Question

A cake recipe calls for \(3 \frac{1}{2}\) cups of flour, \(1 \frac{1}{4}\) cups of brown sugar, and \(\frac{5}{8}\) cup of white sugar. What is the total amount of dry ingredients?

Short answer

Answer: The total amount of dry ingredients is \(5 \frac{3}{8}\) cups.

Step-by-step solution

Convert mixed numbers to improper fractions

First, let's convert the mixed numbers (3 1/2 and 1 1/4) to improper fractions. For 3 1/2: \\[ (3 \times 2) + 1 = \frac{7}{2} \\] For 1 1/4: \\[ (1 \times 4) + 1 = \frac{5}{4} \\] So now we have fractions: \\[ \frac{7}{2} (\text{flour}) + \frac{5}{4} (\text{brown sugar}) + \frac{5}{8} (\text{white sugar}) \\]

Find a common denominator

We need to find a common denominator for the fractions so we can add them together. The lowest common denominator for 2, 4, and 8 is 8. So, we need to convert the fractions with denominators of 2 and 4 to equivalent fractions with a denominator of 8. For 7/2: \\[ \frac{7}{2} \times \frac{4}{4} = \frac{28}{8} \\] For 5/4: \\[ \frac{5}{4} \times \frac{2}{2} = \frac{10}{8} \\]

Add the fractions

Now that all of the fractions have a common denominator of 8, we can add them together. \\[ \frac{28}{8} + \frac{10}{8} + \frac{5}{8} = \frac{(28+10+5)}{8} = \frac{43}{8} \\]

Convert improper fraction back to mixed number

Finally, let's convert the improper fraction back to a mixed number to represent the total amount of dry ingredients. \\[ \frac{43}{8} = 5\frac{3}{8} \\] So, the total amount of dry ingredients is \(5 \frac{3}{8}\) cups.