Operations with Fractions - Basic Math
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Multiply these fractions:

Multiply these fractions:
When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

Simply the fraction to get the final answer:

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:
Simply the fraction to get the final answer:
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To subtract fractions, they need to share the same denominator. To find the same denominator, you will need to find the least common multiple of the two given denominators.
The least common denominator of 5 and 7 is 35. Remember, the number you multiply the denominator by to get the least common denominator you must also multiply by the numerator.

So the original equation becomes,

Now, subtract the numerators.

To subtract fractions, they need to share the same denominator. To find the same denominator, you will need to find the least common multiple of the two given denominators.
The least common denominator of 5 and 7 is 35. Remember, the number you multiply the denominator by to get the least common denominator you must also multiply by the numerator.
So the original equation becomes,
Now, subtract the numerators.
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Please choose the best answer for the question below.
Amanda has
pounds of cake leftover from her birthday. If she eats a third of a pound of cake, how much will she have left over?
Please choose the best answer for the question below.
Amanda has pounds of cake leftover from her birthday. If she eats a third of a pound of cake, how much will she have left over?
To tackle this question, first convert 2 and 3/4ths into a fraction.


Then, you can subtract
from
:



Then you convert to a mixed number for your final answer.
.
To tackle this question, first convert 2 and 3/4ths into a fraction.
Then, you can subtract from
:
Then you convert to a mixed number for your final answer.
.
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Please choose the best answer for the question below.
If you have three pies, and someone eats one quarter of each pie, how much pie do you have left? The answers will be expressed as mixed numbers.
Please choose the best answer for the question below.
If you have three pies, and someone eats one quarter of each pie, how much pie do you have left? The answers will be expressed as mixed numbers.
To find the answer for this problem, first figure out how much of each pie is left:


Then, because
, you know that you have
whole pies left, and a quarter besides.

To find the answer for this problem, first figure out how much of each pie is left:
Then, because , you know that you have
whole pies left, and a quarter besides.
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Determine the answer:

Determine the answer:
1. Find the least common denominator:
The lowest number that both 4 and 5 both go into is 20, making 20 the least common denominator.
2. Find the equivalent fractions using the least common denominator:


3. Subtract:

1. Find the least common denominator:
The lowest number that both 4 and 5 both go into is 20, making 20 the least common denominator.
2. Find the equivalent fractions using the least common denominator:
3. Subtract:
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To subtract fractions, they must have the same number in the denominator. Begin by simplifying
so that its denominator is
.
To simplify, divide the numerator and denominator by 6.



Then, subtract:

To subtract fractions, they must have the same number in the denominator. Begin by simplifying so that its denominator is
.
To simplify, divide the numerator and denominator by 6.
Then, subtract:
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Subtract these fractions:

Subtract these fractions:
To solve this we need to first find common denominators. We do that by multiplying the first fraction by 2 over 2 and the second fraction by 3 over 3.


Subtract these fractions to get the final answer.

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 2 over 2 and the second fraction by 3 over 3.
Subtract these fractions to get the final answer.
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Subtract these fractions:

Subtract these fractions:
To solve this we need to first find common denominators. We do that by multiplying the first fraction by 3 over 3 and the second fraction by 5 over 5.


Subtract the numerators of the fractions to get the final answer.

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 3 over 3 and the second fraction by 5 over 5.
Subtract the numerators of the fractions to get the final answer.
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Subtract these fractions:

Subtract these fractions:
To solve this we need to first find common denominators. We do that by multiplying the first fraction by 4 over 4 and the second fraction by 7 over 7.


Subtract the numerators of these fractions to get the final answer.

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 4 over 4 and the second fraction by 7 over 7.
Subtract the numerators of these fractions to get the final answer.
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Subtract these fractions:

Subtract these fractions:
To solve this we need to first find common denominators. We do that by multiplying the first fraction by 9 over 9 and the second fraction by 8 over 8.


Subtract the numerators of these fractions to get the final answer.

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 9 over 9 and the second fraction by 8 over 8.
Subtract the numerators of these fractions to get the final answer.
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Subtract these fractions:

Subtract these fractions:
To solve this we need to first find common denominators. We do that by multiplying the first fraction by 3 over 3 and the second fraction by 7 over 7.


Subtract the numerators of these fractions to get the final answer.

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 3 over 3 and the second fraction by 7 over 7.
Subtract the numerators of these fractions to get the final answer.
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Simplify 
Simplify
Find the least common denominator (LCD) and convert each fraction to the LCD and then add. Simplify as necessary.

The result is an improper fraction because the numerator is larger than the denominator and can be simplified and converted to a mix numeral.

Find the least common denominator (LCD) and convert each fraction to the LCD and then add. Simplify as necessary.
The result is an improper fraction because the numerator is larger than the denominator and can be simplified and converted to a mix numeral.
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Solve:

Solve:
The least common multiple of 2 and 9 is 18.



