/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 A cake recipe calls for \(3 \fra... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 20

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

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

Step by step solution

01

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}) \\]
02

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} \\]
03

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} \\]
04

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.

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Most popular questions from this chapter

Perform the indicated operation. \(-1 \frac{2}{5}+2 \frac{9}{10}\)
Perform the indicated operation. \(-5 \frac{2}{5}+\left(-6 \frac{4}{9}\right)\)
Solve equation for the unknown quantity. Check your answers. \(2 \frac{1}{3}+x=5 \frac{5}{6}\)
Multiply and write your answer as a mixed number, if necessary. a. \(3 \frac{2}{3} \cdot 1 \frac{4}{5}\) b. \(-2 \frac{2}{15} \cdot 4 \frac{1}{2}\) c. \(2 \frac{4}{11} \cdot 4 \frac{2}{5}\) d. \(\left(-5 \frac{3}{8}\right) \cdot(-24)\)
Perform the indicated operation. \(3 \frac{1}{3}+1 \frac{1}{6}\)
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