7th Grade Solving Real-World Problems with Rational Numbers Test with Point Values (PDF)

7th Grade math test: Solving Real-World Problems with Rational Numbers – Maths PDF

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This rational number problems test for 7th Grade covers solving real-world problems with rational numbers (Common Core 7.NS.A.3), with a free PDF to print.

This 45-minute test checks real-world problems with the four operations on integers, fractions, and decimals, including temperature, elevation, money, and complex fractions (Common Core 7.NS.A.3). It has 9 questions worth 20 points in all. Show your work, because most questions give partial credit for correct steps.

Time and points

About this test

Grade: Grade 7
Chapter: Solving Real-World Problems with Rational Numbers
Standards: 7.NS.A.3
Time: 45 minutes
Total: 20 points

Rational number problems test: questions

Question 1 – Temperature change [2 pts]

Temperatures in degrees F.

The temperature was $-7^{\circ}\text{F}$ at 6 a.m. and $8^{\circ}\text{F}$ at 3 p.m. Find the change in temperature.

Question 2 – Checking account [2 pts]

Jamal’s balance is $-\$23.40$. He deposits $50 and then spends $19.85. Find the new balance.

Question 3 – Complex fraction [2 pts]

Simplify $\frac{\frac{7}{2}}{\frac{21}{8}}$.

Question 4 – Descent [2 pts]

A hot air balloon descends 4.5 feet per second for 6 seconds. Write its change in height as a signed number, and find the final height if it starts at 80 feet.

Question 5 – Mixed fractions [2 pts]

Evaluate $-\frac{5}{6}+\frac{2}{3}-\frac{1}{4}$.

Question 6 – Bake sale [2 pts]

A bake sale’s daily profit.

Find the total profit and the mean daily profit for the four days.

Question 7 – Distance apart [2 pts]

A scuba diver is at $-18.5$ meters and a seagull is at $27.25$ meters. Find the distance between them.

Question 8 – Pool [3 pts]

A pool holds 30,000 gallons.

Find how many gallons are in the pool when it is $\frac{2}{5}$ full. (1 point)
The pool is then drained by $\frac{1}{6}$ of its full capacity (30,000 gallons). Find the number of gallons left. (1 point)
Write the change in water for the draining as a signed number. (1 point)

Question 9 – Weather [3 pts]

Start temperature 5 degrees F.

The temperature is $5^{\circ}\text{F}$. It falls $3.25$ degrees each hour for 2 hours. Then it rises $3\frac{1}{2}$ degrees. (a) Find the temperature after 2 hours. (b) Find the final temperature. (c) Find the total change from the start.

Key facts behind this rational number problems test

Key facts

Positive and negative numbers show opposite directions, such as gains and losses.
The change from a to b is $b – a$; the distance between them is $|b – a|$.
Fraction bars mean division, so a complex fraction is a division problem.
Convert fractions and decimals to one form before combining them.
Check every answer with an estimate and the correct units.

How to use this rational number problems test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 7 chapters: Grade 7 math.

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