Solve 8/5/frac{2{25}-5/16}=frac{8/5}{frac{32-125}{400}}=8

$$\frac{ \frac{ 8 }{ 5 } }{ \frac{ 2 }{ 25 } - \frac{ 5 }{ 16 } } = \frac{ \frac{ 8 }{ 5 } }{ \frac{ 32-125 }{ 400 } } =8$$

Verify

Solution Steps

Least common multiple of 25 and 16 is 400. Convert \frac{2}{25} and \frac{5}{16} to fractions with denominator 400.

$$\frac{\frac{8}{5}}{\frac{32}{400}-\frac{125}{400}}=\frac{\frac{8}{5}}{\frac{32-125}{400}}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Since \frac{32}{400} and \frac{125}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8}{5}}{\frac{32-125}{400}}=\frac{\frac{8}{5}}{\frac{32-125}{400}}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Subtract 125 from 32 to get -93.

$$\frac{\frac{8}{5}}{-\frac{93}{400}}=\frac{\frac{8}{5}}{\frac{32-125}{400}}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Divide \frac{8}{5} by -\frac{93}{400} by multiplying \frac{8}{5} by the reciprocal of -\frac{93}{400}.

$$\frac{8}{5}\left(-\frac{400}{93}\right)=\frac{\frac{8}{5}}{\frac{32-125}{400}}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Multiply \frac{8}{5} times -\frac{400}{93} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\left(-400\right)}{5\times 93}=\frac{\frac{8}{5}}{\frac{32-125}{400}}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Do the multiplications in the fraction \frac{8\left(-400\right)}{5\times 93}.

$$\frac{-3200}{465}=\frac{\frac{8}{5}}{\frac{32-125}{400}}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Reduce the fraction \frac{-3200}{465} to lowest terms by extracting and canceling out 5.

$$-\frac{640}{93}=\frac{\frac{8}{5}}{\frac{32-125}{400}}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Divide \frac{8}{5} by \frac{32-125}{400} by multiplying \frac{8}{5} by the reciprocal of \frac{32-125}{400}.

$$-\frac{640}{93}=\frac{8\times 400}{5\left(32-125\right)}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Cancel out 5 in both numerator and denominator.

$$-\frac{640}{93}=\frac{8\times 80}{32-125}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Multiply 8 and 80 to get 640.

$$-\frac{640}{93}=\frac{640}{32-125}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Subtract 125 from 32 to get -93.

$$-\frac{640}{93}=\frac{640}{-93}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Fraction \frac{640}{-93} can be rewritten as -\frac{640}{93} by extracting the negative sign.

$$-\frac{640}{93}=-\frac{640}{93}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Compare -\frac{640}{93} and -\frac{640}{93}.

$$\text{true}\text{ and }\frac{\frac{8}{5}}{\frac{32-125}{400}}=8$$

Divide \frac{8}{5} by \frac{32-125}{400} by multiplying \frac{8}{5} by the reciprocal of \frac{32-125}{400}.

$$\text{true}\text{ and }\frac{8\times 400}{5\left(32-125\right)}=8$$

Cancel out 5 in both numerator and denominator.

$$\text{true}\text{ and }\frac{8\times 80}{32-125}=8$$

Multiply 8 and 80 to get 640.

$$\text{true}\text{ and }\frac{640}{32-125}=8$$

Subtract 125 from 32 to get -93.

$$\text{true}\text{ and }\frac{640}{-93}=8$$

Fraction \frac{640}{-93} can be rewritten as -\frac{640}{93} by extracting the negative sign.

$$\text{true}\text{ and }-\frac{640}{93}=8$$

Convert 8 to fraction \frac{744}{93}.

$$\text{true}\text{ and }-\frac{640}{93}=\frac{744}{93}$$

Compare -\frac{640}{93} and \frac{744}{93}.

$$\text{true}\text{ and }\text{false}$$

The conjunction of \text{true} and \text{false} is \text{false}.

$$\text{false}$$