# MULTIPLYING AND DIVIDING FRACTIONS Case 2. MULTIPLICATION  Multiplying fractions is actually very easy!  You begin by placing the two fractions you.

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MULTIPLYING AND DIVIDING FRACTIONS Case 2

MULTIPLICATION  Multiplying fractions is actually very easy!  You begin by placing the two fractions you wish to multiply next to each other. Example: 1/3 x 5/8  Next you multiply the two numerators Example- the two numerators are 1 and 5 so the numerator of the answer will be 1 x 5 which is 5

MULTIPLICATION  Next multiply the two denominators together The two denominators are 3 and 8 so the denominator in the answer will be 3 x 8 which equals 24  Combine the final numerator and denominator together to get a final fraction Example- the final numerator was 5 and the final denominator was 24 so the final fraction will be 5/24.

MULTIPLICATION  The final step in multiplying fractions is to check if your final answer can be reduced Reducing means checking to see if the numerator and denominator can be divided by a common number In our case the fraction is 5/24. There is no number that you could divide 5 and 24 by. Therefore, 5/24 is the final answer. An example of a fraction that can be reduced would be 5/30. The common number that you can divide by is 5. You can divide 5 by 5 to get 1 and you can divide 30 by 5 to get 6. So the new numerator will be 1 and the new denominator will be 6. The final fraction is 1/6.

DIVISION  Dividing fractions is actually very similar to multiplying.  Before we begin you will need to know what the term reciprocal means. The reciprocal of a fraction is simply switching the numerator and the denominator. For example, the reciprocal of 5/8 is 8/5

DIVISION  Now that you know what the reciprocal of a fraction is we can learn to divide.  We will begin with the equation 5/8 ÷ 3/4. To divide a fraction, what you really want to do is multiply by the reciprocal. So we want to do 5/8 x the reciprocal of 3/4 As we mentioned earlier, the reciprocal is simply switching the numerator and denominator of a fraction. Therefore the reciprocal of 3/4 would be 4/3

DIVISION  So, if dividing fractions really means multiply by the reciprocal we want to do 5/8 x the reciprocal of 3/4. We know that the reciprocal of 3/4 is 4/3 so the equation we really want to solve is 5/8 x 4/3  From this point you simply solve the equation the exact same way you solve a multiplication problem.

DIVISION  First you multiply the numerators of 5 and 4 to get 20 and then multiply the denominators to get 24. The final fraction is 20/24. Like any multiplication problem, you have to see if the fraction can be reduced by a common number. In this case, 20 and 24 can both be divided by 4 so the new numerator will be 5 and the new denominator will be 6. The result is a final answer of 5/6  So, 5/8 ÷3/4 is 5/6.

SUMMARY  As you can see, multiplying and dividing fractions is really not too difficult.  Some key things to remember are to always make sure your fraction is reduced and also make sure you take the reciprocal in a division problem before solving the equation.

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