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Answer :
To find out how much the diameter of the 7/8-inch shaft must be reduced to become 39/48-inch, we need to determine the difference between the original diameter and the desired diameter.
Let's break it down step-by-step:
1. Original Diameter: The original diameter of the shaft is [tex]\( \frac{7}{8} \)[/tex] inches.
2. Desired Diameter: The desired diameter is [tex]\( \frac{39}{48} \)[/tex] inches.
3. Calculate the Reduction: To find the reduction needed, subtract the desired diameter from the original diameter:
[tex]\[
\text{Reduction} = \frac{7}{8} - \frac{39}{48}
\][/tex]
4. Make the Denominators the Same: Before we can subtract the fractions, we need the same denominator. The least common denominator (LCD) of 8 and 48 is 48.
- Convert [tex]\(\frac{7}{8}\)[/tex] to have a denominator of 48:
[tex]\[
\frac{7}{8} = \frac{7 \times 6}{8 \times 6} = \frac{42}{48}
\][/tex]
5. Perform the Subtraction: Now that both fractions have the same denominator, subtract:
[tex]\[
\frac{42}{48} - \frac{39}{48} = \frac{42 - 39}{48} = \frac{3}{48}
\][/tex]
6. Simplify the Fraction: The fraction [tex]\( \frac{3}{48} \)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[
\frac{3}{48} = \frac{3 \div 3}{48 \div 3} = \frac{1}{16}
\][/tex]
Therefore, the diameter must be reduced by [tex]\( \frac{1}{16} \)[/tex] inch, which corresponds to option b. 1/16.
Let's break it down step-by-step:
1. Original Diameter: The original diameter of the shaft is [tex]\( \frac{7}{8} \)[/tex] inches.
2. Desired Diameter: The desired diameter is [tex]\( \frac{39}{48} \)[/tex] inches.
3. Calculate the Reduction: To find the reduction needed, subtract the desired diameter from the original diameter:
[tex]\[
\text{Reduction} = \frac{7}{8} - \frac{39}{48}
\][/tex]
4. Make the Denominators the Same: Before we can subtract the fractions, we need the same denominator. The least common denominator (LCD) of 8 and 48 is 48.
- Convert [tex]\(\frac{7}{8}\)[/tex] to have a denominator of 48:
[tex]\[
\frac{7}{8} = \frac{7 \times 6}{8 \times 6} = \frac{42}{48}
\][/tex]
5. Perform the Subtraction: Now that both fractions have the same denominator, subtract:
[tex]\[
\frac{42}{48} - \frac{39}{48} = \frac{42 - 39}{48} = \frac{3}{48}
\][/tex]
6. Simplify the Fraction: The fraction [tex]\( \frac{3}{48} \)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[
\frac{3}{48} = \frac{3 \div 3}{48 \div 3} = \frac{1}{16}
\][/tex]
Therefore, the diameter must be reduced by [tex]\( \frac{1}{16} \)[/tex] inch, which corresponds to option b. 1/16.
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