A recipe uses 1/5 cup of sugar per batch. You have 6 cups. How many batches can you make

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We have a recipe that uses one-fifth cup of sugar for each batch. We currently have 6 cups of sugar available. Our goal is to determine how many batches we can make with the sugar we have. To find how many batches we can make, we need to divide the total amount of sugar by the amount needed per batch. This gives us the equation: 6 divided by one-fifth. When we divide by a fraction, we multiply by its reciprocal. The reciprocal of one-fifth is five over one. So our equation becomes: 6 times 5 over 1, which simplifies to 6 times 5. Let's visualize this problem. We have 6 whole cups of sugar. If we divide each cup into fifths, we can see how many one-fifth portions we have in total. Each cup is divided into 5 equal parts. The first portion of each cup is highlighted in red, representing one batch of our recipe. By counting all these one-fifth portions across all 6 cups, we can determine how many batches we can make. Now we perform the calculation. We have 6 divided by one-fifth, which equals 6 times 5 over 1. Multiplying 6 by 5 gives us 30. This means we can make 30 batches of our recipe. To verify this answer, let's work backwards. If we make 30 batches, and each batch uses one-fifth cup of sugar, we multiply 30 by one-fifth. This gives us 30 over 5, which equals 6 cups - exactly the amount of sugar we started with. This confirms our answer is correct. Let's verify our answer and summarize the solution process. First, we identified the division problem: 6 divided by one-fifth. Second, we converted this to multiplication by the reciprocal: 6 times 5 over 1. Third, we calculated the result: 6 times 5 equals 30. Fourth, we verified our answer by working backwards: 30 times one-fifth equals 6 cups, which matches our starting amount. Therefore, we can make exactly 30 batches of our recipe with 6 cups of sugar. This step-by-step approach ensures we correctly solve division problems involving fractions.