Math Skills: Fractions

Lesson 2: Lesson Two-Ratios and Proportions

Section Three: More on proportions

By the way, knowing how to solve proportions is important in learning how to find a common denominator in order to add and subtract fractions (Lessons 5 and 6). The thing is, these problems are solved a little differently. For instance, how would you find the common denominator (remember, a denominator is the bottom number of a fraction) of two fractions, 4/5 and 9/12?

Just a quickie here to illustrate the use of proportion: To find the common denominator, first you figure out what number both 5 and 12 go into evenly so that it is the lowest number they both go into evenly (this number is called the "least common multiple," LCM). It turns out the lowest number both 5 and 12 go into evenly is 60. Thus, 60 will have to be the lowest common denominator (LCD) (NOTE: The LCM and the LCD are the same)

Thus to convert both 4/5 and 9/12 into fractions with a denominator of 60, you need to use a proportion with both fractions and solve the proportion, but the method is different.

4/5 = Y/60. Since 5 and 60 are the denominators and you want to find the appropriate numerator for the fraction over 60, think: 5 x 12 = 60. To find the numerator over 60, think (using the first numerator, 4) 4 x 12 = 48. Thus, the proportion becomes 4/5 = 48/60.

9/12 = Y/60. Since 12 x 5 = 60, use the 9 in the numerator of the first fraction and the 5 you used to get 60 from 12, to get 9 x 5 = 45. Thus, 9/12 = 45/60.

Then you can now add the two fractions: 48/60 + 45/60 = (48 + 45)/60 = 93/60 (which can then be reduced to 1 33/60 or 1 11/20)

More about that in Lesson 5.

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