Solve 42 42 A * 0.6 * 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

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

Evaluate

$\frac{50A}{3}+\frac{83}{72}$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$A\times \frac{50}{3}-\frac{43}{8}+\frac{18+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{43}{8}+\frac{25}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Least common multiple of $8$ and $9$ is $72$. Convert $-\frac{43}{8}$ and $\frac{25}{9}$ to fractions with denominator $72$.

$$A\times \frac{50}{3}-\frac{387}{72}+\frac{200}{72}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Since $-\frac{387}{72}$ and $\frac{200}{72}$ have the same denominator, add them by adding their numerators.

$$A\times \frac{50}{3}+\frac{-387+200}{72}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Add $-387$ and $200$ to get $-187$.

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{4+1}{2}\times \frac{1\times 2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{5}{2}\times \frac{1\times 2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{5}{2}\times \frac{2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{5}{2}\times \frac{3}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{5\times 3}{2\times 2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{15}{4}$$

Least common multiple of $72$ and $4$ is $72$. Convert $-\frac{187}{72}$ and $\frac{15}{4}$ to fractions with denominator $72$.

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{270}{72}$$

Since $-\frac{187}{72}$ and $\frac{270}{72}$ have the same denominator, add them by adding their numerators.

$$A\times \frac{50}{3}+\frac{-187+270}{72}$$

Add $-187$ and $270$ to get $83$.

$$A\times \frac{50}{3}+\frac{83}{72}$$

Expand

$\frac{50A}{3}+\frac{83}{72}$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$A\times \frac{50}{3}-\frac{43}{8}+\frac{18+7}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{43}{8}+\frac{25}{9}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Least common multiple of $8$ and $9$ is $72$. Convert $-\frac{43}{8}$ and $\frac{25}{9}$ to fractions with denominator $72$.

$$A\times \frac{50}{3}-\frac{387}{72}+\frac{200}{72}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Since $-\frac{387}{72}$ and $\frac{200}{72}$ have the same denominator, add them by adding their numerators.

$$A\times \frac{50}{3}+\frac{-387+200}{72}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

Add $-387$ and $200$ to get $-187$.

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{2\times 2+1}{2}\times \frac{1\times 2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{4+1}{2}\times \frac{1\times 2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{5}{2}\times \frac{1\times 2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{5}{2}\times \frac{2+1}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{5}{2}\times \frac{3}{2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{5\times 3}{2\times 2}$$

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

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{15}{4}$$

Least common multiple of $72$ and $4$ is $72$. Convert $-\frac{187}{72}$ and $\frac{15}{4}$ to fractions with denominator $72$.

$$A\times \frac{50}{3}-\frac{187}{72}+\frac{270}{72}$$

Since $-\frac{187}{72}$ and $\frac{270}{72}$ have the same denominator, add them by adding their numerators.

$$A\times \frac{50}{3}+\frac{-187+270}{72}$$

Add $-187$ and $270$ to get $83$.

$$A\times \frac{50}{3}+\frac{83}{72}$$