Question

(1/2)³ + (1/3)³ - (5/6)³ = _____




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Answer 1

Answer:

Calculate \frac{1}{2}=0.5 to the power of 3 and get \frac{1}{8}=0.125.

\frac{1}{8}+\left(\frac{1}{3}\right)^{3}-\left(\frac{5}{6}\right)^{3}\approx -0.416666667

Calculate \frac{1}{3}\approx 0.333333333 to the power of 3 and get \frac{1}{27}\approx 0.037037037.

\frac{1}{8}+\frac{1}{27}-\left(\frac{5}{6}\right)^{3}\approx -0.416666667

Least common multiple of 8 and 27 is 216. Convert \frac{1}{8}=0.125 and \frac{1}{27}\approx 0.037037037 to fractions with denominator 216.

\frac{27}{216}+\frac{8}{216}-\left(\frac{5}{6}\right)^{3}\approx -0.416666667

Since \frac{27}{216}=0.125 and \frac{8}{216}\approx 0.037037037 have the same denominator, add them by adding their numerators.

\frac{27+8}{216}-\left(\frac{5}{6}\right)^{3}\approx -0.416666667

Calculate \frac{5}{6}\approx 0.833333333 to the power of 3 and get \frac{125}{216}\approx 0.578703704.

Since \frac{35}{216}\approx 0.162037037 and \frac{125}{216}\approx 0.578703704 have the same denominator, subtract them by subtracting their numerators.

\frac{35-125}{216}\approx -0.416666667

Subtract 125 from 35 to get -90.

\frac{-90}{216}\approx -0.416666667

Reduce the fraction \frac{-90}{216}\approx -0.416666667 to lowest terms by extracting and canceling out 18.

-\frac{5}{12}\approx -0.416666667

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