Solve [11/50+1/10+16/5+26/38*frac{45}{100}]

$$[ \frac { 11 } { 50 } + \frac { 1 } { 10 } + \frac { 16 } { 5 } + \frac { 26 } { 38 } \cdot \frac { 45 } { 100 } ]$$

Evaluate

$$\frac{7273}{1900}\approx 3.827894737$$

Solution Steps

Least common multiple of 50 and 10 is 50. Convert \frac{11}{50} and \frac{1}{10} to fractions with denominator 50.

$$\frac{11}{50}+\frac{5}{50}+\frac{16}{5}+\frac{26}{38}\times \frac{45}{100}$$

Since \frac{11}{50} and \frac{5}{50} have the same denominator, add them by adding their numerators.

$$\frac{11+5}{50}+\frac{16}{5}+\frac{26}{38}\times \frac{45}{100}$$

Add 11 and 5 to get 16.

$$\frac{16}{50}+\frac{16}{5}+\frac{26}{38}\times \frac{45}{100}$$

Reduce the fraction \frac{16}{50} to lowest terms by extracting and canceling out 2.

$$\frac{8}{25}+\frac{16}{5}+\frac{26}{38}\times \frac{45}{100}$$

Least common multiple of 25 and 5 is 25. Convert \frac{8}{25} and \frac{16}{5} to fractions with denominator 25.

$$\frac{8}{25}+\frac{80}{25}+\frac{26}{38}\times \frac{45}{100}$$

Since \frac{8}{25} and \frac{80}{25} have the same denominator, add them by adding their numerators.

$$\frac{8+80}{25}+\frac{26}{38}\times \frac{45}{100}$$

Add 8 and 80 to get 88.

$$\frac{88}{25}+\frac{26}{38}\times \frac{45}{100}$$

Reduce the fraction \frac{26}{38} to lowest terms by extracting and canceling out 2.

$$\frac{88}{25}+\frac{13}{19}\times \frac{45}{100}$$

Reduce the fraction \frac{45}{100} to lowest terms by extracting and canceling out 5.

$$\frac{88}{25}+\frac{13}{19}\times \frac{9}{20}$$

Multiply \frac{13}{19} times \frac{9}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{88}{25}+\frac{13\times 9}{19\times 20}$$

Do the multiplications in the fraction \frac{13\times 9}{19\times 20}.

$$\frac{88}{25}+\frac{117}{380}$$

Least common multiple of 25 and 380 is 1900. Convert \frac{88}{25} and \frac{117}{380} to fractions with denominator 1900.

$$\frac{6688}{1900}+\frac{585}{1900}$$

Since \frac{6688}{1900} and \frac{585}{1900} have the same denominator, add them by adding their numerators.

$$\frac{6688+585}{1900}$$

Add 6688 and 585 to get 7273.

$$\frac{7273}{1900}$$

Factor

$$\frac{7 \cdot 1039}{2 ^ {2} \cdot 5 ^ {2} \cdot 19} = 3\frac{1573}{1900} = 3.8278947368421052$$