Adding Integers Practice Problems with Answers

The ten (10) practice questions below focus on adding integers. I’m hoping that it will aid in developing your integer addition skills. You get better at something the more often you do it. Have fun!

Below is a quick summary for the rules of adding integers.

rules for adding integers or rules for addition of integers when signs are the same add their absolute values then copy the common sign if the signs are different subtract their absolute values then use the sign of the integer with the bigger absolute value

Problem 1: Add the integers: [latex]2 + 7[/latex]

Answer

[latex]9[/latex]

Explanation: The two integers are both positive that means they have the same sign. It implies that we should add their absolute values and copy the common sign which is positive.


Problem 2: Add the integers: [latex]\left( { – 13} \right) + 9[/latex]

Answer

[latex]-4[/latex]

Explanation: The two integers have different signs. That means we are going to subtract their absolute values. The integer [latex]-13[/latex] has a larger absolute value than [latex]9[/latex] which means the final answer will have a negative sign.


Problem 3: Add the integers: [latex]\left( { – 7} \right) + \left( { – 8} \right)[/latex]

Answer

[latex]-15[/latex]

Explanation: Since both of the integers are negative, they have the same sign. It suggests that we should sum their absolute values and take the common, negative sign.


Problem 4: Add the integers: [latex]23 + \left( { – 6} \right)[/latex]

Answer

[latex]17[/latex]

Explanation: The integers [latex]23[/latex] and [latex]-6[/latex] have different signs which implies that we are going to subtract their absolute values. The sign of the final answer will depend on the sign of the integer with the larger absolute value which in this case is positive coming from [latex]23[/latex].


Problem 5: Add the integers: [latex]\left( { – 15} \right) + 15[/latex]

Answer

[latex]0[/latex]

Explanation: Given that the signs of the integers [latex]15[/latex] and [latex]-15[/latex] differ, we must subtract their absolute values. Since the result after subtraction is [latex]0[/latex], the sign is neither positive nor negative.


Problem 6: Add the integers: [latex]27 + \left( { – 32} \right)[/latex]

Answer

[latex]-5[/latex]

Explanation: Because the signs of [latex]27[/latex] and [latex]-32[/latex] are not the same, we must subtract their absolute values.

The final answer will have a negative sign since the absolute value of [latex]-32[/latex] is greater than the absolute value of [latex]27[/latex], therefore [latex]27 + \left( { – 32} \right) = – 5[/latex].


Problem 7: Add the integers: [latex]\left( { – 1} \right) + \left( { – 2} \right) + \left( { – 3} \right)[/latex]

Answer

[latex]-6[/latex]

Explanation: In general, when adding more than two integers we do it two at a time. However, we can do it all at once because the signs of the integers are all the same which is negative. We simply add the absolute values of the integers then copy the common negative sign.


Problem 8: Add the integers: [latex]10 + \left( { – 16} \right) + 7[/latex]

Answer

[latex]1[/latex]

Explanation: There are more than two integers to add so we are going to add them two at a time.

[latex]10 + \left( { – 16} \right) + 7[/latex] [latex]\\[/latex]

[latex]\left[ {10 + \left( { – 16} \right)} \right] + 7[/latex] [latex]\\[/latex]

[latex]\left[ { – 6} \right] + 7[/latex] [latex]\\[/latex]

[latex]1[/latex] [latex]\checkmark[/latex]


Problem 9: Add the integers: [latex]\left( { – 7} \right) + \left( { – 2} \right) + 5[/latex]

Answer

[latex]-4[/latex]

Explanation: We will add the integers two at a time because there are more than two to add.

[latex]\left( { – 7} \right) + \left( { – 2} \right) + 5[/latex] [latex]\\[/latex]

[latex]\left[ {\left( { – 7} \right) + \left( { – 2} \right)} \right] + 5[/latex] [latex]\\[/latex]

[latex]\left[ { – 9} \right] + 5[/latex] [latex]\\[/latex]

[latex] – 4[/latex] [latex]\checkmark[/latex]


Problem 10: Add the integers: [latex]12 + \left( { – 9} \right) + 12 + \left( { – 13} \right)[/latex]

Answer

[latex]2[/latex]

Explanation: This time, we have to add four integers. Let’s apply everything we know. Once more, we’ll add two integers at a time. Be careful every step of the way.

[latex]12 + \left( { – 9} \right) + 12 + \left( { – 13} \right)[/latex] [latex]\\[/latex]

[latex]\left[ {12 + \left( { – 9} \right)} \right] + 12 + \left( { – 13} \right)[/latex] [latex]\\[/latex]

[latex]3 + 12 + \left( { – 13} \right)[/latex] [latex]\\[/latex]

[latex]\left[ {3 + 12} \right] + \left( { – 13} \right)[/latex] [latex]\\[/latex]

[latex]15 + \left( { – 13} \right)[/latex] [latex]\\[/latex]

[latex]2[/latex] [latex]\checkmark[/latex]


You may also be interested in these related math lessons or tutorials:

Adding Integers