Questions: How many groups of 1/2 are in the following quantities? Type your answers in the boxes. a. 3 5/8 b. 4 1/4 c. 7 3/4

How many groups of 1/2 are in the following quantities? Type your answers in the boxes. a. 3 5/8 b. 4 1/4 c. 7 3/4
Transcript text: How many groups of $\frac{1}{2}$ are in the following quantities? Type your answers in the boxes. a. $3 \frac{5}{8}$ b. $4 \frac{1}{4}$ c. $7 \frac{3}{4}$
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Solution

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Solution Steps

Step 1: Convert mixed numbers to improper fractions
  • For part a: \( 3 \frac{5}{8} = \frac{29}{8} \).
  • For part b: \( 4 \frac{1}{4} = \frac{17}{4} \).
  • For part c: \( 7 \frac{3}{4} = \frac{31}{4} \).
Step 2: Divide each improper fraction by \( \frac{1}{2} \)
  • For part a: \( \frac{29}{8} \div \frac{1}{2} = \frac{29}{8} \times 2 = \frac{29}{4} \).
  • For part b: \( \frac{17}{4} \div \frac{1}{2} = \frac{17}{4} \times 2 = \frac{17}{2} \).
  • For part c: \( \frac{31}{4} \div \frac{1}{2} = \frac{31}{4} \times 2 = \frac{31}{2} \).
Step 3: Simplify the results
  • For part a: \( \frac{29}{4} = 7 \frac{1}{4} \).
  • For part b: \( \frac{17}{2} = 8 \frac{1}{2} \).
  • For part c: \( \frac{31}{2} = 15 \frac{1}{2} \).

Final Answer

a. \( \boxed{7 \frac{1}{4}} \)
b. \( \boxed{8 \frac{1}{2}} \)
c. \( \boxed{15 \frac{1}{2}} \)

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