Solve Date Pege No. (7 1/3) / (2/3) * f * 2 1/5 + (1 3/8) / (2 3/4) - 1 1/2 | 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

$$7 \frac { 1 } { 3 } - \frac { 2 } { 3 } \cdot 2 \frac { 1 } { 3 } + \frac { 13 } { 3 } + \frac { 3 } { 8 } + \frac { 3 } { 2 } \cdot \frac { 3 } { 4 } - \frac { 1 } { 2 }$$

Evaluate

$\frac{100}{9}\approx 11.111111111$

Solution Steps

Multiply $7$ and $3$ to get $21$.

$$\frac{21+1}{3}-\frac{2}{3}\times \frac{2\times 3+1}{3}+\frac{13}{3}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Add $21$ and $1$ to get $22$.

$$\frac{22}{3}-\frac{2}{3}\times \frac{2\times 3+1}{3}+\frac{13}{3}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Multiply $2$ and $3$ to get $6$.

$$\frac{22}{3}-\frac{2}{3}\times \frac{6+1}{3}+\frac{13}{3}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Add $6$ and $1$ to get $7$.

$$\frac{22}{3}-\frac{2}{3}\times \frac{7}{3}+\frac{13}{3}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Multiply $\frac{2}{3}$ times $\frac{7}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{22}{3}-\frac{2\times 7}{3\times 3}+\frac{13}{3}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Do the multiplications in the fraction $\frac{2\times 7}{3\times 3}$.

$$\frac{22}{3}-\frac{14}{9}+\frac{13}{3}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Least common multiple of $3$ and $9$ is $9$. Convert $\frac{22}{3}$ and $\frac{14}{9}$ to fractions with denominator $9$.

$$\frac{66}{9}-\frac{14}{9}+\frac{13}{3}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Since $\frac{66}{9}$ and $\frac{14}{9}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{66-14}{9}+\frac{13}{3}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Subtract $14$ from $66$ to get $52$.

$$\frac{52}{9}+\frac{13}{3}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Least common multiple of $9$ and $3$ is $9$. Convert $\frac{52}{9}$ and $\frac{13}{3}$ to fractions with denominator $9$.

$$\frac{52}{9}+\frac{39}{9}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Since $\frac{52}{9}$ and $\frac{39}{9}$ have the same denominator, add them by adding their numerators.

$$\frac{52+39}{9}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Add $52$ and $39$ to get $91$.

$$\frac{91}{9}+\frac{3}{8}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Least common multiple of $9$ and $8$ is $72$. Convert $\frac{91}{9}$ and $\frac{3}{8}$ to fractions with denominator $72$.

$$\frac{728}{72}+\frac{27}{72}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Since $\frac{728}{72}$ and $\frac{27}{72}$ have the same denominator, add them by adding their numerators.

$$\frac{728+27}{72}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Add $728$ and $27$ to get $755$.

$$\frac{755}{72}+\frac{3}{2}\times \frac{3}{4}-\frac{1}{2}$$

Multiply $\frac{3}{2}$ times $\frac{3}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{755}{72}+\frac{3\times 3}{2\times 4}-\frac{1}{2}$$

Do the multiplications in the fraction $\frac{3\times 3}{2\times 4}$.

$$\frac{755}{72}+\frac{9}{8}-\frac{1}{2}$$

Least common multiple of $72$ and $8$ is $72$. Convert $\frac{755}{72}$ and $\frac{9}{8}$ to fractions with denominator $72$.

$$\frac{755}{72}+\frac{81}{72}-\frac{1}{2}$$

Since $\frac{755}{72}$ and $\frac{81}{72}$ have the same denominator, add them by adding their numerators.

$$\frac{755+81}{72}-\frac{1}{2}$$

Add $755$ and $81$ to get $836$.

$$\frac{836}{72}-\frac{1}{2}$$

Reduce the fraction $\frac{836}{72}$ to lowest terms by extracting and canceling out $4$.

$$\frac{209}{18}-\frac{1}{2}$$

Least common multiple of $18$ and $2$ is $18$. Convert $\frac{209}{18}$ and $\frac{1}{2}$ to fractions with denominator $18$.

$$\frac{209}{18}-\frac{9}{18}$$

Since $\frac{209}{18}$ and $\frac{9}{18}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{209-9}{18}$$

Subtract $9$ from $209$ to get $200$.

$$\frac{200}{18}$$

Reduce the fraction $\frac{200}{18}$ to lowest terms by extracting and canceling out $2$.

$$\frac{100}{9}$$

Factor

$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {2}} = 11\frac{1}{9} = 11.11111111111111$