Integer Operations - Algebra 1
Card 0 of 20
Add:
Add:
When adding complex numbers, add the real parts and the imaginary parts separately to get another complex number in standard form.
Adding the real parts gives 
, and adding the imaginary parts gives 
.
When adding complex numbers, add the real parts and the imaginary parts separately to get another complex number in standard form.
Adding the real parts gives
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Subtract:
Subtract:
This is essentially the following expression after translation:
Now add the real parts together for a sum of 
, and add the imaginary parts for a sum of 
.
This is essentially the following expression after translation:
Now add the real parts together for a sum of
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Multiply:
Answer must be in standard form.
Multiply:
Answer must be in standard form.
The first step is to distribute which gives us:
which is in standard form.
The first step is to distribute which gives us:
which is in standard form.
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What is the following sum:
What is the following sum:
We will convert everything to fractions:
We will convert everything to fractions:
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Solve the expression 
.
Solve the expression
Adding a negative is the same as subtraction.
Adding a negative is the same as subtraction.
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What is the sum of all of the even integers from 2 to 2,000, inclusive?
What is the sum of all of the even integers from 2 to 2,000, inclusive?
Pair the numbers as follows:
...
There are 500 such pairs, so adding all of the even integers from 2 to 2,000 is the same as taking 2,002 as an addend 500 times. This can be rewritten as a multiplication.
Pair the numbers as follows:
...
There are 500 such pairs, so adding all of the even integers from 2 to 2,000 is the same as taking 2,002 as an addend 500 times. This can be rewritten as a multiplication.
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The Venn diagram depicts the number of students taking Spanish and Japanese classes. How many students in total are taking Japanese class?
The Venn diagram depicts the number of students taking Spanish and Japanese classes. How many students in total are taking Japanese class?
There are 48 students taking only Japanese and 15 students taking both Japanese and Spanish. The total number taking Japanese classes is the sum of these two groups.
There are 48 students taking only Japanese and 15 students taking both Japanese and Spanish. The total number taking Japanese classes is the sum of these two groups.
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Simplify
Simplify
When adding integers first consider the signs of the numbers being added. Then simply work right to left. 
So the answer is 
When adding integers first consider the signs of the numbers being added. Then simply work right to left.
So the answer is
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Consider the expression:
If you know the value of 
and 
, then in which order would you carry out the four operations in this expression in order to evaluate it?
Consider the expression:
If you know the value of
According to the order of operations:
Work any operation in parentheses first - here it would be the addition.
What remains would be an exponent (the squaring), a division, and a subtraction, which, according to the order of operations, would be worked in that order.
According to the order of operations:
Work any operation in parentheses first - here it would be the addition.
What remains would be an exponent (the squaring), a division, and a subtraction, which, according to the order of operations, would be worked in that order.
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Solve: 
Solve:
To solve 
, first add the ones digit.
The ones digit is 4. Since 14 is ten or greater, carry the tens digit to the next number.
Add the tens digit with the one carried over.
The tens digit is 1. Since 11 is ten or greater, carry the tens digit to the next number. There are no hundreds digit with 98. Add both the thousands and hundreds digit to the carry over.
Combine this with the tens and ones digits.
The answer is: 
To solve
The ones digit is 4. Since 14 is ten or greater, carry the tens digit to the next number.
Add the tens digit with the one carried over.
The tens digit is 1. Since 11 is ten or greater, carry the tens digit to the next number. There are no hundreds digit with 98. Add both the thousands and hundreds digit to the carry over.
Combine this with the tens and ones digits.
The answer is:
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Solve: 
Solve:
Add the ones digit.
Carry over the 1 since 11 is ten or greater, and then add the tens digit with the carryover.
Repeat the process for the hundreds digit with the carry over.
Combine all the digits.
The answer is 
.
Add the ones digit.
Carry over the 1 since 11 is ten or greater, and then add the tens digit with the carryover.
Repeat the process for the hundreds digit with the carry over.
Combine all the digits.
The answer is
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What is the sum of the integers 
and 
?
What is the sum of the integers
Since there are no negative numbers, we will simply add as normal.
We get an answer of 
Since there are no negative numbers, we will simply add as normal.
We get an answer of
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What is the sum of the integers 
, 
, and 
?
What is the sum of the integers
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.
We get an answer of 
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.
We get an answer of
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What is the sum of the integers 
and 
?
What is the sum of the integers
Since there are no negative numbers, we will simply add as normal. Remember to line up the tens and ones digits.
We get an answer of 
.
Since there are no negative numbers, we will simply add as normal. Remember to line up the tens and ones digits.
We get an answer of
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Find the sum of 
.
Find the sum of
Since there are negative numbers in this problem, we will compare their values without the sign. 
is greater than 
and is negative. This means the answer is negative.
We will treat this problem as normal subtraction.
The difference is 
, but since we want a negative answer our final answer is 
.
Therefore, 
.
Since there are negative numbers in this problem, we will compare their values without the sign.
We will treat this problem as normal subtraction.
The difference is
Therefore,
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Find the sum of 
.
Find the sum of
Since there are negative numbers in this problem, we will compare their values without the sign. 
is greater than 
and is positive. This means the answer is positive.
We will treat this problem as normal subtraction.
The difference and our final answer is 
.
Therefore, 
.
Since there are negative numbers in this problem, we will compare their values without the sign.
We will treat this problem as normal subtraction.
The difference and our final answer is
Therefore,
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Find the sum of 
.
Find the sum of
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.
The sum is 
and we add the negative sign in front to get a final answer of 
.
Therefore,
.
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.
The sum is
Therefore,
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Find the sum of 
.
Find the sum of
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.
The sum is 
and we add the negative sign in front to get a final answer of 
.
Therefore,
.
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.
The sum is
Therefore,
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Find the sum of 
.
Find the sum of
Since there are negative numbers, we compare their values without the sign. 
is greater than 
and is negative. This means the answer is negative and we will treat this problem as normal subtraction.
The difference is 
, but since we want a negative answer our final answer is 
.
Therefore, 
.
Since there are negative numbers, we compare their values without the sign.
The difference is
Therefore,
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