Solve 3(49/50+49/53+49/65+49/74)

$$3 ( \frac { 49 } { 50 } + \frac { 49 } { 53 } + \frac { 49 } { 65 } + \frac { 49 } { 74 } )$$

Evaluate

$$\frac{6348783}{637325}\approx 9.961609854$$

Solution Steps

Least common multiple of 50 and 53 is 2650. Convert \frac{49}{50} and \frac{49}{53} to fractions with denominator 2650.

$$3\left(\frac{2597}{2650}+\frac{2450}{2650}+\frac{49}{65}+\frac{49}{74}\right)$$

Since \frac{2597}{2650} and \frac{2450}{2650} have the same denominator, add them by adding their numerators.

$$3\left(\frac{2597+2450}{2650}+\frac{49}{65}+\frac{49}{74}\right)$$

Add 2597 and 2450 to get 5047.

$$3\left(\frac{5047}{2650}+\frac{49}{65}+\frac{49}{74}\right)$$

Least common multiple of 2650 and 65 is 34450. Convert \frac{5047}{2650} and \frac{49}{65} to fractions with denominator 34450.

$$3\left(\frac{65611}{34450}+\frac{25970}{34450}+\frac{49}{74}\right)$$

Since \frac{65611}{34450} and \frac{25970}{34450} have the same denominator, add them by adding their numerators.

$$3\left(\frac{65611+25970}{34450}+\frac{49}{74}\right)$$

Add 65611 and 25970 to get 91581.

$$3\left(\frac{91581}{34450}+\frac{49}{74}\right)$$

Least common multiple of 34450 and 74 is 1274650. Convert \frac{91581}{34450} and \frac{49}{74} to fractions with denominator 1274650.

$$3\left(\frac{3388497}{1274650}+\frac{844025}{1274650}\right)$$

Since \frac{3388497}{1274650} and \frac{844025}{1274650} have the same denominator, add them by adding their numerators.

$$3\times \frac{3388497+844025}{1274650}$$

Add 3388497 and 844025 to get 4232522.

$$3\times \frac{4232522}{1274650}$$

Reduce the fraction \frac{4232522}{1274650} to lowest terms by extracting and canceling out 2.

$$3\times \frac{2116261}{637325}$$

Express 3\times \frac{2116261}{637325} as a single fraction.

$$\frac{3\times 2116261}{637325}$$

Multiply 3 and 2116261 to get 6348783.

$$\frac{6348783}{637325}$$

Factor

$$\frac{3 \cdot 7 ^ {2} \cdot 43189}{5 ^ {2} \cdot 13 \cdot 37 \cdot 53} = 9\frac{612858}{637325} = 9.961609853685326$$