Solve profit nor los plify : 18 2/3 - 15 5/6 + 4 1/8; 4/15 * (1/4 + 5/6) | 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

$$\left. \begin{array} { l } { 18 \frac { 2 } { 3 } - 15 \frac { 5 } { 6 } + 4 \frac { 1 } { 8 } } \\ { \frac { 4 } { 15 } \times ( \frac { 1 } { 4 } + \frac { 5 } { 6 } ) } \end{array} \right.$$

Sort

$\frac{13}{45},\frac{167}{24}$

Solution Steps

Multiply $18$ and $3$ to get $54$.

$$sort(\frac{54+2}{3}-\frac{15\times 6+5}{6}+\frac{4\times 8+1}{8},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Add $54$ and $2$ to get $56$.

$$sort(\frac{56}{3}-\frac{15\times 6+5}{6}+\frac{4\times 8+1}{8},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Multiply $15$ and $6$ to get $90$.

$$sort(\frac{56}{3}-\frac{90+5}{6}+\frac{4\times 8+1}{8},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Add $90$ and $5$ to get $95$.

$$sort(\frac{56}{3}-\frac{95}{6}+\frac{4\times 8+1}{8},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Least common multiple of $3$ and $6$ is $6$. Convert $\frac{56}{3}$ and $\frac{95}{6}$ to fractions with denominator $6$.

$$sort(\frac{112}{6}-\frac{95}{6}+\frac{4\times 8+1}{8},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Since $\frac{112}{6}$ and $\frac{95}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{112-95}{6}+\frac{4\times 8+1}{8},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Subtract $95$ from $112$ to get $17$.

$$sort(\frac{17}{6}+\frac{4\times 8+1}{8},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Multiply $4$ and $8$ to get $32$.

$$sort(\frac{17}{6}+\frac{32+1}{8},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Add $32$ and $1$ to get $33$.

$$sort(\frac{17}{6}+\frac{33}{8},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Least common multiple of $6$ and $8$ is $24$. Convert $\frac{17}{6}$ and $\frac{33}{8}$ to fractions with denominator $24$.

$$sort(\frac{68}{24}+\frac{99}{24},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Since $\frac{68}{24}$ and $\frac{99}{24}$ have the same denominator, add them by adding their numerators.

$$sort(\frac{68+99}{24},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Add $68$ and $99$ to get $167$.

$$sort(\frac{167}{24},\frac{4}{15}\left(\frac{1}{4}+\frac{5}{6}\right))$$

Least common multiple of $4$ and $6$ is $12$. Convert $\frac{1}{4}$ and $\frac{5}{6}$ to fractions with denominator $12$.

$$sort(\frac{167}{24},\frac{4}{15}\left(\frac{3}{12}+\frac{10}{12}\right))$$

Since $\frac{3}{12}$ and $\frac{10}{12}$ have the same denominator, add them by adding their numerators.

$$sort(\frac{167}{24},\frac{4}{15}\times \frac{3+10}{12})$$

Add $3$ and $10$ to get $13$.

$$sort(\frac{167}{24},\frac{4}{15}\times \frac{13}{12})$$

Multiply $\frac{4}{15}$ times $\frac{13}{12}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{167}{24},\frac{4\times 13}{15\times 12})$$

Do the multiplications in the fraction $\frac{4\times 13}{15\times 12}$.

$$sort(\frac{167}{24},\frac{52}{180})$$

Reduce the fraction $\frac{52}{180}$ to lowest terms by extracting and canceling out $4$.

$$sort(\frac{167}{24},\frac{13}{45})$$

Least common denominator of the numbers in the list $\frac{167}{24},\frac{13}{45}$ is $360$. Convert numbers in the list to fractions with denominator $360$.

$$\frac{2505}{360},\frac{104}{360}$$

To sort the list, start from a single element $\frac{2505}{360}$.

$$\frac{2505}{360}$$

Insert $\frac{104}{360}$ to the appropriate location in the new list.

$$\frac{104}{360},\frac{2505}{360}$$

Replace the obtained fractions with the initial values.

$$\frac{13}{45},\frac{167}{24}$$

Evaluate

$\frac{167}{24},\ \frac{13}{45}$