The Simplifying Fraction Calculator is a free online tool for simplifying a given fraction in milliseconds. The given fraction can be a proper fraction, an improper fraction or a mixed fraction. If the given fraction is an improper fraction, the final simplified form has two cases: improper fraction and mixed fraction. The same goes for the mixed fraction.
How to simplify fractions?
There are several steps to simplify the fraction:
- Find the greatest common divisor of the numerator and denominator, which is the most critical step.
- Divide the numerator by the greatest common divisor to get a new numerator.
- Divide the denominator by the greatest common divisor to get a new denominator.
- Use the new numerator and denominator to form a new fraction, which is the simplified form.
Note that the new fraction after simplification is equivalent to the original fraction.
For example, Convert 48 to its simplest form.
- Find out the greatest common divisor of 4 and 8, which is 4.
- Get the new numerator, 4 ÷ 4 = 1.
- Get the new denominator, 8 ÷ 4 = 2.
- So, the simplified form of 48 is 12.
For improper fractions, the simplification steps are the same. The final result can be converted into the simplest mixed fraction according to actual needs.
For example, Convert 208 to its simplest form.
The greatest common divisor of 20 and 8 is 4.
208 = 20 ÷ 48 ÷ 4 = 52 = 212
If it is a mixed fraction, you need to convert the mixed fraction into an improper fraction first. Then follow the steps above.
For example, Convert 168 to its simplest form.
First, convert the mixed fraction to an improper fraction.
168 = 148
Then follow the 4 steps above to simplify.
148 = 14 ÷ 28 ÷ 2 = 74 = 134
In a word, manual simplification is possible, but it is more troublesome, especially when the numerator and denominator are large. So, we have developed this online free simplifying fraction calculator that not only calculates simplified results in milliseconds, but also display the specific calculation steps. Let’s look at how the simplified fraction calculator is used.
How to use simplifying fractions calculator
The Simplifying Fraction Calculator is easy to use and requires only 2 steps:
- Enter values in the corresponding input fields. Note that in order to support mixed fractions, we keep the whole number input box. If you want to simplify a proper fraction or an improper fraction, you only need to enter the numerator and denominator, and the whole number input box does not need to be entered.
- Click the Calculate button to get the result. Press the Reset button to prepare for another calculation.
Next, let’s take a few examples to see how this calculator is used.
Solved examples using simplifying fractions calculator
Simplify the proper fraction
For example, simplify 1525
- Find out the greatest common divisor of 15 and 25, which is 5.
- Calculate the new numerator, 15 ÷ 5 = 3.
- Calculate the new denominator, 25 ÷ 5 = 5.
- So, the simplified form of 1525 is 35.
Simplify the improper fraction
For example, simplify 3012
- Find out the greatest common divisor of 30 and 12, which is 6.
- Calculate the new numerator, 30 ÷ 6 = 5.
- Calculate the new denominator, 12 ÷ 6 = 2.
- So, the simplified form of 3012 is 52. Convert to the mixed fraction is 212.
Simplify the mixed fraction
For example, simplify 246
First, convert the mixed fraction to an improper fraction.
246 = 166
Then follow the 4 steps above to simplify.
- Find out the greatest common divisor of 16 and 6, which is 2.
- Calculate the new numerator, 16 ÷ 2 = 8.
- Calculate the new denominator, 6 ÷ 2 = 3.
- So, the simplified form of 246 is 83. Convert to the mixed fraction is 223.
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