7th Grade Solving Real-World Problems with Rational Numbers Worksheet Solutions (PDF)

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

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

Use this answer key to check your work on the rational number problems worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.

Grade 7 · Common Core State Standards: 7.NS.A.3

Rational number problems answers: exercises 1 to 10

Exercise 1 – Temperature change

Change = final – start: $-3.5-12.5=-16$.

-16°F (a drop of 16 degrees)

Exercise 2 – Account activity

$-14.50+60=45.50$

$45.50-22.75=22.75$

$22.75

Balance after each step.

Exercise 3 – Elevation gap

$2340.5-(-86.25)=2340.5+86.25=2426.75$

2,426.75 feet

Exercise 4 – Servings

$2\frac{1}{2}\div\frac{3}{4}=\frac{5}{2}\times\frac{4}{3}=\frac{10}{3}=3\frac{1}{3}$.

Only whole servings count.

3 full servings

Exercise 5 – Golf scores

$-3+2-1+4=2$

+2 (two over par)

Exercise 6 – Complex fraction

$\frac{3}{4}\div\frac{5}{8}=\frac{3}{4}\times\frac{8}{5}=\frac{24}{20}=\frac{6}{5}$

$1\frac{1}{5}$

Exercise 7 – Mean temperature

Sum: $-4-7.5+2+1.5=-8$.

$-8\div 4=-2$

-2°F

The four lows.

Exercise 8 – Stock loss

$-\frac{2}{5}\times 350=-140$

-$140

Exercise 9 – Divide a debt

$-75\div 3=-25$

-$25

Exercise 10 – Cutting boards

$8\frac{1}{4}=\frac{33}{4}$ and $1\frac{3}{8}=\frac{11}{8}$.

$\frac{33}{4}\div\frac{11}{8}=\frac{33}{4}\times\frac{8}{11}=6$

6 pieces

Exercises 11 and up

Exercise 11 – Ship and plane

$|120.4-(-45.6)|=120.4+45.6=166$

166 meters

Exercise 12 – Mixed forms

$-\frac{3}{4}\times 8=-6$.

$-6+2.5=-3.5$

-3.5

Exercise 13 – Grouping

Parentheses first: $-2.4+5.1=2.7$.

$2.7\times(-10)=-27$

-27

Exercise 14 – Phone plan

Charges: $3\times 19.99=59.97$.

$-8.40-59.97+25=-43.37$

-$43.37

Account summary.

Exercise 15 – Dive and rise

Rise: $36.5\div 4=9.125$.

$-36.5+9.125=-27.375$.

$-27.375-3=-30.375$

-30.375 feet

Exercise 16 – Snack stand

Total: $45.50-12.25-30.80+18.40=20.85$.

Mean: $20.85\div 4=5.2125\approx 5.21$.

Total $20.85; mean $5.21 per day

Exercise 17 – Earn it back

Earnings: $12.50\times 4.5=56.25$.

$-37.50+56.25=18.75$

$18.75

Exercise 18 – Water tank

Morning: $20\times\frac{3}{8}=7.5$, leaving $12.5$ gallons.

Evening: $12.5\times\frac{1}{4}=3.125$.

$12.5-3.125=9.375$

9.375 gallons

Evening use.

Exercise 19 – Falling temperature

Total drop: $2\frac{1}{4}\times 3\frac{1}{2}=\frac{9}{4}\times\frac{7}{2}=\frac{63}{8}=7\frac{7}{8}$.

$5-7\frac{7}{8}=-2\frac{7}{8}$

$-2\frac{7}{8}$°F

Exercise 20 – Fabric cost

Unit cost: $9\div\frac{3}{4}=9\times\frac{4}{3}=12$ dollars per yard.

$12\times 2\frac{1}{3}=12\times\frac{7}{3}=28$

$12 per yard; $28

Key facts behind this rational number problems answers

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 answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

Download the rational number problems answers as a PDF with the button below and keep it with your notes.

All Grade 7 chapters: Grade 7 math.

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