So far in our series on fractions simplified, we have covered the basic fraction terms, relationships between types of fractions, and adding and subtracting fractions. Now we take our fraction simplicity one step further with multiplying and dividing fractions. Believe it or not, multiplying and dividing fractions is even easier than adding and subtracting fractions!
Unlike addition and subtraction, when you multiply fractions, the denominators do not have to be the same. You simply multiply the numerators together, and then multiply the denominators together. For example, 3⁄4 x 2⁄5 = 6⁄20. (3 x 2 = 6 and 4 x 5 = 20)
Did you know that you can’t actually divide fractions in a simple equation? So unless you want to draw a picture for every division problem, you need a trick. You need to turn your division problem into a multiplication problem. This involves using the reciprocal of your second fraction. (The reciprocal is simply the inverse of your fraction. To get a reciprocal, just flip your fraction upside down. 2⁄3 becomes 3⁄2)
Simply rewrite the problem using the reciprocal of the second fraction. Then multiply just like you normally would to get the correct answer. For example, 1⁄4 ÷ 2⁄5 would become 1⁄4 x 5⁄2 = 5⁄8. You can find out exactly why this works in this short video.
Multiplying Mixed Numbers
Before you can multiply a mixed number, you must change it into an improper fraction. (Remember multiply the denominator by the whole number and add the numerator to find your new numerator. Your denominator will stay the same.) Once you have changed your mixed number into an improper fraction, you can multiply the numerators and denominators to get your answer. Of course, you will want to change your answer back into a mixed number by dividing when you are finished. For example: 2 3⁄4 x 4 1⁄2 = 12 3⁄8. Change 2 3⁄4 into the improper fraction 11⁄4. Then change 5 1⁄2 into 9⁄2. Now multiply 11⁄4 x 9⁄2 to get 99⁄8. Once you divide, you end up with 12 with 3 left over. Your answer then is 12 3⁄8. (Notice that this is not the same as just multiplying your fractions and then your whole numbers which would give you the answer 8 3⁄8.)
Dividing Mixed Numbers
Like multiplying mixed numbers, when dividing mixed numbers, you should change them into improper fractions first. Then find the reciprocal of the second fraction and multiply as normal. For example 3 2⁄4 ÷ 5 1⁄2 = 28⁄44. Change 3 2⁄4 into the improper fraction 14⁄4. Then change 5 1⁄2 into 11⁄2. So your new equation is 14⁄4 ÷ 11⁄2. Once you find the reciprocal, your problem becomes 14⁄4 x 2⁄11 which equals 28⁄44.
As always remember to simply all your answers by putting them in the lowest numbers possible. Multiplying and dividing fractions can be simpler than your children may think once they understand the steps needed to solve each type of problem. How do you make multiplying and dividing fractions simpler for your child?