Solve 1/2+3/5:7/9-1/4

$$\frac { 1 } { 2 } + \frac { 3 } { 5 } : \frac { 7 } { 9 } - \frac { 1 } { 4 }$$

Evaluate

$$\frac{143}{140}\approx 1.021428571$$

Solution Steps

Divide \frac{3}{5} by \frac{7}{9} by multiplying \frac{3}{5} by the reciprocal of \frac{7}{9}.

$$\frac{1}{2}+\frac{3}{5}\times \frac{9}{7}-\frac{1}{4}$$

Multiply \frac{3}{5} times \frac{9}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{3\times 9}{5\times 7}-\frac{1}{4}$$

Do the multiplications in the fraction \frac{3\times 9}{5\times 7}.

$$\frac{1}{2}+\frac{27}{35}-\frac{1}{4}$$

Least common multiple of 2 and 35 is 70. Convert \frac{1}{2} and \frac{27}{35} to fractions with denominator 70.

$$\frac{35}{70}+\frac{54}{70}-\frac{1}{4}$$

Since \frac{35}{70} and \frac{54}{70} have the same denominator, add them by adding their numerators.

$$\frac{35+54}{70}-\frac{1}{4}$$

Add 35 and 54 to get 89.

$$\frac{89}{70}-\frac{1}{4}$$

Least common multiple of 70 and 4 is 140. Convert \frac{89}{70} and \frac{1}{4} to fractions with denominator 140.

$$\frac{178}{140}-\frac{35}{140}$$

Since \frac{178}{140} and \frac{35}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{178-35}{140}$$

Subtract 35 from 178 to get 143.

$$\frac{143}{140}$$

Factor

$$\frac{11 \cdot 13}{2 ^ {2} \cdot 5 \cdot 7} = 1\frac{3}{140} = 1.0214285714285714$$