Solve -10*1/16+-6*1/8+-2*1/4+1*1/16+3*frac{1}{4}+5*frac{1}{16}+8*frac{1}{8}+10*frac{1}{16}

$$-10 \times \frac{ 1 }{ 16 } +-6 \times \frac{ 1 }{ 8 } +-2 \times \frac{ 1 }{ 4 } +1 \times \frac{ 1 }{ 16 } +3 \times \frac{ 1 }{ 4 } +5 \times \frac{ 1 }{ 16 } +8 \times \frac{ 1 }{ 8 } +10 \times \frac{ 1 }{ 16 }$$

Evaluate

$$\frac{7}{8}=0.875$$

Solution Steps

Multiply -10 and \frac{1}{16} to get \frac{-10}{16}.

$$\frac{-10}{16}-6\times \frac{1}{8}-2\times \frac{1}{4}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Reduce the fraction \frac{-10}{16} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{8}-6\times \frac{1}{8}-2\times \frac{1}{4}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Multiply -6 and \frac{1}{8} to get \frac{-6}{8}.

$$-\frac{5}{8}+\frac{-6}{8}-2\times \frac{1}{4}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{8}-\frac{3}{4}-2\times \frac{1}{4}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Least common multiple of 8 and 4 is 8. Convert -\frac{5}{8} and \frac{3}{4} to fractions with denominator 8.

$$-\frac{5}{8}-\frac{6}{8}-2\times \frac{1}{4}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Since -\frac{5}{8} and \frac{6}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-6}{8}-2\times \frac{1}{4}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Subtract 6 from -5 to get -11.

$$-\frac{11}{8}-2\times \frac{1}{4}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Multiply -2 and \frac{1}{4} to get \frac{-2}{4}.

$$-\frac{11}{8}+\frac{-2}{4}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{8}-\frac{1}{2}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Least common multiple of 8 and 2 is 8. Convert -\frac{11}{8} and \frac{1}{2} to fractions with denominator 8.

$$-\frac{11}{8}-\frac{4}{8}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Since -\frac{11}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-4}{8}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Subtract 4 from -11 to get -15.

$$-\frac{15}{8}+1\times \frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Multiply 1 and \frac{1}{16} to get \frac{1}{16}.

$$-\frac{15}{8}+\frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Least common multiple of 8 and 16 is 16. Convert -\frac{15}{8} and \frac{1}{16} to fractions with denominator 16.

$$-\frac{30}{16}+\frac{1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Since -\frac{30}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{-30+1}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Add -30 and 1 to get -29.

$$-\frac{29}{16}+3\times \frac{1}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$-\frac{29}{16}+\frac{3}{4}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Least common multiple of 16 and 4 is 16. Convert -\frac{29}{16} and \frac{3}{4} to fractions with denominator 16.

$$-\frac{29}{16}+\frac{12}{16}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Since -\frac{29}{16} and \frac{12}{16} have the same denominator, add them by adding their numerators.

$$\frac{-29+12}{16}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Add -29 and 12 to get -17.

$$-\frac{17}{16}+5\times \frac{1}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Multiply 5 and \frac{1}{16} to get \frac{5}{16}.

$$-\frac{17}{16}+\frac{5}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Since -\frac{17}{16} and \frac{5}{16} have the same denominator, add them by adding their numerators.

$$\frac{-17+5}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Add -17 and 5 to get -12.

$$\frac{-12}{16}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Reduce the fraction \frac{-12}{16} to lowest terms by extracting and canceling out 4.

$$-\frac{3}{4}+8\times \frac{1}{8}+10\times \frac{1}{16}$$

Cancel out 8 and 8.

$$-\frac{3}{4}+1+10\times \frac{1}{16}$$

Convert 1 to fraction \frac{4}{4}.

$$-\frac{3}{4}+\frac{4}{4}+10\times \frac{1}{16}$$

Since -\frac{3}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{-3+4}{4}+10\times \frac{1}{16}$$

Add -3 and 4 to get 1.

$$\frac{1}{4}+10\times \frac{1}{16}$$

Multiply 10 and \frac{1}{16} to get \frac{10}{16}.

$$\frac{1}{4}+\frac{10}{16}$$

Reduce the fraction \frac{10}{16} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}+\frac{5}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{2}{8}+\frac{5}{8}$$

Since \frac{2}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{2+5}{8}$$

Add 2 and 5 to get 7.

$$\frac{7}{8}$$

Factor

$$\frac{7}{2 ^ {3}} = 0.875$$