Algebra 1 : How to add integers

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #11 : How To Add Integers

Solve: \(\displaystyle 312+99\)

Possible Answers:

\(\displaystyle 412\)

\(\displaystyle 401\)

\(\displaystyle 411\)

\(\displaystyle 391\)

\(\displaystyle 421\)

Correct answer:

\(\displaystyle 411\)

Explanation:

Add the ones digit.  

\(\displaystyle 2+9=11\)

Carry over the 1 since 11 is ten or greater, and then add the tens digit with the carryover.

\(\displaystyle 1+9+(1)=11\)

Repeat the process for the hundreds digit with the carry over.

\(\displaystyle 3+(1)=4\)

Combine all the digits.

The answer is \(\displaystyle 411\).

Example Question #12 : How To Add Integers

Find the sum of \(\displaystyle -8+(-6)\).

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle -2\)

\(\displaystyle -14\)

\(\displaystyle 2\)

\(\displaystyle 86\)

Correct answer:

\(\displaystyle -14\)

Explanation:

Since we are adding two negative numbers, the sign of the answer becomes negative. The overall answer is negative; however, we will treat this problem as a normal addition.

\(\displaystyle 8+6=14\)

The sum is \(\displaystyle 14\) and we add the negative sign in front to get a final answer of \(\displaystyle -14\).

Therefore,\(\displaystyle -8+(-6)=-14\).

Example Question #13 : How To Add Integers

Find the sum of \(\displaystyle 28+(-23)\).

Possible Answers:

\(\displaystyle -51\)

\(\displaystyle 5\)

\(\displaystyle 51\)

\(\displaystyle -5\)

\(\displaystyle 16\)

Correct answer:

\(\displaystyle 5\)

Explanation:

Since there are negative numbers, we compare their values without the sign. \(\displaystyle 28\) is greater than \(\displaystyle 23\) and is positive. This means the answer is positive and we will treat this problem as normal subtraction.

\(\displaystyle 28-23=5\)

The difference and our final answer is \(\displaystyle 5\).

Therefore, \(\displaystyle 28+(-23)=5\).

Example Question #11 : How To Add Integers

What is the sum of the integers \(\displaystyle 16\) and \(\displaystyle 54\)?

Possible Answers:

\(\displaystyle 48\)

\(\displaystyle 80\)

\(\displaystyle 70\)

\(\displaystyle 60\)

\(\displaystyle 38\)

Correct answer:

\(\displaystyle 70\)

Explanation:

Since there are no negative numbers, we will simply add as normal.

\(\displaystyle 16+54=70\)

We get an answer of \(\displaystyle 70.\)

 

Example Question #141 : Integer Operations

What is the sum of the integers \(\displaystyle 12\)\(\displaystyle 13\), and \(\displaystyle 9\)

Possible Answers:

\(\displaystyle 115\)

\(\displaystyle 44\)

\(\displaystyle 18\)

\(\displaystyle 34\)

\(\displaystyle 8\)

Correct answer:

\(\displaystyle 34\)

Explanation:

Since there are no negative numbers, we will simply add as normal. Make sure to line up all the ones digit in place and the tens digit.

\(\displaystyle 12+13+9=34\)

We get an answer of \(\displaystyle 34.\)

Example Question #141 : Integer Operations

What is the sum of the integers \(\displaystyle 198\) and \(\displaystyle 25\)?  

Possible Answers:

\(\displaystyle 213\)

\(\displaystyle 233\)

\(\displaystyle 223\)

\(\displaystyle 448\)

\(\displaystyle 174\)

Correct answer:

\(\displaystyle 223\)

Explanation:

Since there are no negative numbers, we will simply add as normal. Remember to line up the tens and ones digits.

\(\displaystyle 198+25=223\)

We get an answer of \(\displaystyle 223\).

Example Question #143 : Integer Operations

Find the sum of \(\displaystyle -7+9\).

Possible Answers:

\(\displaystyle 16\)

\(\displaystyle -2\)

\(\displaystyle 2\)

\(\displaystyle 8\)

\(\displaystyle -16\)

Correct answer:

\(\displaystyle 2\)

Explanation:

Since there are negative numbers in this problem, we will compare their values without the sign. \(\displaystyle 9\) is greater than \(\displaystyle 7\) and is positive. This means the answer is positive.

We will treat this problem as normal subtraction.

\(\displaystyle 9-7=2\)

 The difference and our final answer is \(\displaystyle 2\).

Therefore, \(\displaystyle -7+9=2\)

Example Question #144 : Integer Operations

Find the sum of \(\displaystyle -3+2\).

Possible Answers:

\(\displaystyle -1\)

\(\displaystyle 6\)

\(\displaystyle 5\)

\(\displaystyle -5\)

\(\displaystyle 1\)

Correct answer:

\(\displaystyle -1\)

Explanation:

Since there are negative numbers in this problem, we will compare their values without the sign. \(\displaystyle 3\) is greater than \(\displaystyle 2\) and is negative. This means the answer is negative.

We will treat this problem as normal subtraction.

\(\displaystyle 3-2=1\)

The difference is \(\displaystyle 1\), but since we want a negative answer our final answer is \(\displaystyle -1\).

Therefore, \(\displaystyle -3+2=-1\).

Example Question #145 : Integer Operations

Find the sum of \(\displaystyle -13+(-9)\).

Possible Answers:

\(\displaystyle 22\)

\(\displaystyle -4\)

\(\displaystyle 9\)

\(\displaystyle -22\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle -22\)

Explanation:

Since we are adding two negative numbers, the sign of the answer becomes negative. The overall answer is negative; however, we will treat this problem as normal addition.

\(\displaystyle 13+9=22\)

The sum is \(\displaystyle 22\) and we add the negative sign in front to get a final answer of \(\displaystyle -22\).

Therefore,\(\displaystyle -13+(-9)=-22\).

Example Question #146 : Integer Operations

Find the sum of \(\displaystyle 10+(-19)\).

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle -29\)

\(\displaystyle -9\)

\(\displaystyle 29\)

\(\displaystyle 9\)

Correct answer:

\(\displaystyle -9\)

Explanation:

Since there are negative numbers, we compare their values without the sign. \(\displaystyle 19\) is greater than \(\displaystyle 10\) and is negative. This means the answer is negative and we will treat this problem as normal subtraction.

\(\displaystyle 19-10=9\)

The difference is \(\displaystyle 9\), but since we want a negative answer our final answer is \(\displaystyle -9\).

Therefore, \(\displaystyle 10+(-19)=-9\).

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