Solve (2/4 * of * 168/63 + 3/4 - 1 4/9) / (15/7) | 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

$$(\frac{2}{4}of\frac{168}{63}+\frac{3}{4}-1\frac{4}{9})\div\frac{15}{7}$$

Evaluate

$\frac{28fo}{45}-\frac{35}{108}$

Solution Steps

Reduce the fraction $\frac{2}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{1}{2}of\times \frac{168}{63}+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Reduce the fraction $\frac{168}{63}$ to lowest terms by extracting and canceling out $21$.

$$\frac{\frac{1}{2}of\times \frac{8}{3}+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Multiply $\frac{1}{2}$ times $\frac{8}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 8}{2\times 3}of+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Do the multiplications in the fraction $\frac{1\times 8}{2\times 3}$.

$$\frac{\frac{8}{6}of+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Reduce the fraction $\frac{8}{6}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{4}{3}of+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Multiply $1$ and $9$ to get $9$.

$$\frac{\frac{4}{3}of+\frac{3}{4}-\frac{9+4}{9}}{\frac{15}{7}}$$

Add $9$ and $4$ to get $13$.

$$\frac{\frac{4}{3}of+\frac{3}{4}-\frac{13}{9}}{\frac{15}{7}}$$

Least common multiple of $4$ and $9$ is $36$. Convert $\frac{3}{4}$ and $\frac{13}{9}$ to fractions with denominator $36$.

$$\frac{\frac{4}{3}of+\frac{27}{36}-\frac{52}{36}}{\frac{15}{7}}$$

Since $\frac{27}{36}$ and $\frac{52}{36}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{3}of+\frac{27-52}{36}}{\frac{15}{7}}$$

Subtract $52$ from $27$ to get $-25$.

$$\frac{\frac{4}{3}of-\frac{25}{36}}{\frac{15}{7}}$$

Divide $\frac{4}{3}of-\frac{25}{36}$ by $\frac{15}{7}$ by multiplying $\frac{4}{3}of-\frac{25}{36}$ by the reciprocal of $\frac{15}{7}$.

$$\frac{\left(\frac{4}{3}of-\frac{25}{36}\right)\times 7}{15}$$

Use the distributive property to multiply $\frac{4}{3}of-\frac{25}{36}$ by $7$.

$$\frac{\frac{4}{3}of\times 7-\frac{25}{36}\times 7}{15}$$

Express $\frac{4}{3}\times 7$ as a single fraction.

$$\frac{\frac{4\times 7}{3}of-\frac{25}{36}\times 7}{15}$$

Multiply $4$ and $7$ to get $28$.

$$\frac{\frac{28}{3}of-\frac{25}{36}\times 7}{15}$$

Express $-\frac{25}{36}\times 7$ as a single fraction.

$$\frac{\frac{28}{3}of+\frac{-25\times 7}{36}}{15}$$

Multiply $-25$ and $7$ to get $-175$.

$$\frac{\frac{28}{3}of+\frac{-175}{36}}{15}$$

Fraction $\frac{-175}{36}$ can be rewritten as $-\frac{175}{36}$ by extracting the negative sign.

$$\frac{\frac{28}{3}of-\frac{175}{36}}{15}$$

Expand

$\frac{28fo}{45}-\frac{35}{108}$

Solution Steps

Reduce the fraction $\frac{2}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{1}{2}of\times \frac{168}{63}+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Reduce the fraction $\frac{168}{63}$ to lowest terms by extracting and canceling out $21$.

$$\frac{\frac{1}{2}of\times \frac{8}{3}+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Multiply $\frac{1}{2}$ times $\frac{8}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 8}{2\times 3}of+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Do the multiplications in the fraction $\frac{1\times 8}{2\times 3}$.

$$\frac{\frac{8}{6}of+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Reduce the fraction $\frac{8}{6}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{4}{3}of+\frac{3}{4}-\frac{1\times 9+4}{9}}{\frac{15}{7}}$$

Multiply $1$ and $9$ to get $9$.

$$\frac{\frac{4}{3}of+\frac{3}{4}-\frac{9+4}{9}}{\frac{15}{7}}$$

Add $9$ and $4$ to get $13$.

$$\frac{\frac{4}{3}of+\frac{3}{4}-\frac{13}{9}}{\frac{15}{7}}$$

Least common multiple of $4$ and $9$ is $36$. Convert $\frac{3}{4}$ and $\frac{13}{9}$ to fractions with denominator $36$.

$$\frac{\frac{4}{3}of+\frac{27}{36}-\frac{52}{36}}{\frac{15}{7}}$$

Since $\frac{27}{36}$ and $\frac{52}{36}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{3}of+\frac{27-52}{36}}{\frac{15}{7}}$$

Subtract $52$ from $27$ to get $-25$.

$$\frac{\frac{4}{3}of-\frac{25}{36}}{\frac{15}{7}}$$

Divide $\frac{4}{3}of-\frac{25}{36}$ by $\frac{15}{7}$ by multiplying $\frac{4}{3}of-\frac{25}{36}$ by the reciprocal of $\frac{15}{7}$.

$$\frac{\left(\frac{4}{3}of-\frac{25}{36}\right)\times 7}{15}$$

Use the distributive property to multiply $\frac{4}{3}of-\frac{25}{36}$ by $7$.

$$\frac{\frac{4}{3}of\times 7-\frac{25}{36}\times 7}{15}$$

Express $\frac{4}{3}\times 7$ as a single fraction.

$$\frac{\frac{4\times 7}{3}of-\frac{25}{36}\times 7}{15}$$

Multiply $4$ and $7$ to get $28$.

$$\frac{\frac{28}{3}of-\frac{25}{36}\times 7}{15}$$

Express $-\frac{25}{36}\times 7$ as a single fraction.

$$\frac{\frac{28}{3}of+\frac{-25\times 7}{36}}{15}$$

Multiply $-25$ and $7$ to get $-175$.

$$\frac{\frac{28}{3}of+\frac{-175}{36}}{15}$$

Fraction $\frac{-175}{36}$ can be rewritten as $-\frac{175}{36}$ by extracting the negative sign.

$$\frac{\frac{28}{3}of-\frac{175}{36}}{15}$$