Solve 6+21/30+5+71/45

$$6 + 2 \frac { 1 } { 30 } + 5 + 7 \frac { 1 } { 45 }$$

Evaluate

$$\frac{361}{18}\approx 20.055555556$$

Solution Steps

Multiply 2 and 30 to get 60.

$$6+\frac{60+1}{30}+5+\frac{7\times 45+1}{45}$$

Add 60 and 1 to get 61.

$$6+\frac{61}{30}+5+\frac{7\times 45+1}{45}$$

Convert 6 to fraction \frac{180}{30}.

$$\frac{180}{30}+\frac{61}{30}+5+\frac{7\times 45+1}{45}$$

Since \frac{180}{30} and \frac{61}{30} have the same denominator, add them by adding their numerators.

$$\frac{180+61}{30}+5+\frac{7\times 45+1}{45}$$

Add 180 and 61 to get 241.

$$\frac{241}{30}+5+\frac{7\times 45+1}{45}$$

Convert 5 to fraction \frac{150}{30}.

$$\frac{241}{30}+\frac{150}{30}+\frac{7\times 45+1}{45}$$

Since \frac{241}{30} and \frac{150}{30} have the same denominator, add them by adding their numerators.

$$\frac{241+150}{30}+\frac{7\times 45+1}{45}$$

Add 241 and 150 to get 391.

$$\frac{391}{30}+\frac{7\times 45+1}{45}$$

Multiply 7 and 45 to get 315.

$$\frac{391}{30}+\frac{315+1}{45}$$

Add 315 and 1 to get 316.

$$\frac{391}{30}+\frac{316}{45}$$

Least common multiple of 30 and 45 is 90. Convert \frac{391}{30} and \frac{316}{45} to fractions with denominator 90.

$$\frac{1173}{90}+\frac{632}{90}$$

Since \frac{1173}{90} and \frac{632}{90} have the same denominator, add them by adding their numerators.

$$\frac{1173+632}{90}$$

Add 1173 and 632 to get 1805.

$$\frac{1805}{90}$$

Reduce the fraction \frac{1805}{90} to lowest terms by extracting and canceling out 5.

$$\frac{361}{18}$$

Factor

$$\frac{19 ^ {2}}{2 \cdot 3 ^ {2}} = 20\frac{1}{18} = 20.055555555555557$$