Solve (1213/25+78/17)2.5+(99/17+1012/25)2frac{1}{2}

$$(12 \frac{ 13 }{ 25 } +7 \frac{ 8 }{ 17 } )2.5+(9 \frac{ 9 }{ 17 } +10 \frac{ 12 }{ 25 } )2 \frac{ 1 }{ 2 }$$

Evaluate

$$100$$

Solution Steps

Multiply 12 and 25 to get 300.

$$\left(\frac{300+13}{25}+\frac{7\times 17+8}{17}\right)\times 2.5+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Add 300 and 13 to get 313.

$$\left(\frac{313}{25}+\frac{7\times 17+8}{17}\right)\times 2.5+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Multiply 7 and 17 to get 119.

$$\left(\frac{313}{25}+\frac{119+8}{17}\right)\times 2.5+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Add 119 and 8 to get 127.

$$\left(\frac{313}{25}+\frac{127}{17}\right)\times 2.5+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Least common multiple of 25 and 17 is 425. Convert \frac{313}{25} and \frac{127}{17} to fractions with denominator 425.

$$\left(\frac{5321}{425}+\frac{3175}{425}\right)\times 2.5+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Since \frac{5321}{425} and \frac{3175}{425} have the same denominator, add them by adding their numerators.

$$\frac{5321+3175}{425}\times 2.5+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Add 5321 and 3175 to get 8496.

$$\frac{8496}{425}\times 2.5+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{8496}{425}\times \frac{5}{2}+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Multiply \frac{8496}{425} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8496\times 5}{425\times 2}+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Do the multiplications in the fraction \frac{8496\times 5}{425\times 2}.

$$\frac{42480}{850}+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Reduce the fraction \frac{42480}{850} to lowest terms by extracting and canceling out 10.

$$\frac{4248}{85}+\left(\frac{9\times 17+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Multiply 9 and 17 to get 153.

$$\frac{4248}{85}+\left(\frac{153+9}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Add 153 and 9 to get 162.

$$\frac{4248}{85}+\left(\frac{162}{17}+\frac{10\times 25+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Multiply 10 and 25 to get 250.

$$\frac{4248}{85}+\left(\frac{162}{17}+\frac{250+12}{25}\right)\times \frac{2\times 2+1}{2}$$

Add 250 and 12 to get 262.

$$\frac{4248}{85}+\left(\frac{162}{17}+\frac{262}{25}\right)\times \frac{2\times 2+1}{2}$$

Least common multiple of 17 and 25 is 425. Convert \frac{162}{17} and \frac{262}{25} to fractions with denominator 425.

$$\frac{4248}{85}+\left(\frac{4050}{425}+\frac{4454}{425}\right)\times \frac{2\times 2+1}{2}$$

Since \frac{4050}{425} and \frac{4454}{425} have the same denominator, add them by adding their numerators.

$$\frac{4248}{85}+\frac{4050+4454}{425}\times \frac{2\times 2+1}{2}$$

Add 4050 and 4454 to get 8504.

$$\frac{4248}{85}+\frac{8504}{425}\times \frac{2\times 2+1}{2}$$

Multiply 2 and 2 to get 4.

$$\frac{4248}{85}+\frac{8504}{425}\times \frac{4+1}{2}$$

Add 4 and 1 to get 5.

$$\frac{4248}{85}+\frac{8504}{425}\times \frac{5}{2}$$

Multiply \frac{8504}{425} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4248}{85}+\frac{8504\times 5}{425\times 2}$$

Do the multiplications in the fraction \frac{8504\times 5}{425\times 2}.

$$\frac{4248}{85}+\frac{42520}{850}$$

Reduce the fraction \frac{42520}{850} to lowest terms by extracting and canceling out 10.

$$\frac{4248}{85}+\frac{4252}{85}$$

Since \frac{4248}{85} and \frac{4252}{85} have the same denominator, add them by adding their numerators.

$$\frac{4248+4252}{85}$$

Add 4248 and 4252 to get 8500.

$$\frac{8500}{85}$$

Divide 8500 by 85 to get 100.

$$100$$

Factor

$$2^{2}\times 5^{2}$$