a recipe calls for a total of $3\frac{2}{3}$ cups flour and sugar. if the recipe calls for $\frac{1}{4}$ cup…

Explanation:

Step1: Convert mixed - number to improper fraction

The total amount of flour and sugar is $3\frac{2}{3}$ cups. Convert it to an improper fraction: $3\frac{2}{3}=\frac{3\times3 + 2}{3}=\frac{9 + 2}{3}=\frac{11}{3}$ cups. The amount of sugar is $\frac{1}{4}$ cup.

Step2: Subtract amount of sugar from total

To find the amount of flour, subtract the amount of sugar from the total amount of flour and sugar. We need to calculate $\frac{11}{3}-\frac{1}{4}$. First, find a common denominator. The least - common multiple of 3 and 4 is 12. So, $\frac{11}{3}-\frac{1}{4}=\frac{11\times4}{3\times4}-\frac{1\times3}{4\times3}=\frac{44}{12}-\frac{3}{12}$.

Step3: Perform subtraction

$\frac{44}{12}-\frac{3}{12}=\frac{44 - 3}{12}=\frac{41}{12}$. Convert $\frac{41}{12}$ back to a mixed - number: $41\div12 = 3\cdots\cdots5$, so $\frac{41}{12}=3\frac{5}{12}$ cups.

Answer:

$3\frac{5}{12}$ cups