How to Add and Subtract Integers

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Integers are whole numbers and their opposites: \(\ldots,-3,-2,-1,0,1,2,3,\ldots\). They do not include fractions or decimals. On a number line, values increase as you move right and decrease as you move left.

Adding integers

When the signs are the same, add the absolute values and keep the common sign. For example, \((-8)+(-5)=-(8+5)=-13\), while \(7+4=11\).

When the signs are different, subtract the smaller absolute value from the larger absolute value. The answer takes the sign of the number with the greater absolute value: \((-14)+9=-(14-9)=-5\).

Subtracting integers

Rewrite subtraction as adding the opposite. For example, \(5-(-9)=5+9=14\), and \(-4-7=-4+(-7)=-11\).

ACT tip

Use parentheses around negative numbers and simplify one operation at a time. Adding a positive moves right, adding a negative moves left, subtracting a positive moves left, and subtracting a negative moves right.

Adding and Subtracting Integers

Think of this lesson as more than a rule to memorize. Adding and Subtracting Integers is about number-line meaning, signs, and distance from zero. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.

Integers are easiest when you picture direction on a number line. Positive numbers move right, negative numbers move left, and absolute value measures distance from zero.

Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.

Read what is given and what is being asked.
Choose the rule that connects them.
Substitute carefully and simplify in small steps.
Check the final answer against the original question.

A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.

Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.

When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.

On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.

Free printable Worksheets

Exercises for Adding and Subtracting Integers

1) \((-9)+(-6)=\)

2) \(14+(-8)=\)

3) \((-12)+19=\)

4) \((-25)-13=\)

5) \(18-(-7)=\)

6) \((-31)+16=\)

7) \(42+(-58)=\)

8) \((-64)-(-21)=\)

9) \(75-98=\)

10) \((-120)+45=\)

11) \(36-(-44)+(-18)=\)

12) \((-27)+(-35)-(-19)=\)

13) \(82+(-46)-39=\)

14) \((-15)-(-28)+(-41)=\)

15) \(64-(-17)-93=\)

16) \((-108)+56-(-22)=\)

17) \(250+(-375)-(-80)=\)

18) \((-43)+18+(-29)-(-12)=\)

19) \(7-(-16)-25+(-9)=\)

20) \((-500)-(-230)+(-75)-125=\)

Answers

1) \((-9)+(-6)=\color{red}{-15}\)

Solution
Both numbers are negative, so add absolute values: \(9+6=15\).
Keep the negative sign: \(-15\).

2) \(14+(-8)=\color{red}{6}\)

Solution
The signs differ, so subtract: \(14-8=6\).
The larger absolute value is positive, so the answer is \(6\).

3) \((-12)+19=\color{red}{7}\)

Solution
The signs differ, so subtract: \(19-12=7\).
The larger absolute value is positive, so the answer is \(7\).

4) \((-25)-13=\color{red}{-38}\)

Solution
Rewrite as \((-25)+(-13)\).
Add absolute values and keep the negative sign: \(25+13=38\), so \(-38\).

5) \(18-(-7)=\color{red}{25}\)

Solution
Subtracting a negative means add the opposite: \(18+7\).
\(18+7=25\).

6) \((-31)+16=\color{red}{-15}\)

Solution
The signs differ, so subtract: \(31-16=15\).
The larger absolute value is negative, so \(-15\).

7) \(42+(-58)=\color{red}{-16}\)

Solution
The signs differ, so subtract: \(58-42=16\).
The larger absolute value is negative, so \(-16\).

8) \((-64)-(-21)=\color{red}{-43}\)

Solution
Rewrite as \((-64)+21\).
\(64-21=43\), and the larger absolute value is negative, so \(-43\).

9) \(75-98=\color{red}{-23}\)

Solution
Rewrite as \(75+(-98)\).
\(98-75=23\), and the larger absolute value is negative, so \(-23\).

10) \((-120)+45=\color{red}{-75}\)

Solution
Subtract absolute values: \(120-45=75\).
The larger absolute value is negative, so \(-75\).

11) \(36-(-44)+(-18)=\color{red}{62}\)

Solution
Rewrite as \(36+44+(-18)\).
\(36+44=80\), then \(80+(-18)=62\).

12) \((-27)+(-35)-(-19)=\color{red}{-43}\)

Solution
Rewrite as \((-27)+(-35)+19\).
\(-27+(-35)=-62\), then \(-62+19=-43\).

13) \(82+(-46)-39=\color{red}{-3}\)

Solution
First \(82+(-46)=36\).
Then \(36-39=-3\).

14) \((-15)-(-28)+(-41)=\color{red}{-28}\)

Solution
Rewrite as \((-15)+28+(-41)\).
\(-15+28=13\), then \(13+(-41)=-28\).

15) \(64-(-17)-93=\color{red}{-12}\)

Solution
Rewrite as \(64+17-93\).
\(64+17=81\), then \(81-93=-12\).

16) \((-108)+56-(-22)=\color{red}{-30}\)

Solution
Rewrite as \((-108)+56+22\).
\(56+22=78\), then \(-108+78=-30\).

17) \(250+(-375)-(-80)=\color{red}{-45}\)

Solution
Rewrite as \(250-375+80\).
\(250-375=-125\), then \(-125+80=-45\).

18) \((-43)+18+(-29)-(-12)=\color{red}{-42}\)

Solution
Rewrite as \((-43)+18+(-29)+12\).
Positives: \(18+12=30\). Negatives: \(-43+(-29)=-72\).
\(-72+30=-42\).

19) \(7-(-16)-25+(-9)=\color{red}{-11}\)

Solution
Rewrite as \(7+16-25-9\).
\(7+16=23\), \(23-25=-2\), and \(-2-9=-11\).

20) \((-500)-(-230)+(-75)-125=\color{red}{-470}\)

Solution
Rewrite as \((-500)+230+(-75)+(-125)\).
\(-500+230=-270\), \(-270+(-75)=-345\), and \(-345+(-125)=-470\).

How to Add and Subtract Integers