Cook Gonzalez
12/13/2023 · Elementary School
Express as a fraction. \( 3 \frac{1}{7} \) pounds to \( 3 \frac{1}{6} \) pounds The answer is \( \square \). (Type a simplified fraction or mixed number.)
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Tutor-Verified Answer
Step-by-step Solution
To express the difference between \( 3 \frac{1}{7} \) pounds and \( 3 \frac{1}{6} \) pounds as a fraction, we first convert both mixed numbers to improper fractions.
1. Convert \( 3 \frac{1}{7} \):
\[
3 \frac{1}{7} = 3 + \frac{1}{7} = \frac{3 \times 7}{7} + \frac{1}{7} = \frac{21}{7} + \frac{1}{7} = \frac{22}{7}
\]
2. Convert \( 3 \frac{1}{6} \):
\[
3 \frac{1}{6} = 3 + \frac{1}{6} = \frac{3 \times 6}{6} + \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{19}{6}
\]
Now we need to find the difference:
\[
3 \frac{1}{7} - 3 \frac{1}{6} = \frac{22}{7} - \frac{19}{6}
\]
To subtract these fractions, we need a common denominator. The least common multiple of 7 and 6 is 42.
3. Convert \( \frac{22}{7} \) to have a denominator of 42:
\[
\frac{22}{7} = \frac{22 \times 6}{7 \times 6} = \frac{132}{42}
\]
4. Convert \( \frac{19}{6} \) to have a denominator of 42:
\[
\frac{19}{6} = \frac{19 \times 7}{6 \times 7} = \frac{133}{42}
\]
Now we can subtract:
\[
\frac{132}{42} - \frac{133}{42} = \frac{132 - 133}{42} = \frac{-1}{42}
\]
Thus, the answer is:
\[
\boxed{-\frac{1}{42}}
\]
Quick Answer
\(-\frac{1}{42}\)
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