Solve 5463/7820+8/30-9/38+10/47-frac{11}{57}+frac{12}{68}

$$\frac{ 5463 }{ 7820 } + \frac{ 8 }{ 30 } - \frac{ 9 }{ 38 } + \frac{ 10 }{ 47 } - \frac{ 11 }{ 57 } + \frac{ 12 }{ 68 }$$

Evaluate

$$\frac{1291445}{1396652}\approx 0.924672001$$

Solution Steps

Reduce the fraction \frac{8}{30} to lowest terms by extracting and canceling out 2.

$$\frac{5463}{7820}+\frac{4}{15}-\frac{9}{38}+\frac{10}{47}-\frac{11}{57}+\frac{12}{68}$$

Least common multiple of 7820 and 15 is 23460. Convert \frac{5463}{7820} and \frac{4}{15} to fractions with denominator 23460.

$$\frac{16389}{23460}+\frac{6256}{23460}-\frac{9}{38}+\frac{10}{47}-\frac{11}{57}+\frac{12}{68}$$

Since \frac{16389}{23460} and \frac{6256}{23460} have the same denominator, add them by adding their numerators.

$$\frac{16389+6256}{23460}-\frac{9}{38}+\frac{10}{47}-\frac{11}{57}+\frac{12}{68}$$

Add 16389 and 6256 to get 22645.

$$\frac{22645}{23460}-\frac{9}{38}+\frac{10}{47}-\frac{11}{57}+\frac{12}{68}$$

Reduce the fraction \frac{22645}{23460} to lowest terms by extracting and canceling out 5.

$$\frac{4529}{4692}-\frac{9}{38}+\frac{10}{47}-\frac{11}{57}+\frac{12}{68}$$

Least common multiple of 4692 and 38 is 89148. Convert \frac{4529}{4692} and \frac{9}{38} to fractions with denominator 89148.

$$\frac{86051}{89148}-\frac{21114}{89148}+\frac{10}{47}-\frac{11}{57}+\frac{12}{68}$$

Since \frac{86051}{89148} and \frac{21114}{89148} have the same denominator, subtract them by subtracting their numerators.

$$\frac{86051-21114}{89148}+\frac{10}{47}-\frac{11}{57}+\frac{12}{68}$$

Subtract 21114 from 86051 to get 64937.

$$\frac{64937}{89148}+\frac{10}{47}-\frac{11}{57}+\frac{12}{68}$$

Least common multiple of 89148 and 47 is 4189956. Convert \frac{64937}{89148} and \frac{10}{47} to fractions with denominator 4189956.

$$\frac{3052039}{4189956}+\frac{891480}{4189956}-\frac{11}{57}+\frac{12}{68}$$

Since \frac{3052039}{4189956} and \frac{891480}{4189956} have the same denominator, add them by adding their numerators.

$$\frac{3052039+891480}{4189956}-\frac{11}{57}+\frac{12}{68}$$

Add 3052039 and 891480 to get 3943519.

$$\frac{3943519}{4189956}-\frac{11}{57}+\frac{12}{68}$$

Least common multiple of 4189956 and 57 is 4189956. Convert \frac{3943519}{4189956} and \frac{11}{57} to fractions with denominator 4189956.

$$\frac{3943519}{4189956}-\frac{808588}{4189956}+\frac{12}{68}$$

Since \frac{3943519}{4189956} and \frac{808588}{4189956} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3943519-808588}{4189956}+\frac{12}{68}$$

Subtract 808588 from 3943519 to get 3134931.

$$\frac{3134931}{4189956}+\frac{12}{68}$$

Reduce the fraction \frac{3134931}{4189956} to lowest terms by extracting and canceling out 3.

$$\frac{1044977}{1396652}+\frac{12}{68}$$

Reduce the fraction \frac{12}{68} to lowest terms by extracting and canceling out 4.

$$\frac{1044977}{1396652}+\frac{3}{17}$$

Least common multiple of 1396652 and 17 is 1396652. Convert \frac{1044977}{1396652} and \frac{3}{17} to fractions with denominator 1396652.

$$\frac{1044977}{1396652}+\frac{246468}{1396652}$$

Since \frac{1044977}{1396652} and \frac{246468}{1396652} have the same denominator, add them by adding their numerators.

$$\frac{1044977+246468}{1396652}$$

Add 1044977 and 246468 to get 1291445.

$$\frac{1291445}{1396652}$$

Factor

$$\frac{5 \cdot 173 \cdot 1493}{2 ^ {2} \cdot 17 \cdot 19 \cdot 23 \cdot 47} = 0.9246720013288923$$