7th Grade Multiplying and Dividing Rational Numbers Worksheet Solutions (PDF)

7th Grade math worksheet solutions: Multiplying and Dividing Rational Numbers – Maths PDF

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This multiply divide rationals answers for 7th Grade covers multiplying and dividing rational numbers (Common Core 7.NS.A.2), with a free PDF to print.

Use this answer key to check your work on the multiplying rational numbers 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.2

Multiply divide rationals answers: exercises 1 to 10

Exercise 1 – Positive times negative

Absolute values: $4 \times 7 = 28$

The signs are different, so the result is negative.

-28

Exercise 2 – Two negatives

Absolute values: $6 \times 5 = 30$

The signs are the same, so the result is positive.

Exercise 3 – Divide negative by positive

Absolute values: $48 \div 6 = 8$

The signs are different, so the result is negative.

-8

Exercise 4 – Divide two negatives

Absolute values: $54 \div 9 = 6$

The signs are the same, so the result is positive.

Exercise 5 – Decimal product

$2.5\times 4=10$. The signs differ, so the product is negative.

-10

Exercise 6 – Product of decimals

$6\times 3=18$, and there are 2 decimal places, so $0.18$. Two negatives give a positive.

0.18

Same signs: positive.

Exercise 7 – Divide decimals

$3.6\div 0.9=4$. The signs differ, so the quotient is negative.

-4

Exercise 8 – Multiply fractions

Multiply the numerators and the denominators: $-\frac{2}{3}\times \frac{3}{4} = -\frac{1}{2}$

$-\frac{1}{2}$

Exercise 9 – Negative fractions

Multiply the numerators and the denominators: $-\frac{5}{6}\times (-\frac{9}{10}) = \frac{3}{4}$

$\frac{3}{4}$

Exercise 10 – Divide fractions

Use the reciprocal: $-\frac{3}{4}\times 2 = -1\frac{1}{2}$

$-1\frac{1}{2}$

Exercises 11 and up

Exercise 11 – Divide by a negative fraction

Use the reciprocal: $-\frac{2}{5}\times (-3\frac{3}{4}) = 1\frac{1}{2}$

$1\frac{1}{2}$

Exercise 12 – Three factors

There are 3 negative factors, an odd number, so the product is negative.

$2\times 3\times 4=24$

-24

Multiply the sizes, then attach the sign.

Exercise 13 – Fraction to decimal

$7\div 8=0.875$. The division ends with a remainder of 0.

0.875, terminating

Long division steps.

Exercise 14 – Repeating decimal

Divide 5 by 11: 0.4545… The digits 45 repeat forever.

$0.\overline{45}$

The block 45 repeats.

Exercise 15 – Mixed number product

Change to fractions: $-\frac{10}{3}\times\frac{3}{2}=-\frac{30}{6}=-5$.

-5

Exercise 16 – Falling temperature

$-3.5\times 6=-21$

-21°F

Exercise 17 – Submarine descent

$-2.4\times 7.5=-18$

-18 feet

7.5 minutes at 2.4 feet per minute gives 18 feet down.

Exercise 18 – Weekly withdrawals

$-12.75\times 8=-102$

-$102

Exercise 19 – Share the debt

$-96\div 4=-24$

-$24

Exercise 20 – Average change

Sum: $-1.5+2.25-3.75+0.5=-2.5$.

$-2.5\div 4=-0.625$

-$0.625 per day

Daily changes.

Exercise 21 – Hiking down

$-\frac{3}{4}\times\frac{5}{2}=-\frac{15}{8}=-1\frac{7}{8}$

$-1\frac{7}{8}$ feet

Key facts behind this multiply divide rationals answers

Key facts

Same signs: positive. Different signs: negative.
An even number of negative factors gives a positive product; an odd number gives a negative product.
Divide by a fraction by multiplying by its reciprocal.
Division by 0 is undefined.
A fraction is a terminating decimal or a repeating decimal, found by long division.

How to use this multiply divide rationals 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.

All Grade 7 chapters: Grade 7 math.

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