To solve the equation ( \frac{8 \frac{1}{4}}{c} = \frac{13 \frac{3}{4}}{2 \frac{1}{3}} ), we first need to rewrite the mixed numbers as improper fractions.
Convert ( 8 \frac{1}{4} ) to an improper fraction:
[
8 \frac{1}{4} = 8 \times 4 + 1 = 32 + 1 = \frac{33}{4}
]
Convert ( 13 \frac{3}{4} ) to an improper fraction:
[
13 \frac{3}{4} = 13 \times 4 + 3 = 52 + 3 = \frac{55}{4}
]
Convert ( 2 \frac{1}{3} ) to an improper fraction:
[
2 \frac{1}{3} = 2 \times 3 + 1 = 6 + 1 = \frac{7}{3}
]
Now the equation becomes:
[
\frac{\frac{33}{4}}{c} = \frac{\frac{55}{4}}{\frac{7}{3}}
]
Next, we simplify the right side:
[
\frac{\frac{55}{4}}{\frac{7}{3}} = \frac{55}{4} \times \frac{3}{7} = \frac{55 \times 3}{4 \times 7} = \frac{165}{28}
]
Now we have:
[
\frac{\frac{33}{4}}{c} = \frac{165}{28}
]
Cross-multiply to solve for ( c ):
[
33 \times 28 = 165 \times c
]
Calculating ( 33 \times 28 ):
[
33 \times 28 = 924
]
So we have:
[
924 = 165c
]
Now, solve for ( c ):
[
c = \frac{924}{165}
]
Now we can simplify ( \frac{924}{165} ) by finding the GCD of 924 and 165, which is 33:
- Divide both the numerator and the denominator by 33:
[
c = \frac{924 \div 33}{165 \div 33} = \frac{28}{5}
]
Thus, the value of ( c ) is:
[
c = 5.6 \quad \text{or} \quad c = \frac{28}{5}
]
