Solve 3/8-2+3/16*3+3/16*3+1/8*2+frac{1}{86}*3+frac{1}{32}*4+frac{1}{32}*4

$$\frac { 3 } { 8 } - 2 + \frac { 3 } { 16 } \cdot 3 + \frac { 3 } { 16 } \cdot 3 + \frac { 1 } { 8 } \cdot 2 + \frac { 1 } { 86 } \cdot 3 + \frac { 1 } { 32 } \cdot 4 + \frac { 1 } { 32 } \cdot 4$$

Evaluate

$$\frac{3}{86}\approx 0.034883721$$

Solution Steps

Convert 2 to fraction \frac{16}{8}.

$$\frac{3}{8}-\frac{16}{8}+\frac{3}{16}\times 3+\frac{3}{16}\times 3+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Since \frac{3}{8} and \frac{16}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-16}{8}+\frac{3}{16}\times 3+\frac{3}{16}\times 3+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Subtract 16 from 3 to get -13.

$$-\frac{13}{8}+\frac{3}{16}\times 3+\frac{3}{16}\times 3+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Express \frac{3}{16}\times 3 as a single fraction.

$$-\frac{13}{8}+\frac{3\times 3}{16}+\frac{3}{16}\times 3+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Multiply 3 and 3 to get 9.

$$-\frac{13}{8}+\frac{9}{16}+\frac{3}{16}\times 3+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Least common multiple of 8 and 16 is 16. Convert -\frac{13}{8} and \frac{9}{16} to fractions with denominator 16.

$$-\frac{26}{16}+\frac{9}{16}+\frac{3}{16}\times 3+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Since -\frac{26}{16} and \frac{9}{16} have the same denominator, add them by adding their numerators.

$$\frac{-26+9}{16}+\frac{3}{16}\times 3+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Add -26 and 9 to get -17.

$$-\frac{17}{16}+\frac{3}{16}\times 3+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Express \frac{3}{16}\times 3 as a single fraction.

$$-\frac{17}{16}+\frac{3\times 3}{16}+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Multiply 3 and 3 to get 9.

$$-\frac{17}{16}+\frac{9}{16}+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Since -\frac{17}{16} and \frac{9}{16} have the same denominator, add them by adding their numerators.

$$\frac{-17+9}{16}+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Add -17 and 9 to get -8.

$$\frac{-8}{16}+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Reduce the fraction \frac{-8}{16} to lowest terms by extracting and canceling out 8.

$$-\frac{1}{2}+\frac{1}{8}\times 2+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Multiply \frac{1}{8} and 2 to get \frac{2}{8}.

$$-\frac{1}{2}+\frac{2}{8}+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}+\frac{1}{4}+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Least common multiple of 2 and 4 is 4. Convert -\frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$-\frac{2}{4}+\frac{1}{4}+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Since -\frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{-2+1}{4}+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Add -2 and 1 to get -1.

$$-\frac{1}{4}+\frac{1}{86}\times 3+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Multiply \frac{1}{86} and 3 to get \frac{3}{86}.

$$-\frac{1}{4}+\frac{3}{86}+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Least common multiple of 4 and 86 is 172. Convert -\frac{1}{4} and \frac{3}{86} to fractions with denominator 172.

$$-\frac{43}{172}+\frac{6}{172}+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Since -\frac{43}{172} and \frac{6}{172} have the same denominator, add them by adding their numerators.

$$\frac{-43+6}{172}+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Add -43 and 6 to get -37.

$$-\frac{37}{172}+\frac{1}{32}\times 4+\frac{1}{32}\times 4$$

Multiply \frac{1}{32} and 4 to get \frac{4}{32}.

$$-\frac{37}{172}+\frac{4}{32}+\frac{1}{32}\times 4$$

Reduce the fraction \frac{4}{32} to lowest terms by extracting and canceling out 4.

$$-\frac{37}{172}+\frac{1}{8}+\frac{1}{32}\times 4$$

Least common multiple of 172 and 8 is 344. Convert -\frac{37}{172} and \frac{1}{8} to fractions with denominator 344.

$$-\frac{74}{344}+\frac{43}{344}+\frac{1}{32}\times 4$$

Since -\frac{74}{344} and \frac{43}{344} have the same denominator, add them by adding their numerators.

$$\frac{-74+43}{344}+\frac{1}{32}\times 4$$

Add -74 and 43 to get -31.

$$-\frac{31}{344}+\frac{1}{32}\times 4$$

Multiply \frac{1}{32} and 4 to get \frac{4}{32}.

$$-\frac{31}{344}+\frac{4}{32}$$

Reduce the fraction \frac{4}{32} to lowest terms by extracting and canceling out 4.

$$-\frac{31}{344}+\frac{1}{8}$$

Least common multiple of 344 and 8 is 344. Convert -\frac{31}{344} and \frac{1}{8} to fractions with denominator 344.

$$-\frac{31}{344}+\frac{43}{344}$$

Since -\frac{31}{344} and \frac{43}{344} have the same denominator, add them by adding their numerators.

$$\frac{-31+43}{344}$$

Add -31 and 43 to get 12.

$$\frac{12}{344}$$

Reduce the fraction \frac{12}{344} to lowest terms by extracting and canceling out 4.

$$\frac{3}{86}$$

Factor

$$\frac{3}{2 \cdot 43} = 0.03488372093023256$$