Solve (5(1)/(4)-3(2)/(5))of(5(1)/(2)/2(1)/(4)) | 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

$$(5 \frac{ 1 }{ 4 } -3 \frac{ 2 }{ 5 } )of(5 \frac{ 1 }{ 2 } /2 \frac{ 1 }{ 4 } )$$

Evaluate

$\frac{407fo}{90}$

Solution Steps

Multiply $5$ and $4$ to get $20$.

$$\left(\frac{20+1}{4}-\frac{3\times 5+2}{5}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Add $20$ and $1$ to get $21$.

$$\left(\frac{21}{4}-\frac{3\times 5+2}{5}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Multiply $3$ and $5$ to get $15$.

$$\left(\frac{21}{4}-\frac{15+2}{5}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Add $15$ and $2$ to get $17$.

$$\left(\frac{21}{4}-\frac{17}{5}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Least common multiple of $4$ and $5$ is $20$. Convert $\frac{21}{4}$ and $\frac{17}{5}$ to fractions with denominator $20$.

$$\left(\frac{105}{20}-\frac{68}{20}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Since $\frac{105}{20}$ and $\frac{68}{20}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{105-68}{20}of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Subtract $68$ from $105$ to get $37$.

$$\frac{37}{20}of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Divide $\frac{5\times 2+1}{2}$ by $\frac{2\times 4+1}{4}$ by multiplying $\frac{5\times 2+1}{2}$ by the reciprocal of $\frac{2\times 4+1}{4}$.

$$\frac{37}{20}of\times \frac{\left(5\times 2+1\right)\times 4}{2\left(2\times 4+1\right)}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{37}{20}of\times \frac{2\left(1+2\times 5\right)}{1+2\times 4}$$

Multiply $2$ and $5$ to get $10$.

$$\frac{37}{20}of\times \frac{2\left(1+10\right)}{1+2\times 4}$$

Add $1$ and $10$ to get $11$.

$$\frac{37}{20}of\times \frac{2\times 11}{1+2\times 4}$$

Multiply $2$ and $11$ to get $22$.

$$\frac{37}{20}of\times \frac{22}{1+2\times 4}$$

Multiply $2$ and $4$ to get $8$.

$$\frac{37}{20}of\times \frac{22}{1+8}$$

Add $1$ and $8$ to get $9$.

$$\frac{37}{20}of\times \frac{22}{9}$$

Multiply $\frac{37}{20}$ times $\frac{22}{9}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{37\times 22}{20\times 9}of$$

Do the multiplications in the fraction $\frac{37\times 22}{20\times 9}$.

$$\frac{814}{180}of$$

Reduce the fraction $\frac{814}{180}$ to lowest terms by extracting and canceling out $2$.

$$\frac{407}{90}of$$

Expand

$\frac{407fo}{90}$

Solution Steps

Multiply $5$ and $4$ to get $20$.

$$\left(\frac{20+1}{4}-\frac{3\times 5+2}{5}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Add $20$ and $1$ to get $21$.

$$\left(\frac{21}{4}-\frac{3\times 5+2}{5}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Multiply $3$ and $5$ to get $15$.

$$\left(\frac{21}{4}-\frac{15+2}{5}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Add $15$ and $2$ to get $17$.

$$\left(\frac{21}{4}-\frac{17}{5}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Least common multiple of $4$ and $5$ is $20$. Convert $\frac{21}{4}$ and $\frac{17}{5}$ to fractions with denominator $20$.

$$\left(\frac{105}{20}-\frac{68}{20}\right)of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Since $\frac{105}{20}$ and $\frac{68}{20}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{105-68}{20}of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Subtract $68$ from $105$ to get $37$.

$$\frac{37}{20}of\times \frac{\frac{5\times 2+1}{2}}{\frac{2\times 4+1}{4}}$$

Divide $\frac{5\times 2+1}{2}$ by $\frac{2\times 4+1}{4}$ by multiplying $\frac{5\times 2+1}{2}$ by the reciprocal of $\frac{2\times 4+1}{4}$.

$$\frac{37}{20}of\times \frac{\left(5\times 2+1\right)\times 4}{2\left(2\times 4+1\right)}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{37}{20}of\times \frac{2\left(1+2\times 5\right)}{1+2\times 4}$$

Multiply $2$ and $5$ to get $10$.

$$\frac{37}{20}of\times \frac{2\left(1+10\right)}{1+2\times 4}$$

Add $1$ and $10$ to get $11$.

$$\frac{37}{20}of\times \frac{2\times 11}{1+2\times 4}$$

Multiply $2$ and $11$ to get $22$.

$$\frac{37}{20}of\times \frac{22}{1+2\times 4}$$

Multiply $2$ and $4$ to get $8$.

$$\frac{37}{20}of\times \frac{22}{1+8}$$

Add $1$ and $8$ to get $9$.

$$\frac{37}{20}of\times \frac{22}{9}$$

Multiply $\frac{37}{20}$ times $\frac{22}{9}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{37\times 22}{20\times 9}of$$

Do the multiplications in the fraction $\frac{37\times 22}{20\times 9}$.

$$\frac{814}{180}of$$

Reduce the fraction $\frac{814}{180}$ to lowest terms by extracting and canceling out $2$.

$$\frac{407}{90}of$$