Solve (1-1/3+4/7)+4/9

$$( 1 - \frac { 1 } { 3 } + \frac { 4 } { 7 } ) + \frac { 4 } { 9 }$$

Evaluate

$$\frac{106}{63}\approx 1.682539683$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}-\frac{1}{3}+\frac{4}{7}+\frac{4}{9}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-1}{3}+\frac{4}{7}+\frac{4}{9}$$

Subtract 1 from 3 to get 2.

$$\frac{2}{3}+\frac{4}{7}+\frac{4}{9}$$

Least common multiple of 3 and 7 is 21. Convert \frac{2}{3} and \frac{4}{7} to fractions with denominator 21.

$$\frac{14}{21}+\frac{12}{21}+\frac{4}{9}$$

Since \frac{14}{21} and \frac{12}{21} have the same denominator, add them by adding their numerators.

$$\frac{14+12}{21}+\frac{4}{9}$$

Add 14 and 12 to get 26.

$$\frac{26}{21}+\frac{4}{9}$$

Least common multiple of 21 and 9 is 63. Convert \frac{26}{21} and \frac{4}{9} to fractions with denominator 63.

$$\frac{78}{63}+\frac{28}{63}$$

Since \frac{78}{63} and \frac{28}{63} have the same denominator, add them by adding their numerators.

$$\frac{78+28}{63}$$

Add 78 and 28 to get 106.

$$\frac{106}{63}$$

Factor

$$\frac{2 \cdot 53}{3 ^ {2} \cdot 7} = 1\frac{43}{63} = 1.6825396825396826$$