7th Grade Multistep Problems with Rational Numbers Test Solutions and Scoring (PDF)

7th Grade math test solutions: Multistep Problems with Rational Numbers – Maths PDF

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This grade 7 multistep problems test answers for 7th Grade covers multistep problems with rational numbers (Common Core 7.EE.B.3), with a free PDF to print.

Use this answer key and scoring guide to grade the multistep 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.EE.B.3

Grade 7 multistep problems test answers: worked solutions

Question 1 – Forms of a number [2 pts]

$5\div 8=0.625=62.5\%$.

$0.04=\frac{4}{100}=\frac{1}{25}$

0.625; 62.5%; $\frac{1}{25}$

Scoring: 1 point for the decimal and percent; 1 point for the fraction.

Question 2 – Estimate and compute [2 pts]

Estimate: $30\times 2=60$.

Exact: $29.7\times 2.1=62.37$, which is close to 60.

About 60; 62.37 is reasonable

Scoring: 1 point for a reasonable estimate; 1 point for the exact value and the comparison.

Question 3 – Mixed forms [2 pts]

$60-10=50$

Scoring: 1 point for each product; the final subtraction is included in the second point.

Question 4 – Overtime [2 pts]

Regular: $15\times 40=600$.

Overtime: $15\times 1.5\times 4=90$.

$600+90=690$

$690

Scoring: 1 point for the regular pay; 1 point for the overtime and total.

Question 5 – Recipe [2 pts]

$0.6\times 3\frac{1}{3}=\frac{3}{5}\times\frac{10}{3}=2$

2 quarts

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

Question 6 – Team dinner [2 pts]

Total: $18.50+7.25+6.75=32.50$.

With tip: $1.2\times 32.50=39$.

$39\div 6=6.50$

$6.50

Scoring: 1 point for the total with tip; 1 point for the share.

Question 7 – Debt and earnings [2 pts]

$-18+42=24$.

$\frac{1}{3}\times 24=8$ given; $24-8=16$ kept.

Gives $8; keeps $16

Scoring: 1 point for the balance; 1 point for the gift and the amount kept.

Question 8 – Budget [3 pts]

$\frac{3}{10}\times 2400=720$ for rent; $\frac{1}{4}\times 2400=600$ for food.
$720+600=1320$; $1320\div 2400=0.55=55\%$.
$2400-1320-300=780$.

Budget summary.

Scoring: 1 point for each part.

Question 9 – Coat purchase [3 pts]

$0.75\times 120=90$.
$1.08\times 90=97.20$.
$100-97.20=2.80$, so her change is $2.80.

Results.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this grade 7 multistep problems test answers

Key facts

Fractions, decimals, and percents are different names for the same numbers.
Convert to one form before you combine numbers.
Break the problem into steps and write the expression for each step.
Round only at the end; round money to the nearest cent.
Estimate with friendly numbers to check reasonableness.

How to use this grade 7 multistep 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.

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