Question

unit: fractions and mixed numbers
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question #2: 5/60/31
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rosa has $3\frac{3}{4}$ pounds of dough. she uses $\frac{1}{8}$ of a pound for one roll.
how many rolls could be made from rosas dough?
\\( 3\frac{1}{6} \\)
9
18
30

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \( 3\frac{3}{4} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 3\frac{3}{4} \), we have \( \frac{3\times4 + 3}{4}=\frac{12 + 3}{4}=\frac{15}{4} \).

Step2: Divide by the amount per roll

To find the number of rolls, we divide the total amount of dough by the amount used per roll. That is, we calculate \( \frac{15}{4}\div\frac{1}{8} \). When dividing by a fraction, we multiply by its reciprocal, so \( \frac{15}{4}\times8 \).

Step3: Simplify the multiplication

Simplify \( \frac{15}{4}\times8 \). We can rewrite 8 as \( \frac{8}{1} \), then multiply the numerators and denominators: \( \frac{15\times8}{4\times1}=\frac{120}{4} = 30 \). Wait, no, wait, let's check again. Wait, \( \frac{15}{4}\times8=\frac{15\times8}{4}=15\times2 = 30 \)? Wait, no, that can't be right. Wait, no, wait, \( 3\frac{3}{4} \) pounds is \( 3.75 \) pounds, and each roll uses \( \frac{1}{8}=0.125 \) pounds. Then \( 3.75\div0.125 = 30 \)? Wait, but let's check the calculation again. Wait, \( 3\frac{3}{4}=\frac{15}{4} \), dividing by \( \frac{1}{8} \) is \( \frac{15}{4}\times8=\frac{15\times8}{4}=15\times2 = 30 \). Wait, but the options have 30 as an option. Wait, but let's check the problem again. Wait, the problem says "She uses \( \frac{1}{8} \) of a pound for one roll". So total dough is \( 3\frac{3}{4} \) pounds. So \( 3\frac{3}{4}\div\frac{1}{8}=\frac{15}{4}\times8 = 30 \).

Wait, but let's check the arithmetic again. Wait, \( 3\frac{3}{4} \) is 3.75, \( \frac{1}{8} \) is 0.125. 3.75 divided by 0.125: 0.125 times 30 is 3.75. Yes, that's correct. So the number of rolls is 30.

Answer:

30