Solve {l}{3/25+4/1:3+24/98}{-1/28}

$$\left. \begin{array} { l } { \frac { 3 } { 25 } + \frac { 4 } { 1 } : 3 + \frac { 24 } { 98 } } \\ { - \frac { 1 } { 28 } } \end{array} \right.$$

Evaluate

$$\frac{24439}{14700}\approx 1.662517007$$

Solution Steps

Express \frac{\frac{4}{1}}{3} as a single fraction.

$$\frac{3}{25}+\frac{4}{3}+\frac{24}{98}-\frac{1}{28}$$

Least common multiple of 25 and 3 is 75. Convert \frac{3}{25} and \frac{4}{3} to fractions with denominator 75.

$$\frac{9}{75}+\frac{100}{75}+\frac{24}{98}-\frac{1}{28}$$

Since \frac{9}{75} and \frac{100}{75} have the same denominator, add them by adding their numerators.

$$\frac{9+100}{75}+\frac{24}{98}-\frac{1}{28}$$

Add 9 and 100 to get 109.

$$\frac{109}{75}+\frac{24}{98}-\frac{1}{28}$$

Reduce the fraction \frac{24}{98} to lowest terms by extracting and canceling out 2.

$$\frac{109}{75}+\frac{12}{49}-\frac{1}{28}$$

Least common multiple of 75 and 49 is 3675. Convert \frac{109}{75} and \frac{12}{49} to fractions with denominator 3675.

$$\frac{5341}{3675}+\frac{900}{3675}-\frac{1}{28}$$

Since \frac{5341}{3675} and \frac{900}{3675} have the same denominator, add them by adding their numerators.

$$\frac{5341+900}{3675}-\frac{1}{28}$$

Add 5341 and 900 to get 6241.

$$\frac{6241}{3675}-\frac{1}{28}$$

Least common multiple of 3675 and 28 is 14700. Convert \frac{6241}{3675} and \frac{1}{28} to fractions with denominator 14700.

$$\frac{24964}{14700}-\frac{525}{14700}$$

Since \frac{24964}{14700} and \frac{525}{14700} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24964-525}{14700}$$

Subtract 525 from 24964 to get 24439.

$$\frac{24439}{14700}$$

Factor

$$\frac{24439}{2 ^ {2} \cdot 3 \cdot 5 ^ {2} \cdot 7 ^ {2}} = 1\frac{9739}{14700} = 1.662517006802721$$