William only has 1 3/4 cups of flour, so he can only make 2/3 of a batch of biscuits. How much flour is needed for a full batch of biscuits
The Correct Answer and Explanation is:
To find how much flour is needed for a full batch of biscuits, we use the information that:
William has 1 3/4 cups of flour, and that is only enough to make 2/3 of a batch.
Step 1: Convert the mixed number to an improper fraction.
1 3/4 = 74\frac{7}{4}
Step 2: Set up the proportion.
If 74\frac{7}{4} cups makes 23\frac{2}{3} of a batch, then we can find the flour needed for a whole batch by dividing 74\frac{7}{4} by 23\frac{2}{3}: 74÷23=74×32=218\frac{7}{4} \div \frac{2}{3} = \frac{7}{4} \times \frac{3}{2} = \frac{21}{8}
Step 3: Convert 218\frac{21}{8} to a mixed number.
218=258\frac{21}{8} = 2 \frac{5}{8}
✅ Final Answer:
A full batch of biscuits requires 2 5/8 cups of flour.
📚 Explanation
To solve this problem, we use a proportion to scale up from a part of a batch to a whole batch. William has 1 3/4 cups of flour, and this amount only allows him to make 2/3 of a full batch. This means the full batch must require more flour than he currently has.
The first step is to convert 1 3/4 to an improper fraction so that calculations are easier. 1 3/4 equals 7/4. We are told that this amount of flour (7/4 cups) makes 2/3 of a batch. We want to know how much flour would be needed to make a whole batch, so we divide the amount of flour by the fraction of the batch it produces.
Dividing by a fraction is the same as multiplying by its reciprocal. So, we divide 7/4 by 2/3, which is the same as multiplying 7/4 by 3/2. This gives us 21/8, which is the amount of flour needed for a full batch.
To better understand this number, we convert 21/8 into a mixed number. 21 divided by 8 is 2 with a remainder of 5, so the result is 2 5/8.
Therefore, a full batch of biscuits requires 2 5/8 cups of flour. This type of problem is common in cooking or baking, where recipes are scaled up or down depending on how much of an ingredient is available. Using ratios or proportions is a reliable method to solve such real-life math situations.
