A recipe uses 1/5 cup of sugar per batch. You have 5 cups. How many batches can you make
视频信息
答案文本
视频字幕
We have a recipe problem. Each batch of our recipe needs one fifth cup of sugar. We have 5 whole cups of sugar. Our question is: how many batches can we make with 5 cups if each batch uses one fifth cup?
This word problem translates to a division equation. We need to divide our total sugar by the amount needed per batch. That means 5 divided by one fifth. But how do we divide by a fraction?
To divide by a fraction, we multiply by its reciprocal. The reciprocal of a fraction is just flipping the numerator and denominator. So the reciprocal of one fifth is five over one. Our equation becomes 5 times five over one.
Now we perform the multiplication. Five times five over one equals five times five in the numerator and one times one in the denominator. That's twenty five over one, which simplifies to twenty five. So we can make 25 batches.
Let's visualize this. If each batch needs one fifth cup, we can think of our 5 cups as being divided into portions of one fifth cup each. Each whole cup contains 5 portions of one fifth. So 5 whole cups contain 5 times 5, which is 25 portions. That confirms we can make 25 batches.
This reciprocal method works for any division by fractions. For example, three divided by one fourth is three times four over one, which equals twelve. Six divided by two thirds is six times three halves, which equals nine. The pattern is always the same: when dividing by a fraction, multiply by its reciprocal.