The least common multiple of 2 and 9 is 18.
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Simplify the following fraction:

Simplify the following fraction:
Determine the factors of both the numerator and the denominator:


We notice that 3 is a factor of both 12 and 39 so we can simplify by dividing both 12 and 39 by 3.


The result is therefore,

Determine the factors of both the numerator and the denominator:
We notice that 3 is a factor of both 12 and 39 so we can simplify by dividing both 12 and 39 by 3.
The result is therefore,
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Find the simplified result:

Find the simplified result:
Start by making both fractions into the same denominator. One option is 
Then adjust the numerators by multiplying each fraction's numerator by the other fraction's denominator:


Then add the adjusted numerators:

Then we simplify by dividing both numerator and denominator by 2:

which gives us the final result.
Start by making both fractions into the same denominator. One option is
Then adjust the numerators by multiplying each fraction's numerator by the other fraction's denominator:
Then add the adjusted numerators:
Then we simplify by dividing both numerator and denominator by 2:
which gives us the final result.
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Solve the following expression:

Solve the following expression:
The correct answer is
.
In order to start solving this problem, we need to get each term to have a common denominator.
The common denominator between 2 and 6 is 6. We can rewrite the expression and solve using the following method:

The correct answer is .
In order to start solving this problem, we need to get each term to have a common denominator.
The common denominator between 2 and 6 is 6. We can rewrite the expression and solve using the following method:
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Please read the following question thoroughly, and then choose the answer which is most correct.
If Billy has
of a gallon of water, and Bobby has
of a gallon of water, how much water do they have between the two of them?
Please read the following question thoroughly, and then choose the answer which is most correct.
If Billy has of a gallon of water, and Bobby has
of a gallon of water, how much water do they have between the two of them?
To complete this question, you need to find the least common denominator in order to add the fractions. Cross multiply the fractions so that they are in the same terms, and then add. To do this, simply multiply each fraction by the denominator of the other, over itself (so that the fraction equals 1). Follow the steps below:




To complete this question, you need to find the least common denominator in order to add the fractions. Cross multiply the fractions so that they are in the same terms, and then add. To do this, simply multiply each fraction by the denominator of the other, over itself (so that the fraction equals 1). Follow the steps below:
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Evaluate:

Evaluate:
In fractions, to add or subtract the numerator, the denominators must be equal.
Find the least common denominator, multiply the top and bottom with what was multiplied on the denominator, and simplify.

=
In fractions, to add or subtract the numerator, the denominators must be equal.
Find the least common denominator, multiply the top and bottom with what was multiplied on the denominator, and simplify.
=
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Determine the answer as a mixed number:

Determine the answer as a mixed number:
1. Find the least common denominator:
The lowest number that both 4 and 6 can go into is 12 meaning that it is the least common denominator.
2. Use the new least common denominator to create two equivalent fractions with a denominator of 12.


3. Add the two fractions together.

4. Convert the fraction to a mixed number:

1. Find the least common denominator:
The lowest number that both 4 and 6 can go into is 12 meaning that it is the least common denominator.
2. Use the new least common denominator to create two equivalent fractions with a denominator of 12.
3. Add the two fractions together.
4. Convert the fraction to a mixed number:
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What is the sum of
and
?
What is the sum of and
?
When adding two fractions, the denominators must be the same. When the denominators are the same, we merely add the numerators together to see what the sum is. The trickiest part is transforming the two fractions into fractions with the same denominator.
When we transform a fraction, we are multiplying it by
. For example,
is the same fraction as
because
. Because
, we are not changing the value of the fraction, we are merely expressing the same value in a different form. This is essential when adding fractions with different denominators.
To rewrite these fractions with the same denominator, we need to find the Least Common Denominator (LCD). In this case, the least common denominator is
, as
contains both
and
as factors. Our next step is to rewrite our two fractions as fractions with denominators of
.
To transform our first fraction,
, into a fraction with
as its denominator, we need to multiply the fraction by
.
To transform our second fraction,
, into a fraction with
as its denominator, we need to multiply the fraction by
. Therefore, our answer becomes:



When adding two fractions, the denominators must be the same. When the denominators are the same, we merely add the numerators together to see what the sum is. The trickiest part is transforming the two fractions into fractions with the same denominator.
When we transform a fraction, we are multiplying it by . For example,
is the same fraction as
because
. Because
, we are not changing the value of the fraction, we are merely expressing the same value in a different form. This is essential when adding fractions with different denominators.
To rewrite these fractions with the same denominator, we need to find the Least Common Denominator (LCD). In this case, the least common denominator is , as
contains both
and
as factors. Our next step is to rewrite our two fractions as fractions with denominators of
.
To transform our first fraction, , into a fraction with
as its denominator, we need to multiply the fraction by
.
To transform our second fraction, , into a fraction with
as its denominator, we need to multiply the fraction by
. Therefore, our answer becomes:
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