Solve 0.7*[0.25*4*100+0.38*3*200+0.37*1*100]/400+0.3*3=

$$0.7 \times \frac { [ 0.25 \times 4 \times 100 + 0.38 \times 3 \times 200 + 0.37 \times 1 \times 100 ] } { 400 } + 0.3 \times 3 =$$

Evaluate

$$1.53875$$

Solution Steps

Multiply 0.25 and 4 to get 1.

$$0.7\times \frac{100+0.38\times 3\times 200+0.37\times 1\times 100}{400}+0.3\times 3$$

Multiply 0.38 and 3 to get 1.14.

$$0.7\times \frac{100+1.14\times 200+0.37\times 1\times 100}{400}+0.3\times 3$$

Multiply 1.14 and 200 to get 228.

$$0.7\times \frac{100+228+0.37\times 1\times 100}{400}+0.3\times 3$$

Add 100 and 228 to get 328.

$$0.7\times \frac{328+0.37\times 1\times 100}{400}+0.3\times 3$$

Multiply 0.37 and 1 to get 0.37.

$$0.7\times \frac{328+0.37\times 100}{400}+0.3\times 3$$

Multiply 0.37 and 100 to get 37.

$$0.7\times \frac{328+37}{400}+0.3\times 3$$

Add 328 and 37 to get 365.

$$0.7\times \frac{365}{400}+0.3\times 3$$

Reduce the fraction \frac{365}{400} to lowest terms by extracting and canceling out 5.

$$0.7\times \frac{73}{80}+0.3\times 3$$

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$\frac{7}{10}\times \frac{73}{80}+0.3\times 3$$

Multiply \frac{7}{10} times \frac{73}{80} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 73}{10\times 80}+0.3\times 3$$

Do the multiplications in the fraction \frac{7\times 73}{10\times 80}.

$$\frac{511}{800}+0.3\times 3$$

Multiply 0.3 and 3 to get 0.9.

$$\frac{511}{800}+0.9$$

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$\frac{511}{800}+\frac{9}{10}$$

Least common multiple of 800 and 10 is 800. Convert \frac{511}{800} and \frac{9}{10} to fractions with denominator 800.

$$\frac{511}{800}+\frac{720}{800}$$

Since \frac{511}{800} and \frac{720}{800} have the same denominator, add them by adding their numerators.

$$\frac{511+720}{800}$$

Add 511 and 720 to get 1231.

$$\frac{1231}{800}$$

Factor

$$\frac{1231}{2 ^ {5} \cdot 5 ^ {2}} = 1\frac{431}{800} = 1.53875$$