How to simplify a fraction - ACT Math
Card 0 of 216
What is the average of
and
?
What is the average of and
?
To average, we have to add the values and divide by two. To do this we need to find a common denomenator of 6. We then add and divide by 2, yielding 4.5/6. This reduces to 3/4.
To average, we have to add the values and divide by two. To do this we need to find a common denomenator of 6. We then add and divide by 2, yielding 4.5/6. This reduces to 3/4.
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Simplify the following expression:

Simplify the following expression:
Following this equation, you divide 4 by 8 to get 1/2. When a variable is raised to an exponent, and you are dividing, you subtract the exponents, so 6 – 3 = 3.
Following this equation, you divide 4 by 8 to get 1/2. When a variable is raised to an exponent, and you are dividing, you subtract the exponents, so 6 – 3 = 3.
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Simplify the given fraction:

Simplify the given fraction:
125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.
125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.
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Simplify:

Simplify:
With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:

Now we can see that the equation can all be divided by y, leaving the answer to be:

With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:
Now we can see that the equation can all be divided by y, leaving the answer to be:
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Simplify:

Simplify:
_x_2 – _y_2 can be also expressed as (x + y)(x – y).
Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).
This simplifies to (x – y).
_x_2 – _y_2 can be also expressed as (x + y)(x – y).
Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).
This simplifies to (x – y).
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Which of the following is equivalent to
?
Which of the following is equivalent to ?
This problem is solved the same way ½ + 1/3 is solved. For example, ½ + 1/3 = 3/6 + 2/6 = 5/6. Find a common denominator then convert each fraction into an equivalent fraction using that common denominator. The final step is to add the two new fractions and simplify.
This problem is solved the same way ½ + 1/3 is solved. For example, ½ + 1/3 = 3/6 + 2/6 = 5/6. Find a common denominator then convert each fraction into an equivalent fraction using that common denominator. The final step is to add the two new fractions and simplify.
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A train travels at a constant rate of
meters per second. How many kilometers does it travel in
minutes? 
A train travels at a constant rate of meters per second. How many kilometers does it travel in
minutes?
Set up the conversions as fractions and solve:

Set up the conversions as fractions and solve:
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Simplify. 
Simplify.
To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified
To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified
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Simplify the following expression:

Simplify the following expression:
Factor both the numerator and the denominator:

After reducing the fraction, all that remains is:

Factor both the numerator and the denominator:
After reducing the fraction, all that remains is:
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Simplify:

Simplify:
Notice that the
term appears frequently. Let's try to factor that out:

Now multiply both the numerator and denominator by the conjugate of the denominator:

Notice that the term appears frequently. Let's try to factor that out:
Now multiply both the numerator and denominator by the conjugate of the denominator:
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Change to a mixed number
Change to a mixed number
To convert from a fraction to a mixed number we must find out how many times the denominator goes into the numerator using division and the remainder becomes the new fraction.

To convert from a fraction to a mixed number we must find out how many times the denominator goes into the numerator using division and the remainder becomes the new fraction.
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Reduce the fraction:

Reduce the fraction:
The numerator and denominator are both divisible by 12. Thus, we divide both by 12 to get our final answer.
If we instead divide by another common factor, we may need to complete the process again to make sure that we have completely reduced the fraction.
In mathematical words we get the following:

The numerator and denominator are both divisible by 12. Thus, we divide both by 12 to get our final answer.
If we instead divide by another common factor, we may need to complete the process again to make sure that we have completely reduced the fraction.
In mathematical words we get the following:
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Simplify: 
Simplify:
is one third of
, so
in its simplest form is
. To reach this answer, divide both
and
by
.
is one third of
, so
in its simplest form is
. To reach this answer, divide both
and
by
.
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What is
in its simplest form?
What is in its simplest form?
To reach the answer, divide both the numerator and denominator by
. After doing that, the answer is
.
To reach the answer, divide both the numerator and denominator by . After doing that, the answer is
.
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Simplify: 
Simplify:
To find the answer, divide both the numerator and the denominator by
. The result is
.
To find the answer, divide both the numerator and the denominator by . The result is
.
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Simplify the following fraction:

Simplify the following fraction:
Find the largest number that divides into both
and 



Find the largest number that divides into both and
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Which of the following is the least common denominator for the expression below?

Which of the following is the least common denominator for the expression below?
Finding the least common denominator in rational expressions follows the same procedue as finding the least common denominator in fractions.
The least common denominator for this rational exresspion will use all terms with the highest exponents of each.
The first fraction has
as the highest term, the second fraction has
as the highest term, and the third fraction has
as the highest term. Now we combine these and get the least common denominator to be:

Finding the least common denominator in rational expressions follows the same procedue as finding the least common denominator in fractions.
The least common denominator for this rational exresspion will use all terms with the highest exponents of each.
The first fraction has as the highest term, the second fraction has
as the highest term, and the third fraction has
as the highest term. Now we combine these and get the least common denominator to be:
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Simplify the following fraction until the numerator and denominator share no factors.

Simplify the following fraction until the numerator and denominator share no factors.
To simplify a fraction you need to find all the factors that the numerator and denominator have in common. You can see that both share 2 so when you divide both by 2 you get

this is close to the answer but it asks for no common factors, it is hard to see but both of these share 7 as a common factor. When you divide both by 7 you get

To simplify a fraction you need to find all the factors that the numerator and denominator have in common. You can see that both share 2 so when you divide both by 2 you get
this is close to the answer but it asks for no common factors, it is hard to see but both of these share 7 as a common factor. When you divide both by 7 you get
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Simplify the following fraction:

Simplify the following fraction:
To simplify a fraction, find the gcf (gcd) of the numerator and denominator and divide both by the gcf (gcd). the gcf of
and
is
so:

To simplify a fraction, find the gcf (gcd) of the numerator and denominator and divide both by the gcf (gcd). the gcf of and
is
so:
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Simplify the following fraction:

Simplify the following fraction:
The first and easiest simplification for this fraction is to divide numerator and denominator by
. This gives you:

Next, notice that the two fractions do not both contain factors of
. This is because the denominator's digits, when added up come to
, which is not divisible by
. This means
is not divisible by
. Now,
is
. There is no shared
between these numbers. However, if you try, you will see that they are both divisible by
, which gives you:

This is simplest form.
The first and easiest simplification for this fraction is to divide numerator and denominator by . This gives you:
Next, notice that the two fractions do not both contain factors of . This is because the denominator's digits, when added up come to
, which is not divisible by
. This means
is not divisible by
. Now,
is
. There is no shared
between these numbers. However, if you try, you will see that they are both divisible by
, which gives you:
This is simplest form.
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