Solve 7/36+11/34+7/32+9/25

$$\frac{ 7 }{ 36 } + \frac{ 11 }{ 34 } + \frac{ 7 }{ 32 } + \frac{ 9 }{ 25 }$$

Evaluate

$$\frac{134239}{122400}\approx 1.096723856$$

Solution Steps

Least common multiple of 36 and 34 is 612. Convert \frac{7}{36} and \frac{11}{34} to fractions with denominator 612.

$$\frac{119}{612}+\frac{198}{612}+\frac{7}{32}+\frac{9}{25}$$

Since \frac{119}{612} and \frac{198}{612} have the same denominator, add them by adding their numerators.

$$\frac{119+198}{612}+\frac{7}{32}+\frac{9}{25}$$

Add 119 and 198 to get 317.

$$\frac{317}{612}+\frac{7}{32}+\frac{9}{25}$$

Least common multiple of 612 and 32 is 4896. Convert \frac{317}{612} and \frac{7}{32} to fractions with denominator 4896.

$$\frac{2536}{4896}+\frac{1071}{4896}+\frac{9}{25}$$

Since \frac{2536}{4896} and \frac{1071}{4896} have the same denominator, add them by adding their numerators.

$$\frac{2536+1071}{4896}+\frac{9}{25}$$

Add 2536 and 1071 to get 3607.

$$\frac{3607}{4896}+\frac{9}{25}$$

Least common multiple of 4896 and 25 is 122400. Convert \frac{3607}{4896} and \frac{9}{25} to fractions with denominator 122400.

$$\frac{90175}{122400}+\frac{44064}{122400}$$

Since \frac{90175}{122400} and \frac{44064}{122400} have the same denominator, add them by adding their numerators.

$$\frac{90175+44064}{122400}$$

Add 90175 and 44064 to get 134239.

$$\frac{134239}{122400}$$

Factor

$$\frac{7 \cdot 127 \cdot 151}{2 ^ {5} \cdot 3 ^ {2} \cdot 5 ^ {2} \cdot 17} = 1\frac{11839}{122400} = 1.0967238562091504$$