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Published byNorman Gordon Modified over 6 years ago

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MULTIPLYING AND DIVIDING FRACTIONS Case 2

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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

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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.

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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.

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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

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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

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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.

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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.

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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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