Solve 412 42 A 6 2/3 * 2 1/2 + (- 5 3/8) / (2 7/9) + 2 1/2 * 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

$$6 \frac { 2 } { 3 } \times 2 \frac { 1 } { 2 } - 5 \frac { 3 } { 8 } + 2 \frac { 7 } { 9 } + 2 \frac { 1 } { 2 } \times 1 \frac { 1 } { 2 }$$

Evaluate

$\frac{1283}{72}\approx 17.819444444$

Solution Steps

Multiply $6$ and $3$ to get $18$.

$$\frac{18+2}{3}\times \frac{2\times 2+1}{2}-\frac{5\times 8+3}{8}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Add $18$ and $2$ to get $20$.

$$\frac{20}{3}\times \frac{2\times 2+1}{2}-\frac{5\times 8+3}{8}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

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

$$\frac{20}{3}\times \frac{4+1}{2}-\frac{5\times 8+3}{8}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Add $4$ and $1$ to get $5$.

$$\frac{20}{3}\times \frac{5}{2}-\frac{5\times 8+3}{8}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Multiply $\frac{20}{3}$ times $\frac{5}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{20\times 5}{3\times 2}-\frac{5\times 8+3}{8}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Do the multiplications in the fraction $\frac{20\times 5}{3\times 2}$.

$$\frac{100}{6}-\frac{5\times 8+3}{8}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Reduce the fraction $\frac{100}{6}$ to lowest terms by extracting and canceling out $2$.

$$\frac{50}{3}-\frac{5\times 8+3}{8}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Multiply $5$ and $8$ to get $40$.

$$\frac{50}{3}-\frac{40+3}{8}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Add $40$ and $3$ to get $43$.

$$\frac{50}{3}-\frac{43}{8}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Least common multiple of $3$ and $8$ is $24$. Convert $\frac{50}{3}$ and $\frac{43}{8}$ to fractions with denominator $24$.

$$\frac{400}{24}-\frac{129}{24}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Since $\frac{400}{24}$ and $\frac{129}{24}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{400-129}{24}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Subtract $129$ from $400$ to get $271$.

$$\frac{271}{24}+\frac{2\times 9+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Multiply $2$ and $9$ to get $18$.

$$\frac{271}{24}+\frac{18+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Add $18$ and $7$ to get $25$.

$$\frac{271}{24}+\frac{25}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Least common multiple of $24$ and $9$ is $72$. Convert $\frac{271}{24}$ and $\frac{25}{9}$ to fractions with denominator $72$.

$$\frac{813}{72}+\frac{200}{72}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Since $\frac{813}{72}$ and $\frac{200}{72}$ have the same denominator, add them by adding their numerators.

$$\frac{813+200}{72}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Add $813$ and $200$ to get $1013$.

$$\frac{1013}{72}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

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

$$\frac{1013}{72}+\frac{4+1}{2}\times \frac{1\times 2+1}{2}$$

Add $4$ and $1$ to get $5$.

$$\frac{1013}{72}+\frac{5}{2}\times \frac{1\times 2+1}{2}$$

Multiply $1$ and $2$ to get $2$.

$$\frac{1013}{72}+\frac{5}{2}\times \frac{2+1}{2}$$

Add $2$ and $1$ to get $3$.

$$\frac{1013}{72}+\frac{5}{2}\times \frac{3}{2}$$

Multiply $\frac{5}{2}$ times $\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1013}{72}+\frac{5\times 3}{2\times 2}$$

Do the multiplications in the fraction $\frac{5\times 3}{2\times 2}$.

$$\frac{1013}{72}+\frac{15}{4}$$

Least common multiple of $72$ and $4$ is $72$. Convert $\frac{1013}{72}$ and $\frac{15}{4}$ to fractions with denominator $72$.

$$\frac{1013}{72}+\frac{270}{72}$$

Since $\frac{1013}{72}$ and $\frac{270}{72}$ have the same denominator, add them by adding their numerators.

$$\frac{1013+270}{72}$$

Add $1013$ and $270$ to get $1283$.

$$\frac{1283}{72}$$

Factor

$\frac{1283}{2 ^ {3} \cdot 3 ^ {2}} = 17\frac{59}{72} = 17.819444444444443$