Solve 33/66+32/39+30/40

$$\frac { 33 } { 66 } + \frac { 32 } { 39 } + \frac { 30 } { 40 }$$

Evaluate

$$\frac{323}{156}\approx 2.070512821$$

Solution Steps

Reduce the fraction \frac{33}{66} to lowest terms by extracting and canceling out 33.

$$\frac{1}{2}+\frac{32}{39}+\frac{30}{40}$$

Least common multiple of 2 and 39 is 78. Convert \frac{1}{2} and \frac{32}{39} to fractions with denominator 78.

$$\frac{39}{78}+\frac{64}{78}+\frac{30}{40}$$

Since \frac{39}{78} and \frac{64}{78} have the same denominator, add them by adding their numerators.

$$\frac{39+64}{78}+\frac{30}{40}$$

Add 39 and 64 to get 103.

$$\frac{103}{78}+\frac{30}{40}$$

Reduce the fraction \frac{30}{40} to lowest terms by extracting and canceling out 10.

$$\frac{103}{78}+\frac{3}{4}$$

Least common multiple of 78 and 4 is 156. Convert \frac{103}{78} and \frac{3}{4} to fractions with denominator 156.

$$\frac{206}{156}+\frac{117}{156}$$

Since \frac{206}{156} and \frac{117}{156} have the same denominator, add them by adding their numerators.

$$\frac{206+117}{156}$$

Add 206 and 117 to get 323.

$$\frac{323}{156}$$

Factor

$$\frac{17 \cdot 19}{2 ^ {2} \cdot 3 \cdot 13} = 2\frac{11}{156} = 2.0705128205128207$$