Solve A = \frac { 9 } { 10 } \div \frac { 10 } { 11 } \div \frac { 11 } { 12 }

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Question

$$A = \frac { 9 } { 10 } \div \frac { 10 } { 11 } \div \frac { 11 } { 12 }$$

$A = \frac{27}{25} = 1\frac{2}{25} = 1.08$

Divide $\frac{9}{10}$ by $\frac{10}{11}$ by multiplying $\frac{9}{10}$ by the reciprocal of $\frac{10}{11}$.

$$A=\frac{\frac{9}{10}\times \frac{11}{10}}{\frac{11}{12}}$$

Multiply $\frac{9}{10}$ times $\frac{11}{10}$ by multiplying numerator times numerator and denominator times denominator.

$$A=\frac{\frac{9\times 11}{10\times 10}}{\frac{11}{12}}$$

Do the multiplications in the fraction $\frac{9\times 11}{10\times 10}$.

$$A=\frac{\frac{99}{100}}{\frac{11}{12}}$$

Divide $\frac{99}{100}$ by $\frac{11}{12}$ by multiplying $\frac{99}{100}$ by the reciprocal of $\frac{11}{12}$.

$$A=\frac{99}{100}\times \frac{12}{11}$$

Multiply $\frac{99}{100}$ times $\frac{12}{11}$ by multiplying numerator times numerator and denominator times denominator.

$$A=\frac{99\times 12}{100\times 11}$$

Do the multiplications in the fraction $\frac{99\times 12}{100\times 11}$.

$$A=\frac{1188}{1100}$$

Reduce the fraction $\frac{1188}{1100}$ to lowest terms by extracting and canceling out $44$.

$$A=\frac{27}{25}$$

$A≔\frac{27}{25}$