$5 / 11$ of $66 / 30 \div 1 / 25-16 / 9$ .

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Grade 8

Writing from expanded to exponent form

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5 / 11

66 / 30 \div 1 / 25-16 / 9

Simplify Fractions Division: First, we need to simplify the expression inside the parentheses, which is the division of $\frac{66}{30}$ by $\frac{1}{25}$ . To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. $\frac{66}{30} \div \frac{1}{25} = \frac{66}{30} \times \frac{25}{1}$
Perform Multiplication: Now, we perform the multiplication. $\newline$ $(66 \times 25) / (30 \times 1) = 1650 / 30$
Simplify Result: Next, we simplify the fraction $\frac{1650}{30}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $30$ . $\newline$ $\frac{1650}{30} = \frac{55}{1} = 55$
Convert to Common Denominator: Now we need to subtract $\frac{16}{9}$ from $55$ . To do this, we need to find a common denominator. The common denominator for $1$ and $9$ is $9$ . So we convert $55$ to a fraction with a denominator of $9$ . $55 = \frac{55}{1} = \frac{55\times9}{1\times9} = \frac{495}{9}$
Subtract Fractions: Now we subtract $\frac{16}{9}$ from $\frac{495}{9}$ . $\newline$ $(\frac{495}{9}) - (\frac{16}{9}) = \frac{495 - 16}{9}$
Perform Subtraction: Perform the subtraction in the numerator. $495 - 16 = 479$
Find Fraction of Fraction: Now we have $\frac{479}{9}$ as the result of the subtraction.
Perform Multiplication: Finally, we need to find $\frac{5}{11}$ of $\frac{479}{9}$ . $\newline$ To find a fraction of another fraction, we multiply them. $\newline$ $\frac{5}{11} \times \frac{479}{9} = \frac{5 \times 479}{11 \times 9}$
Simplify Final Fraction: Perform the multiplication in the numerator and the denominator. $\newline$ $(5 \times 479) / (11 \times 9) = 2395 / 99$
Simplify Final Fraction: Perform the multiplication in the numerator and the denominator. $\newline$ $(5 \times 479) / (11 \times 9) = 2395 / 99$ The fraction $2395/99$ can be simplified if there is a common divisor. However, $2395$ and $99$ do not have a common divisor other than $1$ , so the fraction is already in its simplest form.