Algebra 1 : Integer Operations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #141 : Real Numbers

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

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 44\)

\(\displaystyle 18\)

\(\displaystyle 115\)

\(\displaystyle 34\)

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:

\(\displaystyle 174\)

\(\displaystyle 223\)

\(\displaystyle 233\)

\(\displaystyle 213\)

\(\displaystyle 448\)

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 #142 : Integer Operations

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

Possible Answers:

\(\displaystyle -2\)

\(\displaystyle -16\)

\(\displaystyle 2\)

\(\displaystyle 8\)

\(\displaystyle 16\)

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 #143 : Real Numbers

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

Possible Answers:

\(\displaystyle -1\)

\(\displaystyle 5\)

\(\displaystyle -5\)

\(\displaystyle 6\)

\(\displaystyle 1\)

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 #144 : Real Numbers

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

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle -4\)

\(\displaystyle 9\)

\(\displaystyle 22\)

\(\displaystyle -22\)

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 #13 : How To Add Integers

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

Possible Answers:

\(\displaystyle -9\)

\(\displaystyle 29\)

\(\displaystyle 9\)

\(\displaystyle 14\)

\(\displaystyle -29\)

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, \(\displaystyle 10+(-19)=-9\).

Example Question #2603 : Algebra 1

Find the sum of \(\displaystyle 1+7+(-9)\).

Possible Answers:

\(\displaystyle 15\)

\(\displaystyle -1\)

\(\displaystyle -15\)

\(\displaystyle 3\)

\(\displaystyle 1\)

Correct answer:

\(\displaystyle -1\)

Explanation:

Let's add the left side first.

\(\displaystyle 1+7=8\)

We get \(\displaystyle 8\). Since there are negative numbers in this problem, we will compare their values without the sign. \(\displaystyle 9\) is greater than \(\displaystyle 8\) and is negative. This means the answer is negative. We will treat this problem as normal subtraction.

\(\displaystyle 9-8=1\)

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

Therefore, \(\displaystyle 1+7+(-9)=-1\).

Example Question #21 : How To Add Integers

Find the sum of \(\displaystyle 123+(-84)+(-38)\).

Possible Answers:

\(\displaystyle 1\)

\(\displaystyle -1\)

\(\displaystyle 245\)

\(\displaystyle -245\)

\(\displaystyle -13\)

Correct answer:

\(\displaystyle 1\)

Explanation:

Let's work from left to right. Since there are negative numbers, we compare their values without the sign. \(\displaystyle 123\) is greater than \(\displaystyle 84\) and is positive. This means the answer to \(\displaystyle 123+(-84)\) is positive. We will treat this section of the problem as normal subtraction.

\(\displaystyle 123-84=39\)

The difference and answer is \(\displaystyle 39\).

We will continue this problem using the same method.  Since there are negative numbers, we compare their values without the sign. \(\displaystyle 39\) is greater than \(\displaystyle 38\) and is positive. This means the answer will be positive. We will treat this problem as normal subtraction.

\(\displaystyle 39-38=1\)

The difference and final answer is \(\displaystyle 1\).

Therefore, \(\displaystyle 123+(-84)+(-38)=1\).

Example Question #21 : How To Add Integers

Find the sum of \(\displaystyle -76+(-45)+121\).

Possible Answers:

\(\displaystyle 2\)

\(\displaystyle -1\)

\(\displaystyle 0\)

\(\displaystyle 1\)

\(\displaystyle -2\)

Correct answer:

\(\displaystyle 0\)

Explanation:

Let's work from left to right. Since we are adding two negative numbers, the sign becomes negative and the overall answer is negative. We will then treat this section of problem as normal addition.

\(\displaystyle 76+45=121\)

The sum is \(\displaystyle 121\) and we add the negative sign in front to get a final answer of \(\displaystyle -121\).

Now we add to a positive \(\displaystyle 121\).

\(\displaystyle (-121)+121=0\)

The final sum is \(\displaystyle 0\)

Therefore, \(\displaystyle -76+(-45)+121=0\).

Example Question #2611 : Algebra 1

What is the following sum:

\(\displaystyle 88\%+\frac{2}{3}+4.75\)

Possible Answers:

\(\displaystyle 6.29\)

\(\displaystyle 6\)

\(\displaystyle 6\frac{89}{300}\)

\(\displaystyle 6.3\)

\(\displaystyle 5.995\)

Correct answer:

\(\displaystyle 6\frac{89}{300}\)

Explanation:

We will convert everything to fractions:

\(\displaystyle 88\%+\frac{2}{3}+4.75=\frac{88}{100}+\frac{2}{3}+4\frac{3}{4}=\frac{22}{25}+\frac{2}{3}+\frac{3}{4}+4=\frac{264}{300}+\frac{200}{300}+\frac{225}{300}+4\)

\(\displaystyle \frac{264}{300}+\frac{200}{300}+\frac{225}{300}+4=4\frac{689}{300}=6\frac{89}{300}\)

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