7th Grade Solving Real-World Problems with Rational Numbers Test Solutions and Scoring (PDF)

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

Cover of the book Grade 7 Math Tests with Answer Keys (PDF)

Download as a PDFThe Grade 7 tests book with answer keysPrintable PDFSee the book ›

Sommaire

This rational number problems test 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 and scoring guide to grade the rational number problems test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.

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

Rational number problems test answers: worked solutions

Question 1 – Temperature change [2 pts]

$8-(-7)=15$

15 degrees higher

Scoring: 1 point for the correct operation; 1 point for the answer.

Question 2 – Checking account [2 pts]

$-23.40+50=26.60$; $26.60-19.85=6.75$

$6.75

Scoring: 1 point for each step.

Question 3 – Complex fraction [2 pts]

$\frac{7}{2}\times\frac{8}{21}=\frac{56}{42}=\frac{4}{3}$

$1\frac{1}{3}$

Scoring: 1 point for multiplying by the reciprocal; 1 point for the simplified value.

Question 4 – Descent [2 pts]

$-4.5\times 6=-27$.

$80+(-27)=53$

-27 feet; 53 feet

Scoring: 1 point for the change; 1 point for the final height.

Question 5 – Mixed fractions [2 pts]

$-\frac{10}{12}+\frac{8}{12}-\frac{3}{12}=-\frac{5}{12}$

$-\frac{5}{12}$

Scoring: 1 point for a common denominator; 1 point for the value.

Question 6 – Bake sale [2 pts]

$32.50-8.75+15.25-4.00=35$; $35\div 4=8.75$

Total $35.00; mean $8.75

Scoring: 1 point for the total; 1 point for the mean.

Question 7 – Distance apart [2 pts]

$|27.25-(-18.5)|=45.75$

45.75 meters

Scoring: 1 point for the setup with absolute value or addition; 1 point for the value.

Question 8 – Pool [3 pts]

$30000\times\frac{2}{5}=12000$ gallons.
$30000\times\frac{1}{6}=5000$, so $12000-5000=7000$ gallons are left.
$-5000$ gallons.

Results.

Scoring: 1 point for each part.

Question 9 – Weather [3 pts]

$5-3.25\times 2=5-6.5=-1.5$°F.
$-1.5+3.5=2$°F.
$2-5=-3$ degrees.

Temperatures after the fall and after the rise.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this rational number problems test 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 test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 7 chapters: Grade 7 math.

Voter.. post

Free printable PDF