Solve 100*1/5+95*2/25+83*6/25+68*2/25+75*frac{2}{25}+89*frac{3}{25}+60*frac{1}{25}+91*frac{2}{25}+89*frac{2}{25}

$$100 \times \frac{ 1 }{ 5 } +95 \times \frac{ 2 }{ 25 } +83 \times \frac{ 6 }{ 25 } +68 \times \frac{ 2 }{ 25 } +75 \times \frac{ 2 }{ 25 } +89 \times \frac{ 3 }{ 25 } +60 \times \frac{ 1 }{ 25 } +91 \times \frac{ 2 }{ 25 } +89 \times \frac{ 2 }{ 25 }$$

Evaluate

$$\frac{2161}{25}=86.44$$

Solution Steps

Multiply 100 and \frac{1}{5} to get \frac{100}{5}.

$$\frac{100}{5}+95\times \frac{2}{25}+83\times \frac{6}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Divide 100 by 5 to get 20.

$$20+95\times \frac{2}{25}+83\times \frac{6}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Express 95\times \frac{2}{25} as a single fraction.

$$20+\frac{95\times 2}{25}+83\times \frac{6}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Multiply 95 and 2 to get 190.

$$20+\frac{190}{25}+83\times \frac{6}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Reduce the fraction \frac{190}{25} to lowest terms by extracting and canceling out 5.

$$20+\frac{38}{5}+83\times \frac{6}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Convert 20 to fraction \frac{100}{5}.

$$\frac{100}{5}+\frac{38}{5}+83\times \frac{6}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Since \frac{100}{5} and \frac{38}{5} have the same denominator, add them by adding their numerators.

$$\frac{100+38}{5}+83\times \frac{6}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Add 100 and 38 to get 138.

$$\frac{138}{5}+83\times \frac{6}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Express 83\times \frac{6}{25} as a single fraction.

$$\frac{138}{5}+\frac{83\times 6}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Multiply 83 and 6 to get 498.

$$\frac{138}{5}+\frac{498}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Least common multiple of 5 and 25 is 25. Convert \frac{138}{5} and \frac{498}{25} to fractions with denominator 25.

$$\frac{690}{25}+\frac{498}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Since \frac{690}{25} and \frac{498}{25} have the same denominator, add them by adding their numerators.

$$\frac{690+498}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Add 690 and 498 to get 1188.

$$\frac{1188}{25}+68\times \frac{2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Express 68\times \frac{2}{25} as a single fraction.

$$\frac{1188}{25}+\frac{68\times 2}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Multiply 68 and 2 to get 136.

$$\frac{1188}{25}+\frac{136}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Since \frac{1188}{25} and \frac{136}{25} have the same denominator, add them by adding their numerators.

$$\frac{1188+136}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Add 1188 and 136 to get 1324.

$$\frac{1324}{25}+75\times \frac{2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Express 75\times \frac{2}{25} as a single fraction.

$$\frac{1324}{25}+\frac{75\times 2}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Multiply 75 and 2 to get 150.

$$\frac{1324}{25}+\frac{150}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Since \frac{1324}{25} and \frac{150}{25} have the same denominator, add them by adding their numerators.

$$\frac{1324+150}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Add 1324 and 150 to get 1474.

$$\frac{1474}{25}+89\times \frac{3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Express 89\times \frac{3}{25} as a single fraction.

$$\frac{1474}{25}+\frac{89\times 3}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Multiply 89 and 3 to get 267.

$$\frac{1474}{25}+\frac{267}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Since \frac{1474}{25} and \frac{267}{25} have the same denominator, add them by adding their numerators.

$$\frac{1474+267}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Add 1474 and 267 to get 1741.

$$\frac{1741}{25}+60\times \frac{1}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Multiply 60 and \frac{1}{25} to get \frac{60}{25}.

$$\frac{1741}{25}+\frac{60}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Since \frac{1741}{25} and \frac{60}{25} have the same denominator, add them by adding their numerators.

$$\frac{1741+60}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Add 1741 and 60 to get 1801.

$$\frac{1801}{25}+91\times \frac{2}{25}+89\times \frac{2}{25}$$

Express 91\times \frac{2}{25} as a single fraction.

$$\frac{1801}{25}+\frac{91\times 2}{25}+89\times \frac{2}{25}$$

Multiply 91 and 2 to get 182.

$$\frac{1801}{25}+\frac{182}{25}+89\times \frac{2}{25}$$

Since \frac{1801}{25} and \frac{182}{25} have the same denominator, add them by adding their numerators.

$$\frac{1801+182}{25}+89\times \frac{2}{25}$$

Add 1801 and 182 to get 1983.

$$\frac{1983}{25}+89\times \frac{2}{25}$$

Express 89\times \frac{2}{25} as a single fraction.

$$\frac{1983}{25}+\frac{89\times 2}{25}$$

Multiply 89 and 2 to get 178.

$$\frac{1983}{25}+\frac{178}{25}$$

Since \frac{1983}{25} and \frac{178}{25} have the same denominator, add them by adding their numerators.

$$\frac{1983+178}{25}$$

Add 1983 and 178 to get 2161.

$$\frac{2161}{25}$$

Factor

$$\frac{2161}{5 ^ {2}} = 86\frac{11}{25} = 86.44$$