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Lesson 46: Solving Problems Involving Fractions
You've learned the basics of fractions in previous lessons. There is a great deal to know about them, and in this lesson you'll learn a bit more.
Very often we are asked to compute a fraction of a whole number. For example, if you have 12 pencils, you might need to compute how many 1/4 (one-fourth) of them are.
There are a few ways of solving this problem. The first way is to divide the 12 into four equal groups. If you do this using counters, you'll see that each group has 3. That means that 3 is 1/4 of 12, so our answer is 3.
Another of solving this problem is to just do division, and do 12 ÷ 4 = 3. Important, this only works if the problem involves a fraction with 1 in the numerator, like 1/4. If the problem asked you to find 3/4 of the pencils, you would need to do an additional step.
Yet another way of solving the problem, and the way that will work no matter what fraction is involved, is to multiply. Here is what we do: First multiply the whole number times the numerator of the fraction. That's 12 x 1 = 12. Make that the new numerator, and keep the denominator the same. So we have 12/4. Now, a fraction is really just a division problem. 12/4 (twelve-fourths) means 12 ÷ 4, and the answer is 3.
Let's try a more tricky problem. Let's find 3/4 of 12. We'll use the multiplication method above, which works for any fraction. We'll multiply 12 times the numerator, which is 12 x 3 = 36, and we'll place that over the denominator of 4. So we have 36/4. Do 36 ÷ 4 to get 9. To check your answer, divide 12 counters into 4 equal groups. You will have 3 in each group. Count how many are in three of those groups, and there are 9.
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