Solve 3div8*1.415+2+3div4+3div8

$$3 \div 8 \times 1.415+2+3 \div 4+3 \div 8$$

Evaluate

$$3.655625$$

Solution Steps

Convert decimal number 1.415 to fraction \frac{1415}{1000}. Reduce the fraction \frac{1415}{1000} to lowest terms by extracting and canceling out 5.

$$\frac{3}{8}\times \frac{283}{200}+2+\frac{3}{4}+\frac{3}{8}$$

Multiply \frac{3}{8} times \frac{283}{200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 283}{8\times 200}+2+\frac{3}{4}+\frac{3}{8}$$

Do the multiplications in the fraction \frac{3\times 283}{8\times 200}.

$$\frac{849}{1600}+2+\frac{3}{4}+\frac{3}{8}$$

Convert 2 to fraction \frac{3200}{1600}.

$$\frac{849}{1600}+\frac{3200}{1600}+\frac{3}{4}+\frac{3}{8}$$

Since \frac{849}{1600} and \frac{3200}{1600} have the same denominator, add them by adding their numerators.

$$\frac{849+3200}{1600}+\frac{3}{4}+\frac{3}{8}$$

Add 849 and 3200 to get 4049.

$$\frac{4049}{1600}+\frac{3}{4}+\frac{3}{8}$$

Least common multiple of 1600 and 4 is 1600. Convert \frac{4049}{1600} and \frac{3}{4} to fractions with denominator 1600.

$$\frac{4049}{1600}+\frac{1200}{1600}+\frac{3}{8}$$

Since \frac{4049}{1600} and \frac{1200}{1600} have the same denominator, add them by adding their numerators.

$$\frac{4049+1200}{1600}+\frac{3}{8}$$

Add 4049 and 1200 to get 5249.

$$\frac{5249}{1600}+\frac{3}{8}$$

Least common multiple of 1600 and 8 is 1600. Convert \frac{5249}{1600} and \frac{3}{8} to fractions with denominator 1600.

$$\frac{5249}{1600}+\frac{600}{1600}$$

Since \frac{5249}{1600} and \frac{600}{1600} have the same denominator, add them by adding their numerators.

$$\frac{5249+600}{1600}$$

Add 5249 and 600 to get 5849.

$$\frac{5849}{1600}$$

Factor

$$\frac{5849}{2 ^ {6} \cdot 5 ^ {2}} = 3\frac{1049}{1600} = 3.655625$$