Solve (4/7 / (16/35)) / (25/32) = 4/7 / (16/35 / (25/32)) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(\frac{4}{7}\div\frac{16}{35})\div\frac{25}{32}=\frac{4}{7}\div(\frac{16}{35}\div\frac{25}{32})$$

Verify

$\text{false}$

Solution Steps

Divide $\frac{\frac{4}{7}}{\frac{16}{35}}$ by $\frac{25}{32}$ by multiplying $\frac{\frac{4}{7}}{\frac{16}{35}}$ by the reciprocal of $\frac{25}{32}$.

$$\frac{\frac{4}{7}\times 32}{\frac{16}{35}\times 25}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Express $\frac{4}{7}\times 32$ as a single fraction.

$$\frac{\frac{4\times 32}{7}}{\frac{16}{35}\times 25}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Multiply $4$ and $32$ to get $128$.

$$\frac{\frac{128}{7}}{\frac{16}{35}\times 25}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Express $\frac{16}{35}\times 25$ as a single fraction.

$$\frac{\frac{128}{7}}{\frac{16\times 25}{35}}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Multiply $16$ and $25$ to get $400$.

$$\frac{\frac{128}{7}}{\frac{400}{35}}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Reduce the fraction $\frac{400}{35}$ to lowest terms by extracting and canceling out $5$.

$$\frac{\frac{128}{7}}{\frac{80}{7}}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Divide $\frac{128}{7}$ by $\frac{80}{7}$ by multiplying $\frac{128}{7}$ by the reciprocal of $\frac{80}{7}$.

$$\frac{128}{7}\times \frac{7}{80}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Multiply $\frac{128}{7}$ times $\frac{7}{80}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{128\times 7}{7\times 80}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Cancel out $7$ in both numerator and denominator.

$$\frac{128}{80}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Reduce the fraction $\frac{128}{80}$ to lowest terms by extracting and canceling out $16$.

$$\frac{8}{5}=\frac{\frac{4}{7}}{\frac{\frac{16}{35}}{\frac{25}{32}}}$$

Divide $\frac{4}{7}$ by $\frac{\frac{16}{35}}{\frac{25}{32}}$ by multiplying $\frac{4}{7}$ by the reciprocal of $\frac{\frac{16}{35}}{\frac{25}{32}}$.

$$\frac{8}{5}=\frac{4\times \frac{25}{32}}{7\times \frac{16}{35}}$$

Express $4\times \frac{25}{32}$ as a single fraction.

$$\frac{8}{5}=\frac{\frac{4\times 25}{32}}{7\times \frac{16}{35}}$$

Multiply $4$ and $25$ to get $100$.

$$\frac{8}{5}=\frac{\frac{100}{32}}{7\times \frac{16}{35}}$$

Reduce the fraction $\frac{100}{32}$ to lowest terms by extracting and canceling out $4$.

$$\frac{8}{5}=\frac{\frac{25}{8}}{7\times \frac{16}{35}}$$

Express $7\times \frac{16}{35}$ as a single fraction.

$$\frac{8}{5}=\frac{\frac{25}{8}}{\frac{7\times 16}{35}}$$

Multiply $7$ and $16$ to get $112$.

$$\frac{8}{5}=\frac{\frac{25}{8}}{\frac{112}{35}}$$

Reduce the fraction $\frac{112}{35}$ to lowest terms by extracting and canceling out $7$.

$$\frac{8}{5}=\frac{\frac{25}{8}}{\frac{16}{5}}$$

Divide $\frac{25}{8}$ by $\frac{16}{5}$ by multiplying $\frac{25}{8}$ by the reciprocal of $\frac{16}{5}$.

$$\frac{8}{5}=\frac{25}{8}\times \frac{5}{16}$$

Multiply $\frac{25}{8}$ times $\frac{5}{16}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{5}=\frac{25\times 5}{8\times 16}$$

Do the multiplications in the fraction $\frac{25\times 5}{8\times 16}$.

$$\frac{8}{5}=\frac{125}{128}$$

Least common multiple of $5$ and $128$ is $640$. Convert $\frac{8}{5}$ and $\frac{125}{128}$ to fractions with denominator $640$.

$$\frac{1024}{640}=\frac{625}{640}$$

Compare $\frac{1024}{640}$ and $\frac{625}{640}$.

$$\text{false}$$