A recipe uses 1/4 cup of sugar per batch. You have 4 cups. How many batches can you make
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We have a recipe that uses one fourth cup of sugar per batch. We have 4 cups of sugar available. The question is: how many batches can we make? This is a division problem where we divide the total sugar by the amount needed per batch.
To find how many batches we can make, we need to divide the total sugar by the amount needed per batch. This gives us the expression 4 divided by one fourth. Visually, we can represent this by showing 4 whole units, and then dividing each unit into quarters. Counting all the quarter pieces will give us our answer.
There's a mathematical rule that says dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is just flipping the numerator and denominator. So the reciprocal of one fourth is four over one. This means our division problem 4 divided by one fourth becomes 4 times four over one.
Now let's work through the calculation step by step. We start with 4 divided by one fourth. Using our rule, this becomes 4 times four over one. We can write 4 as four over one to make it clear we're multiplying fractions. When multiplying fractions, we multiply the numerators together and the denominators together. Four times four is sixteen, and one times one is one. Sixteen over one is just sixteen. So we can make sixteen batches.
Let's verify our answer visually. If we make sixteen batches, and each batch uses one fourth cup of sugar, we should use exactly four cups of sugar in total. We can show this by grouping the quarter cups. Each group of four quarter cups makes one whole cup. Since we have sixteen quarter cups, we get four whole cups. This confirms our answer of sixteen batches is correct.
In our original problem, we can make sixteen batches with four cups of sugar. Let's explore similar problems. What if we had six cups of sugar instead? We would calculate six divided by one fourth, which is six times four, giving us twenty-four batches. What if each batch needed one third cup instead? We would calculate four divided by one third, which is four times three, giving us twelve batches. The same division-by-fraction method applies to all these variations.