Questions: Sophie is baking chocolate chip cookies for her friends. The recipe for one batch requires 2 1/3 cups of flour. Sophie wants to make 1 3/4 times the recipe to have enough cookies for everyone. How many cups of flour does she need in total?

Solution Steps

To solve this problem, we need to multiply two mixed numbers: \(2 \frac{1}{3}\) and \(1 \frac{3}{4}\). The approach involves converting the mixed numbers to improper fractions, performing the multiplication, and then converting the result back to a mixed number if necessary.

We start by converting the mixed numbers to improper fractions: \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3} \] \[ 1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4} \]

Next, we multiply the two improper fractions: \[ \frac{7}{3} \times \frac{7}{4} = \frac{7 \times 7}{3 \times 4} = \frac{49}{12} \]

Now, we convert \(\frac{49}{12}\) back to a mixed number:

• The whole number part is given by \(49 \div 12 = 4\) (with a remainder).
• The remainder is \(49 - (4 \times 12) = 49 - 48 = 1\).

Thus, we can express \(\frac{49}{12}\) as: \[ 4 \frac{1}{12} \]

Final Answer