Simplifying Fractions

This calculator will show you step by step how to simplify a fraction that you provide, or even an expression containing fractions. It could be a numeric expression such as '3/5 + 1/2', or it could be symbolic, such as 'x/2 + 2/3'.

Once you provide a valid fraction expression, you can use the "Calculate" button, in order to see all the steps of the calculation process.

The methodology for approaching the simplification of fractions is usually the same: simplify first as many simple terms as possible (such as grouping integer values). Then the procedure will vary according to the type of fraction operations you are presented with.

How to Reduce Fractions?

Usually you will have to operate and simplify to its lowest expression anything that involves integers and fractions together. Whenever you have the sum of fractions, you will use the basic fraction addition formula:

\[\displaystyle \frac{a}{b} + \frac{c}{d} = \displaystyle \frac{ad + cb}{bd} \]

Often times, there is no need to use \(bd\) in the denominator, and you will find what is called the lowest common multiple for \(b\) and \(d\). So then, \(b \cdot d\) is a common multiple for \(b\) and \(d\), but it may not be the lowest.

What are the steps to arrive to a simplest fraction

• Step 1: The expression and identify the fractions involved, if any. If there are not fractions involved, you still can reduce the expression, but take note that not fractions are in there
• Step 2: If there are fractions involved in the expression given, you will attempt to simplify the simplest terms first, such as integer operations
• Step 3: Be mindful of PEMDAS rules, as when you go simplifying first the simplest expressions, you should strictly follow the hierarchy where for example, fraction multiplications need to be conducted BEFORE fraction additions and subtractions
• Step 4: Once you have simplified things by grouping, you may need to reduce any remaining fraction to its lowest terms

Now, for the last step, you may be wondering, how do you simplify and reduce a fraction to its simplest form. This is achieved by factoring both the numerator and denominator and cancelling any common factors they may have .

The simplification process can be daunting at times, but fortunately you can use this fraction simplifier to show all the steps, in a very organized manner

When do I need multiply fractions? How do I do it?

In the process of reduction to simplest term, when following PEMDAS sequence, you will likely have to multiply fractions first, if fraction multiplications are present in the expression. The formula you will use is:

\[\displaystyle \frac{a}{b} \times \frac{c}{d} = \displaystyle \frac{ac}{bd} \]

Make sure to simplify the multiplied expression after it is completed.

Are Fractions Useful?

Fractions are for a reason one of the first math things taught in elementary school, as it is so foundational to our understanding of numbers. Indeed you cannot really have integer numbers without fractions, the two concepts are tightly bound together.

Fractions allow us to transition into more complex objects, and without them, Math would need to restrict itself to the use of integer numbers, which are truly not sufficient to do all the Math we do today..

Example: Sum of fractions

Simplify the following fraction operation: \(\frac{1}{2} + \frac{5}{4} - \frac{4}{6}\)

Solution: In this case we just have a sum and subtraction of fractions, so we can go straight into finding a common denominator and operating it. The denominators are "2", "4" and "6", so then the common denominator is 12:

\[ \frac{1}{2} + \frac{5}{4} - \frac{4}{6} = \frac{6}{12} + \frac{15}{12} - \frac{8}{12} \] \[= \frac{6+15-8}{12} = \frac{13}{12}\]

which cannot be further simplified, as the numerator (13) and denominator (12) do not have any common factors. This concludes the calculation.

Other fraction calculators you can use

Simplifying and reducing fractions can prove to be a fundamental skill. You can try this for simplifying a fraction, which reduces to its simplest terms. Also, there is this fraction to percentage converter that can come in handy when dealing with fractions, as well as this fraction to decimal converter.

A less commonly used, but still something useful is this mixed fraction calculator. Mixed fractions are somewhat deprecated objects, as it is easier and a lot clearer to write them as regular fractions.