GRE Adding Fractions with the Same or Different Denominators

Dividing Fractions

Dividing fractions is almost the same as multiplying fractions, but with one curious twist. You don't actually do any dividing! Instead, you multiply the first term by the reciprocal (see the chart at the beginning of Chapter 3) of the second term. The product of that operation is your answer. So 5/6 ÷ 2/3 becomes 5/6x 3/2 , which equals 15/12 If this were the answer to a number entry question, you'd just type 15 in the numerator box and 12 in the denominator box. If it's for a multiple-choice question, you may have to reduce the improper fraction and change it to a mixed number to find it in the choices: 15/12=5/4=1and1/4

Least Common Denominator

First, you find the LCD, which in this case is 30 because 30 is the smallest number that 5, 6, and 3 go into. Next, you find out how many times each of the denominators goes into 30. Five goes in 6 times, six goes in 5 times, and three goes in 10 times. Then you multiply each numerator by the number you multiplied its denominator by. Four times six is 24 , one times five is 5 , and two times ten is 20 . Finally, you take all the newly multiplied numerators, add them together, and put that sum over a denominator of 30, like this: 24/ 30 plus 5 / 30 plus 20 / 30 equals 49 / 30.

Multiplying Fractions

Multiplying fractions is a piece of cake because you don't need a common denominator. For this operation you simply multiply the numerators together, then the denominators, and there's your answer. Here's a quick example. 5/9 x 3/4 Five times three makes your numerator 15 , and nine times four makes your denominator 36 . The numerator and denominator in the fraction 15/36 have a common factor of 3 , so you can reduce the fraction to 5/12 for multiple-choice questions. And don't forget: you don't have to reduce a fraction if you're answering a number entry problem. 15/36 = 5/12

Subtracting Fractions

Our next stop on this journey is subtracting fractions. Subtracting fractions follows the same rules as those for adding fractions except you subtract instead of add. First, make sure that all fractions have the same denominator, and if they don't, figure out the LCD and convert each fraction accordingly. Then, subtract the numerators and place the difference over the denominator that they have in common.

4/5+ 1/6+2/3=?

You simply add the numerators together and place the sum over the denominator that they have in common. If you have to solve the problem 3/5 + 1/5, you simply add the numerators 3 and 1 and place the sum over the denominator 5. The answer is 4/5. Remember, however, that you don't add denominators, only the numerators. 3/5+ 1/5 = 4/5