To solve the expression [tex]\( 17 \times 5 \frac{3}{14} \times \frac{4}{73} \times \frac{7}{17} \)[/tex], follow these steps:
1. Convert the mixed number to an improper fraction:
The mixed number [tex]\( 5 \frac{3}{14} \)[/tex] can be converted to an improper fraction:
[tex]\[
5 \frac{3}{14} = 5 + \frac{3}{14}
\][/tex]
To combine these, express 5 as a fraction with the same denominator as [tex]\(\frac{3}{14}\)[/tex]:
[tex]\[
5 = \frac{5 \times 14}{14} = \frac{70}{14}
\][/tex]
Now add the two fractions:
[tex]\[
5 \frac{3}{14} = \frac{70}{14} + \frac{3}{14} = \frac{70 + 3}{14} = \frac{73}{14}
\][/tex]
2. Simplify each term and multiply:
Write the given expression in terms of fractions:
[tex]\[
17 \times \frac{73}{14} \times \frac{4}{73} \times \frac{7}{17}
\][/tex]
3. Cancel common factors:
Rearrange and simplify the fractions:
[tex]\[
17 \times \frac{73}{14} \times \frac{4}{73} \times \frac{7}{17} = \left( 17 \times \frac{7}{17} \right) \times \left( \frac{73}{14} \times \frac{4}{73} \right)
\][/tex]
Simplifying [tex]\( 17 \times \frac{7}{17} \)[/tex] first:
[tex]\[
17 \times \frac{7}{17} = \frac{17 \times 7}{17} = 7
\][/tex]
Next, simplify [tex]\( \frac{73}{14} \times \frac{4}{73} \)[/tex]:
[tex]\[
\frac{73}{14} \times \frac{4}{73} = \frac{73 \times 4}{14 \times 73} = \frac{4}{14} = \frac{2}{7}
\][/tex]
Now multiply the simplified terms together:
[tex]\[
7 \times \frac{2}{7} = \frac{7 \times 2}{7} = 2
\][/tex]
4. Final product:
Therefore, the simplified result of [tex]\( 17 \times 5 \frac{3}{14} \times \frac{4}{73} \times \frac{7}{17} \)[/tex] is [tex]\( 2 \)[/tex].
