7th Grade Adding and Subtracting Rational Numbers Worksheet Solutions (PDF)

7th Grade math worksheet solutions: Adding and Subtracting Rational Numbers – Maths PDF

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This add subtract rationals answers for 7th Grade covers adding and subtracting rational numbers (Common Core 7.NS.A.1), with a free PDF to print.

Use this answer key to check your work on the adding 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.1

Add subtract rationals answers: exercises 1 to 10

Exercise 1 – Add with opposite signs

$-5 + 8 = 3$

The jump ends at 3.

Exercise 2 – Positive plus negative

$7 + (-12) = -5$

-5

Exercise 3 – Two negatives

$-6 + (-9) = -15$

-15

Exercise 4 – Subtract to a negative

Rewrite as adding the opposite: $4 + (-9)$

$= -5$

-5

Exercise 5 – Negative minus positive

Rewrite as adding the opposite: $-3 + (-8)$

$= -11$

-11

Exercise 6 – Subtract a negative

Rewrite as adding the opposite: $-7 + 4$

$= -3$

-3

Subtracting -4 moves 4 units right.

Exercise 7 – Opposites

The two numbers are opposites, the same distance from 0 on opposite sides.

$-\frac{3}{4}+\frac{3}{4}=0$

0; a number plus its opposite is 0

Exercise 8 – Distance on a number line

$|7-(-4)|=|7+4|=11$

11 units

Exercise 9 – Add decimals

The signs differ: $8.2-3.6=4.6$. The positive number is larger in size.

4.6

Exercise 10 – Subtract decimals

$-1.75-2.5=-1.75+(-2.5)$. The signs are the same: $1.75+2.5=4.25$.

-4.25

Exercises 11 and up

Exercise 11 – Unlike fractions

Use a common denominator 6.

$-\frac{1}{2} + \frac{1}{3} = -\frac{1}{6}$

$-\frac{1}{6}$

Exercise 12 – Subtract a negative fraction

Use a common denominator 12.

$\frac{2}{3} – (-\frac{1}{4}) = \frac{11}{12}$

$\frac{11}{12}$

Exercise 13 – Mixed numbers

Use a common denominator 4.

$-2\frac{1}{2} + 4\frac{3}{4} = 2\frac{1}{4}$

$2\frac{1}{4}$

Exercise 14 – Negative fractions

Use a common denominator 6.

$-\frac{5}{6} – \frac{1}{2} = -1\frac{1}{3}$

$-1\frac{1}{3}$

Exercise 15 – Temperature rise

$-8+15=7$

7°F

Exercise 16 – Overdrawn account

$42.50-65.75=-23.25$

-$23.25 (overdrawn by $23.25)

Balance after the check.

Exercise 17 – Submarine

$-120+45=-75$

$-75-80=-155$

-155 feet

Exercise 18 – Football yardage

$12-7-15+9=-1$

a loss of 1 yard ($-1$)

Exercise 19 – Diver and bird

$|62.25-(-35.5)|=62.25+35.5=97.75$

97.75 feet

Exercise 20 – Account balance

$-18.40+50=31.60$

$31.60-22.35=9.25$

$9.25-9.80=-0.55$

-$0.55

Balance after each step.

Key facts behind this add subtract rationals answers

Key facts

Opposites add to 0: $p + (-p) = 0$.
Same signs: add sizes and keep the sign. Different signs: subtract sizes and keep the sign of the larger size.
Subtracting $q$ means adding the opposite of $q$.
$|p|$ is the distance from p to 0.
The distance between p and q on a number line is $|p – q|$.

How to use this add subtract 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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