Solve 0.3*3/40+0.2*1/5+0.3/10+.4/40

$$0.3 \times \frac { 3 } { 40 } + 0.2 \times \frac { 1 } { 5 } + \frac { 0.3 } { 10 } + \frac { .4 } { 40 }$$

Evaluate

$$0.1025$$

Solution Steps

Convert decimal number 0.3 to fraction \frac{3}{10}.

$$\frac{3}{10}\times \frac{3}{40}+0.2\times \frac{1}{5}+\frac{0.3}{10}+\frac{0.4}{40}$$

Multiply \frac{3}{10} times \frac{3}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 3}{10\times 40}+0.2\times \frac{1}{5}+\frac{0.3}{10}+\frac{0.4}{40}$$

Do the multiplications in the fraction \frac{3\times 3}{10\times 40}.

$$\frac{9}{400}+0.2\times \frac{1}{5}+\frac{0.3}{10}+\frac{0.4}{40}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{9}{400}+\frac{1}{5}\times \frac{1}{5}+\frac{0.3}{10}+\frac{0.4}{40}$$

Multiply \frac{1}{5} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{400}+\frac{1\times 1}{5\times 5}+\frac{0.3}{10}+\frac{0.4}{40}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 5}.

$$\frac{9}{400}+\frac{1}{25}+\frac{0.3}{10}+\frac{0.4}{40}$$

Least common multiple of 400 and 25 is 400. Convert \frac{9}{400} and \frac{1}{25} to fractions with denominator 400.

$$\frac{9}{400}+\frac{16}{400}+\frac{0.3}{10}+\frac{0.4}{40}$$

Since \frac{9}{400} and \frac{16}{400} have the same denominator, add them by adding their numerators.

$$\frac{9+16}{400}+\frac{0.3}{10}+\frac{0.4}{40}$$

Add 9 and 16 to get 25.

$$\frac{25}{400}+\frac{0.3}{10}+\frac{0.4}{40}$$

Reduce the fraction \frac{25}{400} to lowest terms by extracting and canceling out 25.

$$\frac{1}{16}+\frac{0.3}{10}+\frac{0.4}{40}$$

Expand \frac{0.3}{10} by multiplying both numerator and the denominator by 10.

$$\frac{1}{16}+\frac{3}{100}+\frac{0.4}{40}$$

Least common multiple of 16 and 100 is 400. Convert \frac{1}{16} and \frac{3}{100} to fractions with denominator 400.

$$\frac{25}{400}+\frac{12}{400}+\frac{0.4}{40}$$

Since \frac{25}{400} and \frac{12}{400} have the same denominator, add them by adding their numerators.

$$\frac{25+12}{400}+\frac{0.4}{40}$$

Add 25 and 12 to get 37.

$$\frac{37}{400}+\frac{0.4}{40}$$

Expand \frac{0.4}{40} by multiplying both numerator and the denominator by 10.

$$\frac{37}{400}+\frac{4}{400}$$

Since \frac{37}{400} and \frac{4}{400} have the same denominator, add them by adding their numerators.

$$\frac{37+4}{400}$$

Add 37 and 4 to get 41.

$$\frac{41}{400}$$

Factor

$$\frac{41}{2 ^ {4} \cdot 5 ^ {2}} = 0.1025$$