Solve 1/1.5+1/10+1/4.7+1/100

$$\frac{ 1 }{ 1.5 } + \frac{ 1 }{ 10 } + \frac{ 1 }{ 4.7 } + \frac{ 1 }{ 100 }$$

Evaluate

$$\frac{13951}{14100}\approx 0.989432624$$

Solution Steps

Expand \frac{1}{1.5} by multiplying both numerator and the denominator by 10.

$$\frac{10}{15}+\frac{1}{10}+\frac{1}{4.7}+\frac{1}{100}$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{2}{3}+\frac{1}{10}+\frac{1}{4.7}+\frac{1}{100}$$

Least common multiple of 3 and 10 is 30. Convert \frac{2}{3} and \frac{1}{10} to fractions with denominator 30.

$$\frac{20}{30}+\frac{3}{30}+\frac{1}{4.7}+\frac{1}{100}$$

Since \frac{20}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{20+3}{30}+\frac{1}{4.7}+\frac{1}{100}$$

Add 20 and 3 to get 23.

$$\frac{23}{30}+\frac{1}{4.7}+\frac{1}{100}$$

Expand \frac{1}{4.7} by multiplying both numerator and the denominator by 10.

$$\frac{23}{30}+\frac{10}{47}+\frac{1}{100}$$

Least common multiple of 30 and 47 is 1410. Convert \frac{23}{30} and \frac{10}{47} to fractions with denominator 1410.

$$\frac{1081}{1410}+\frac{300}{1410}+\frac{1}{100}$$

Since \frac{1081}{1410} and \frac{300}{1410} have the same denominator, add them by adding their numerators.

$$\frac{1081+300}{1410}+\frac{1}{100}$$

Add 1081 and 300 to get 1381.

$$\frac{1381}{1410}+\frac{1}{100}$$

Least common multiple of 1410 and 100 is 14100. Convert \frac{1381}{1410} and \frac{1}{100} to fractions with denominator 14100.

$$\frac{13810}{14100}+\frac{141}{14100}$$

Since \frac{13810}{14100} and \frac{141}{14100} have the same denominator, add them by adding their numerators.

$$\frac{13810+141}{14100}$$

Add 13810 and 141 to get 13951.

$$\frac{13951}{14100}$$

Factor

$$\frac{7 \cdot 1993}{3 \cdot 47 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 0.9894326241134752$$