Solve 1-1/6+1/42+1/56+1/72+frac{1}{90}

$$1- \frac{ 1 }{ 6 } + \frac{ 1 }{ 42 } + \frac{ 1 }{ 56 } + \frac{ 1 }{ 72 } + \frac{ 1 }{ 90 }$$

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

Convert 1 to fraction \frac{6}{6}.

$$\frac{6}{6}-\frac{1}{6}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{6}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Subtract 1 from 6 to get 5.

$$\frac{5}{6}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 6 and 42 is 42. Convert \frac{5}{6} and \frac{1}{42} to fractions with denominator 42.

$$\frac{35}{42}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{35}{42} and \frac{1}{42} have the same denominator, add them by adding their numerators.

$$\frac{35+1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 35 and 1 to get 36.

$$\frac{36}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{36}{42} to lowest terms by extracting and canceling out 6.

$$\frac{6}{7}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 7 and 56 is 56. Convert \frac{6}{7} and \frac{1}{56} to fractions with denominator 56.

$$\frac{48}{56}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{48}{56} and \frac{1}{56} have the same denominator, add them by adding their numerators.

$$\frac{48+1}{56}+\frac{1}{72}+\frac{1}{90}$$

Add 48 and 1 to get 49.

$$\frac{49}{56}+\frac{1}{72}+\frac{1}{90}$$

Reduce the fraction \frac{49}{56} to lowest terms by extracting and canceling out 7.

$$\frac{7}{8}+\frac{1}{72}+\frac{1}{90}$$

Least common multiple of 8 and 72 is 72. Convert \frac{7}{8} and \frac{1}{72} to fractions with denominator 72.

$$\frac{63}{72}+\frac{1}{72}+\frac{1}{90}$$

Since \frac{63}{72} and \frac{1}{72} have the same denominator, add them by adding their numerators.

$$\frac{63+1}{72}+\frac{1}{90}$$

Add 63 and 1 to get 64.

$$\frac{64}{72}+\frac{1}{90}$$

Reduce the fraction \frac{64}{72} to lowest terms by extracting and canceling out 8.

$$\frac{8}{9}+\frac{1}{90}$$

Least common multiple of 9 and 90 is 90. Convert \frac{8}{9} and \frac{1}{90} to fractions with denominator 90.

$$\frac{80}{90}+\frac{1}{90}$$

Since \frac{80}{90} and \frac{1}{90} have the same denominator, add them by adding their numerators.

$$\frac{80+1}{90}$$

Add 80 and 1 to get 81.

$$\frac{81}{90}$$

Reduce the fraction \frac{81}{90} to lowest terms by extracting and canceling out 9.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$