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How to Express a Ratio as A Fully Simplified Fraction - Help with Simplifying Fractions

By Edited Nov 13, 2013 1 0

In mathematics, a ratio is the relationship between two amounts. If there are thirty men and twenty women in the room, then the ration of men to women is 20 to 30. If the amount of men increased, then the amount of women would also increase. Ratios can be expressed as fractions, and it is important to know how. Moreover, it is important to know how to simplify your answer.

Step one: Convert units. If your ratio deals with interchangeable units, such as feet and inches, it is easier to work with the ratio when all the units are the same. Example: 2 feet to 10 inches. Here the ratio has two units: feet, and inches. Let's change them both to inches. Since there are twelve inches in a foot, and there are two feet, then we can replace 2 feet with 24 inches. Therefore: 24 inches to 10 inches

Step two: Drop the units. When we are working with fractions, units are simply a bother. Right now, focus on the numbers. Therefore 24 inches to 10 inches is now just 24 to 10.

Step three: Change the form of the ratio. Rather than expressing your ratio as 24 to 10 or 24 : 10, express the two numbers in the form of a fraction. The numerator in the fraction is always the first number in the ratio. So, 24 to 10 becomes 24/10.

Step four: See if the denominator of the fraction can evenly divide into the numerator of the fraction, or, in this case, see if 10 can evenly divide into 24. If it can, then the quotient of the numerator and the denominator is your fully simplified answer. If it cannot, move to step five.

Step five: Simplify your answer. In order to do this, you need to reduce your two numbers into their simplest factors. For example, 24 can be expressed as 3x8, and while 3 cannot be broken down any further, 8 can be expressed as 2x2x2. Therefore 24=3x2x2x2. As for 10, 10=2x5. 24 and 10 share only one factor, and that is 2. Therefore, we remove one two from each. 24 becomes 3x2x2, and 10 becomes 5. Since 3x2x2 equals 12, and 5=5, the fraction becomes 12/5. This is fully simplified.


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