One batch of walnut muffins uses 1 1/3 cups of walnuts. How many cups of walnuts are needed to make 3 3/4 batch of muffins?
A. 4 cups
B. 5 cups
C. 3 3/12 cups
D. 5 1/12 cups
The correct answer and explanation is:
Let’s solve the problem step-by-step:
Problem:
- One batch of walnut muffins requires 1 1/3 cups of walnuts.
- How many cups of walnuts are needed for 3 3/4 batches?
Step 1: Convert mixed numbers to improper fractions
- 1 1/3 cups = 1+13=33+13=431 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} cups.
- 3 3/4 batches = 3+34=124+34=1543 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4} batches.
Step 2: Multiply the walnuts per batch by the number of batches
We want: Total walnuts=43×154\text{Total walnuts} = \frac{4}{3} \times \frac{15}{4}
Multiply the numerators and denominators: =4×153×4=6012=5= \frac{4 \times 15}{3 \times 4} = \frac{60}{12} = 5
So, 5 cups of walnuts are needed.
Step 3: Match the answer to the options
- A. 4 cups
- B. 5 cups ← This is the correct answer.
- C. 3 3/12 cups
- D. 5 1/12 cups
Explanation:
This problem requires you to multiply a fractional amount by another fractional amount. When multiplying mixed numbers (like 1 1/3 and 3 3/4), it’s easier to first convert them into improper fractions. This allows straightforward multiplication of numerators and denominators.
Here, 1 1/3 cups converted to 43\frac{4}{3} cups represents the amount of walnuts per single batch. Then, multiplying by 3 3/4 batches (154\frac{15}{4}) gives the total amount of walnuts needed.
Multiplying 43\frac{4}{3} by 154\frac{15}{4}, the 4 in the numerator cancels with the 4 in the denominator, simplifying the multiplication to 153\frac{15}{3}, which is 5.
Therefore, to make 3 3/4 batches, you need 5 cups of walnuts.
Final answer: B. 5 cups