Solve 7/6 + (3 1/2 - 2 1/4) + 5 1/8 + 3/16 - 1/9 | 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

$$\frac{7}{6}+(3\frac{1}{2}-2\frac{1}{4})+5\frac{1}{8}+\frac{3}{16}-\frac{1}{9}$$

Evaluate

$\frac{1097}{144}\approx 7.618055556$

Solution Steps

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

$$\frac{7}{6}+\frac{6+1}{2}-\frac{2\times 4+1}{4}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

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

$$\frac{7}{6}+\frac{7}{2}-\frac{2\times 4+1}{4}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Least common multiple of $6$ and $2$ is $6$. Convert $\frac{7}{6}$ and $\frac{7}{2}$ to fractions with denominator $6$.

$$\frac{7}{6}+\frac{21}{6}-\frac{2\times 4+1}{4}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Since $\frac{7}{6}$ and $\frac{21}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{7+21}{6}-\frac{2\times 4+1}{4}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Add $7$ and $21$ to get $28$.

$$\frac{28}{6}-\frac{2\times 4+1}{4}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Reduce the fraction $\frac{28}{6}$ to lowest terms by extracting and canceling out $2$.

$$\frac{14}{3}-\frac{2\times 4+1}{4}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Multiply $2$ and $4$ to get $8$.

$$\frac{14}{3}-\frac{8+1}{4}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Add $8$ and $1$ to get $9$.

$$\frac{14}{3}-\frac{9}{4}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Least common multiple of $3$ and $4$ is $12$. Convert $\frac{14}{3}$ and $\frac{9}{4}$ to fractions with denominator $12$.

$$\frac{56}{12}-\frac{27}{12}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Since $\frac{56}{12}$ and $\frac{27}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{56-27}{12}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Subtract $27$ from $56$ to get $29$.

$$\frac{29}{12}+\frac{5\times 8+1}{8}+\frac{3}{16}-\frac{1}{9}$$

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

$$\frac{29}{12}+\frac{40+1}{8}+\frac{3}{16}-\frac{1}{9}$$

Add $40$ and $1$ to get $41$.

$$\frac{29}{12}+\frac{41}{8}+\frac{3}{16}-\frac{1}{9}$$

Least common multiple of $12$ and $8$ is $24$. Convert $\frac{29}{12}$ and $\frac{41}{8}$ to fractions with denominator $24$.

$$\frac{58}{24}+\frac{123}{24}+\frac{3}{16}-\frac{1}{9}$$

Since $\frac{58}{24}$ and $\frac{123}{24}$ have the same denominator, add them by adding their numerators.

$$\frac{58+123}{24}+\frac{3}{16}-\frac{1}{9}$$

Add $58$ and $123$ to get $181$.

$$\frac{181}{24}+\frac{3}{16}-\frac{1}{9}$$

Least common multiple of $24$ and $16$ is $48$. Convert $\frac{181}{24}$ and $\frac{3}{16}$ to fractions with denominator $48$.

$$\frac{362}{48}+\frac{9}{48}-\frac{1}{9}$$

Since $\frac{362}{48}$ and $\frac{9}{48}$ have the same denominator, add them by adding their numerators.

$$\frac{362+9}{48}-\frac{1}{9}$$

Add $362$ and $9$ to get $371$.

$$\frac{371}{48}-\frac{1}{9}$$

Least common multiple of $48$ and $9$ is $144$. Convert $\frac{371}{48}$ and $\frac{1}{9}$ to fractions with denominator $144$.

$$\frac{1113}{144}-\frac{16}{144}$$

Since $\frac{1113}{144}$ and $\frac{16}{144}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1113-16}{144}$$

Subtract $16$ from $1113$ to get $1097$.

$$\frac{1097}{144}$$

Factor

$\frac{1097}{2 ^ {4} \cdot 3 ^ {2}} = 7\frac{89}{144} = 7.618055555555555$