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Understanding Fractions.

Learning fractions can be rather complicated. All fractions have a top number (numerator) and a bottom number (denominator). For starters, it is worth to note that there are some problems involving fractions that require one to follow steps in order to solve them. Various basic math operations are utilized in order to be able to solve most fractions.

The four operations are addition, subtraction, multiplication, and division. For one to be proficient in fractions, they must first understand the four areas mentioned above. However, for one to be able to master fractions; a lot of practice is required. In this article, I will present various examples to demonstrate how the four math operations come into play with solving fractions.

Addition of fractions with the same denominator
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When adding five-ninths and two-ninths, you simply add the numerators of 5 and 2, which become 7. 9 is the denominator in this case and it 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 in the fractions presented above are 12 and 8. First, you must figure out the lowest number in which both 8 and 12 can be evenly multiplied into. 24 is the lowest number that can be multiplied to the denominators. 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. The other step is to add them up so as to get 18/24. In order to get the answer 18/24, they two fractions are added together.


It involves the numerator and denominator multiplication.

Multiplication of fractions;15/ 25 x 5/30 = 1/5 x 1/2 = 1/10

The two fractions can be reduced to simplest form by cross canceling out each other’s numerator and denominator. Multiply the numerators and denominators.

Dividing fractions (simple problem)

Division involves flipping of the second fraction and also changing of the division sign to multiplication sign. 11/7 results from 7/11. You will now multiply the fractions.

Fraction division to its simplest form;3/9 / 7/8 = 3/9 x 8/7 = 24/63 = 8/21

First change the second fraction by flipping it to 8/7 from 7/8. The second step is to change the sign into multiplication and then carry it out. One goes further to reduce the results obtained by determining a common factor. 24 and 63 are both divisible by 3 (greatest common factor).

How to divide fractions that are reduced to their simplest form 36/45 / 18/15 = 36/45 x 15/18 = 2/3 x 1/1 = 2/3;

Flip 18/15 into 15/18 and change the sign from division to multiplication. 15/18 and 36/45 are further reduced. Both 36(top number for the first fraction) and 18 (bottom part of the second fraction) have one common factor which is 18. The other part of the fraction is also cross cancelled because they have a common factor. Finally, the resulting fractions are multiplied to get the answer.