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Operation of Fractions.

Most children consider learning fractions to be a very complicated exercise. All fractions have a top number (numerator) and a bottom number (denominator). There are problems involving fractions which require several steps to be taken before you get to the solution. Various basic math operations are utilized in order to be able to solve most fractions.

Addition, Division, Subtraction and multiplication are the four basic math operations. In order for one not to struggle in maths, they must first gain proficiency in the four areas mentioned above. Mastering fractions require lots of practice. This article therefore aims at clearly articulating how to solve fractions while using math operations mentioned above.

Adding fractions (same denominator)
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It is only the numerators that are 2 and 5 that are added together. The denominator being the same which is 9, remains the same.
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Adding fractions (different denominator and reduced to simplest form)

The first step is to make the two denominators equal before carrying out addition. The denominators here are 8 and 12. First, you must figure out the lowest number in which both 8 and 12 can be evenly multiplied into. The lowest number would be 24. You then need to convert both 4/8 and 3/12 into fractions that will have 24 as the denominator. For 4/8, you will multiply both numbers by 3 to come up with 12/24;For 3/12, you will multiply both numbers by 2 to come up with 6/24. You will then add 12/24 and 6/24 to come up with 18/24.

How to multiply fractions;7/8 x 3/4 = 21/32

To get the answers, the denominators and numerators are multiplied.

Multiplying fractions (reduced to simplest form – cross canceling)

The two fractions can be reduced to simplest form by cross canceling out each other’s numerator and denominator. Upon reduction of the fractions, the bottom and top numbers are then multiplied to get the final answer.

Division of fractions.

Division involves flipping of the second fraction and also changing of the division sign to multiplication sign. The second fraction in the example above is 7/11 which is changed to 11/7. You will now multiply the fractions.

Dividing fractions when reducing them to the simplest form.

Begin by flipping the second fraction from 7/8 to 8/7. Then replace the division sign with the multiplication sign and carry out the operation. The results obtained which is 24/63 can further be reduced. The common factor of the resulting fraction is 3, divide both of them by it.

Dividing fractions (reduced to simplest form – cross canceling)

As always, flip the second fraction and the change the division sign. 36/45 and 15/18 can be reduced through cross canceling. Both 36(top number for the first fraction) and 18 (bottom part of the second fraction) have one common factor which is 18. Cross canceling is now done for the numerator of the second fraction (15) and the denominator of the first fraction (45). The last part is to multiply the resulting fractions.