Solve (1+1/37)+2(1/5+9/153)]

$$( 1 + \frac { 1 } { 37 } ) + 2 ( \frac { 1 } { 5 } + \frac { 9 } { 153 } ) ]$$

Evaluate

$$\frac{4858}{3145}\approx 1.544674086$$

Solution Steps

Convert 1 to fraction \frac{37}{37}.

$$\frac{37}{37}+\frac{1}{37}+2\left(\frac{1}{5}+\frac{9}{153}\right)$$

Since \frac{37}{37} and \frac{1}{37} have the same denominator, add them by adding their numerators.

$$\frac{37+1}{37}+2\left(\frac{1}{5}+\frac{9}{153}\right)$$

Add 37 and 1 to get 38.

$$\frac{38}{37}+2\left(\frac{1}{5}+\frac{9}{153}\right)$$

Reduce the fraction \frac{9}{153} to lowest terms by extracting and canceling out 9.

$$\frac{38}{37}+2\left(\frac{1}{5}+\frac{1}{17}\right)$$

Least common multiple of 5 and 17 is 85. Convert \frac{1}{5} and \frac{1}{17} to fractions with denominator 85.

$$\frac{38}{37}+2\left(\frac{17}{85}+\frac{5}{85}\right)$$

Since \frac{17}{85} and \frac{5}{85} have the same denominator, add them by adding their numerators.

$$\frac{38}{37}+2\times \frac{17+5}{85}$$

Add 17 and 5 to get 22.

$$\frac{38}{37}+2\times \frac{22}{85}$$

Express 2\times \frac{22}{85} as a single fraction.

$$\frac{38}{37}+\frac{2\times 22}{85}$$

Multiply 2 and 22 to get 44.

$$\frac{38}{37}+\frac{44}{85}$$

Least common multiple of 37 and 85 is 3145. Convert \frac{38}{37} and \frac{44}{85} to fractions with denominator 3145.

$$\frac{3230}{3145}+\frac{1628}{3145}$$

Since \frac{3230}{3145} and \frac{1628}{3145} have the same denominator, add them by adding their numerators.

$$\frac{3230+1628}{3145}$$

Add 3230 and 1628 to get 4858.

$$\frac{4858}{3145}$$

Factor

$$\frac{2 \cdot 7 \cdot 347}{5 \cdot 17 \cdot 37} = 1\frac{1713}{3145} = 1.5446740858505565$$