Solve =3/70+5/130+3/208+3/304+frac{3}{410}+frac{1}{222}

$$= \frac { 3 } { 70 } + \frac { 5 } { 130 } + \frac { 3 } { 208 } + \frac { 3 } { 304 } + \frac { 3 } { 410 } + \frac { 1 } { 222 }$$

Evaluate

$$\frac{4620164}{39343395}\approx 0.117431757$$

Solution Steps

Reduce the fraction \frac{5}{130} to lowest terms by extracting and canceling out 5.

$$\frac{3}{70}+\frac{1}{26}+\frac{3}{208}+\frac{3}{304}+\frac{3}{410}+\frac{1}{222}$$

Least common multiple of 70 and 26 is 910. Convert \frac{3}{70} and \frac{1}{26} to fractions with denominator 910.

$$\frac{39}{910}+\frac{35}{910}+\frac{3}{208}+\frac{3}{304}+\frac{3}{410}+\frac{1}{222}$$

Since \frac{39}{910} and \frac{35}{910} have the same denominator, add them by adding their numerators.

$$\frac{39+35}{910}+\frac{3}{208}+\frac{3}{304}+\frac{3}{410}+\frac{1}{222}$$

Add 39 and 35 to get 74.

$$\frac{74}{910}+\frac{3}{208}+\frac{3}{304}+\frac{3}{410}+\frac{1}{222}$$

Reduce the fraction \frac{74}{910} to lowest terms by extracting and canceling out 2.

$$\frac{37}{455}+\frac{3}{208}+\frac{3}{304}+\frac{3}{410}+\frac{1}{222}$$

Least common multiple of 455 and 208 is 7280. Convert \frac{37}{455} and \frac{3}{208} to fractions with denominator 7280.

$$\frac{592}{7280}+\frac{105}{7280}+\frac{3}{304}+\frac{3}{410}+\frac{1}{222}$$

Since \frac{592}{7280} and \frac{105}{7280} have the same denominator, add them by adding their numerators.

$$\frac{592+105}{7280}+\frac{3}{304}+\frac{3}{410}+\frac{1}{222}$$

Add 592 and 105 to get 697.

$$\frac{697}{7280}+\frac{3}{304}+\frac{3}{410}+\frac{1}{222}$$

Least common multiple of 7280 and 304 is 138320. Convert \frac{697}{7280} and \frac{3}{304} to fractions with denominator 138320.

$$\frac{13243}{138320}+\frac{1365}{138320}+\frac{3}{410}+\frac{1}{222}$$

Since \frac{13243}{138320} and \frac{1365}{138320} have the same denominator, add them by adding their numerators.

$$\frac{13243+1365}{138320}+\frac{3}{410}+\frac{1}{222}$$

Add 13243 and 1365 to get 14608.

$$\frac{14608}{138320}+\frac{3}{410}+\frac{1}{222}$$

Reduce the fraction \frac{14608}{138320} to lowest terms by extracting and canceling out 16.

$$\frac{913}{8645}+\frac{3}{410}+\frac{1}{222}$$

Least common multiple of 8645 and 410 is 708890. Convert \frac{913}{8645} and \frac{3}{410} to fractions with denominator 708890.

$$\frac{74866}{708890}+\frac{5187}{708890}+\frac{1}{222}$$

Since \frac{74866}{708890} and \frac{5187}{708890} have the same denominator, add them by adding their numerators.

$$\frac{74866+5187}{708890}+\frac{1}{222}$$

Add 74866 and 5187 to get 80053.

$$\frac{80053}{708890}+\frac{1}{222}$$

Least common multiple of 708890 and 222 is 78686790. Convert \frac{80053}{708890} and \frac{1}{222} to fractions with denominator 78686790.

$$\frac{8885883}{78686790}+\frac{354445}{78686790}$$

Since \frac{8885883}{78686790} and \frac{354445}{78686790} have the same denominator, add them by adding their numerators.

$$\frac{8885883+354445}{78686790}$$

Add 8885883 and 354445 to get 9240328.

$$\frac{9240328}{78686790}$$

Reduce the fraction \frac{9240328}{78686790} to lowest terms by extracting and canceling out 2.

$$\frac{4620164}{39343395}$$

Factor

$$\frac{2 ^ {2} \cdot 29 \cdot 39829}{3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \cdot 37 \cdot 41} = 0.11743175696962603$$