Solve (5/8 - 7/16)(1/3 + 11/6 - 5/18) Grades Average Good Excellent | 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

$$\left. \begin{array} { l } { ( \frac { 5 } { 8 } - \frac { 7 } { 16 } ) \times ( \frac { 11 } { 3 } + \frac { 11 } { 6 } - \frac { 5 } { 18 } ) } \\ { \quad 600000 } \end{array} \right.$$

Sort

$\frac{47}{48},\ 600000$

Solution Steps

Least common multiple of $8$ and $16$ is $16$. Convert $\frac{5}{8}$ and $\frac{7}{16}$ to fractions with denominator $16$.

$$sort(\left(\frac{10}{16}-\frac{7}{16}\right)\left(\frac{11}{3}+\frac{11}{6}-\frac{5}{18}\right),600000)$$

Since $\frac{10}{16}$ and $\frac{7}{16}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{10-7}{16}\left(\frac{11}{3}+\frac{11}{6}-\frac{5}{18}\right),600000)$$

Subtract $7$ from $10$ to get $3$.

$$sort(\frac{3}{16}\left(\frac{11}{3}+\frac{11}{6}-\frac{5}{18}\right),600000)$$

Least common multiple of $3$ and $6$ is $6$. Convert $\frac{11}{3}$ and $\frac{11}{6}$ to fractions with denominator $6$.

$$sort(\frac{3}{16}\left(\frac{22}{6}+\frac{11}{6}-\frac{5}{18}\right),600000)$$

Since $\frac{22}{6}$ and $\frac{11}{6}$ have the same denominator, add them by adding their numerators.

$$sort(\frac{3}{16}\left(\frac{22+11}{6}-\frac{5}{18}\right),600000)$$

Add $22$ and $11$ to get $33$.

$$sort(\frac{3}{16}\left(\frac{33}{6}-\frac{5}{18}\right),600000)$$

Reduce the fraction $\frac{33}{6}$ to lowest terms by extracting and canceling out $3$.

$$sort(\frac{3}{16}\left(\frac{11}{2}-\frac{5}{18}\right),600000)$$

Least common multiple of $2$ and $18$ is $18$. Convert $\frac{11}{2}$ and $\frac{5}{18}$ to fractions with denominator $18$.

$$sort(\frac{3}{16}\left(\frac{99}{18}-\frac{5}{18}\right),600000)$$

Since $\frac{99}{18}$ and $\frac{5}{18}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{3}{16}\times \frac{99-5}{18},600000)$$

Subtract $5$ from $99$ to get $94$.

$$sort(\frac{3}{16}\times \frac{94}{18},600000)$$

Reduce the fraction $\frac{94}{18}$ to lowest terms by extracting and canceling out $2$.

$$sort(\frac{3}{16}\times \frac{47}{9},600000)$$

Multiply $\frac{3}{16}$ times $\frac{47}{9}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{3\times 47}{16\times 9},600000)$$

Do the multiplications in the fraction $\frac{3\times 47}{16\times 9}$.

$$sort(\frac{141}{144},600000)$$

Reduce the fraction $\frac{141}{144}$ to lowest terms by extracting and canceling out $3$.

$$sort(\frac{47}{48},600000)$$

Convert decimal numbers in the list $\frac{47}{48},600000$ to fractions.

$$\frac{47}{48},600000$$

Evaluate

$\frac{47}{48},\ 600000$