent of $-35$ meters is the right way to say the submarine went 35 meters deeper.

D.

The student should have computed $|{-95}| - |{-60}| = 95 - 60 = 35$ to find the distance.

F

Challenge

1.

A store's temperature is $-4^\circ$ C. A heating system raises the temperature at a rate of $\frac{3}{2}^\circ$ C per hour for $6$ hours. The heating then fails, and the temperature drops at $1.5^\circ$ C per hour for $4$ hours. What is the final temperature?

2.

A chemical compound's temperature starts at $-12.8^\circ$ C. Over 3 days, the temperature changes as follows:

Days 1 and 2: rises $2\frac{1}{4}^\circ$ C per day
Day 3: rises $1\frac{1}{2}^\circ$ C