Solve min1/400+1/50+3/10+1/25+frac{9}{16}+frac{3}{40}

$$\min \frac { 1 } { 400 } + \frac { 1 } { 50 } + \frac { 3 } { 10 } + \frac { 1 } { 25 } + \frac { 9 } { 16 } + \frac { 3 } { 40 }$$

Evaluate

$$1$$

Solution Steps

To find the minimum of \frac{1}{400}, first put the numbers in order from least to greatest. This set is already in order.

$$\frac{1}{400}$$

The minimum is \frac{1}{400}, the leftmost value in the set ordered from least to greatest.

$$\frac{1}{400}+\frac{1}{50}+\frac{3}{10}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Least common multiple of 400 and 50 is 400. Convert \frac{1}{400} and \frac{1}{50} to fractions with denominator 400.

$$\frac{1}{400}+\frac{8}{400}+\frac{3}{10}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Since \frac{1}{400} and \frac{8}{400} have the same denominator, add them by adding their numerators.

$$\frac{1+8}{400}+\frac{3}{10}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Add 1 and 8 to get 9.

$$\frac{9}{400}+\frac{3}{10}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Least common multiple of 400 and 10 is 400. Convert \frac{9}{400} and \frac{3}{10} to fractions with denominator 400.

$$\frac{9}{400}+\frac{120}{400}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Since \frac{9}{400} and \frac{120}{400} have the same denominator, add them by adding their numerators.

$$\frac{9+120}{400}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Add 9 and 120 to get 129.

$$\frac{129}{400}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Least common multiple of 400 and 25 is 400. Convert \frac{129}{400} and \frac{1}{25} to fractions with denominator 400.

$$\frac{129}{400}+\frac{16}{400}+\frac{9}{16}+\frac{3}{40}$$

Since \frac{129}{400} and \frac{16}{400} have the same denominator, add them by adding their numerators.

$$\frac{129+16}{400}+\frac{9}{16}+\frac{3}{40}$$

Add 129 and 16 to get 145.

$$\frac{145}{400}+\frac{9}{16}+\frac{3}{40}$$

Reduce the fraction \frac{145}{400} to lowest terms by extracting and canceling out 5.

$$\frac{29}{80}+\frac{9}{16}+\frac{3}{40}$$

Least common multiple of 80 and 16 is 80. Convert \frac{29}{80} and \frac{9}{16} to fractions with denominator 80.

$$\frac{29}{80}+\frac{45}{80}+\frac{3}{40}$$

Since \frac{29}{80} and \frac{45}{80} have the same denominator, add them by adding their numerators.

$$\frac{29+45}{80}+\frac{3}{40}$$

Add 29 and 45 to get 74.

$$\frac{74}{80}+\frac{3}{40}$$

Reduce the fraction \frac{74}{80} to lowest terms by extracting and canceling out 2.

$$\frac{37}{40}+\frac{3}{40}$$

Since \frac{37}{40} and \frac{3}{40} have the same denominator, add them by adding their numerators.

$$\frac{37+3}{40}$$

Add 37 and 3 to get 40.

$$\frac{40}{40}$$

Divide 40 by 40 to get 1.

$$1$$

Factor

$$1$$