Solve 76/7-52/9

$$7 \frac { 6 } { 7 } - 5 \frac { 2 } { 9 }$$

Evaluate

$$\frac{166}{63}\approx 2.634920635$$

Solution Steps

Multiply 7 and 7 to get 49.

$$\frac{49+6}{7}-\frac{5\times 9+2}{9}$$

Add 49 and 6 to get 55.

$$\frac{55}{7}-\frac{5\times 9+2}{9}$$

Multiply 5 and 9 to get 45.

$$\frac{55}{7}-\frac{45+2}{9}$$

Add 45 and 2 to get 47.

$$\frac{55}{7}-\frac{47}{9}$$

Least common multiple of 7 and 9 is 63. Convert \frac{55}{7} and \frac{47}{9} to fractions with denominator 63.

$$\frac{495}{63}-\frac{329}{63}$$

Since \frac{495}{63} and \frac{329}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{495-329}{63}$$

Subtract 329 from 495 to get 166.

$$\frac{166}{63}$$

Factor

$$\frac{2 \cdot 83}{3 ^ {2} \cdot 7} = 2\frac{40}{63} = 2.634920634920635$$