How to Solve Fractions

It looks like a headache, but in fact, as long as you know how to do it and practice a little, fractions problems will become really easy. Fractional math won’t be a problem once you get the hang of them. Let’s start with step 1, from basic addition and subtraction and then move on to more complex operations.

Table of Contents

Multiply two fractions

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Here, we work with two fractions. This instruction is only true in case you need to multiply two fractions. If you have mixed numbers, you need to first convert them to non-true fractions (fractions with numerators greater than denominators).

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Multiply numerator by numerator, denominator by denominator.

For example, to multiply 1/2 by 3/4, we take 1 times 3 and 2 times 4. The result is 3/8.

Divide two fractions

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Here, we work with two fractions. This instruction is ONLY true if all mixed numbers have been converted to non-true fractions.

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Invert the second fraction.

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Change the division sign to the multiplication sign.

For example, 8/15 3/4 will be converted to 8/15 x 4/3

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Multiply the top number by the top number, the bottom number by the bottom number.

8 x 4 equals 32 and 15 x 3 equals 45, so the final answer is 32/45.

Convert mixed numbers to real fractions

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Convert mixed numbers to real fractions. Fractions are not really fractions where the numerator is greater than the denominator (such as 17/5). When multiplying or dividing, you must first convert the mixed number into a non-real fraction before you can do the calculation.

For example, the mixed number 3 2/5 (three and two fifths).

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Multiply the integer part (not fraction) by the denominator.

Here, we’ll take 3 x 5, and get 15.

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Add the result to the numerator.

Here, we add 15 + 2 and get 17.

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Substituting the original numerator with the value obtained above, we have a fraction that is not really.

In this example, we get 17/5.

Add and subtract fractions

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Find the least common denominator (the denominator is the number below). With both addition and subtraction of two fractions, we all start with this step: Find the least common denominator of both fractions.

For example, for 1/4 and 1/6, the least common denominator is 12 (4×3=12, 6×2=12)

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Convert fractions so that they have the same denominator as the least common denominator. Remember that in doing so, we are only transforming, not changing the value of the numbers. Just like with a cake, 1/2 or 2/4 of a cake is the same.

Calculate how many times the current sample must be multiplied to equal the least common denominator. With 1/4, 4 times 3 equals 12. With 1/6, 6 times 2 equals 12.
Multiply both the numerator and denominator of the given fraction by the number above. With 1/4, you would multiply 3 by both 1 and 4 and get 3/12. The remaining 1/6 is multiplied by 2 and becomes 2/12. At this point, the problem becomes 3/12 + 2/12 or 3/12 – 2/12.

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Add or subtract the two numerators (top number) and KEEP the denominator AS. Here, we are trying to calculate how many pieces we have in total. When you add the denominators, you change the “part” itself.

With 3/12 + 2/12, the final answer will be 5/12. In the case of 3/12 – 2/12, that’s 1/12.

Advice

Basic skills in the four operations (addition, subtraction, multiplication, division) make calculations faster and easier.
To find the inverse of an integer, you simply put 1 as the numerator and convert that number to the denominator. For example, the inverse of 5 is 1/5.
You can multiply and divide mixed numbers without having to convert them to real fractions. But doing so requires the use of distributive computations in a complex and stressful way. Therefore, you’d better switch to non-real fractions for calculations.
“Invert fraction” is also “find the inverse “. You still just swap the places of the numerator and denominator. For example 2/4 will become 4/2.
Fractions never have a denominator of zero. The denominator of zero doesn’t make sense because dividing by zero is mathematically illegal.

Warning

Convert mixed numbers to real fractions before starting.
Check with your teacher to see if you are required to convert your answers to mixed numbers. Some teachers prefer answers expressed in mixed numbers, others prefer to use fractions that aren’t real.
- For example, 3 1/4 instead of 13/4.
Check with your teacher if you need to reduce your answer to the simplest fraction.
- For example, 2/5 is a simple fraction and 16/40 is not. 16/40 can be reduced to 2/5 by 16 divided by 8 equals 2 and 40 divided by 8 gives 5.8. 8 is the greatest common divisor of 16 and 40.

Steps