Solve 1+1+2+2+1+2+2/365+371+385+395+412+418+430+435+440+445*1000

$$\frac{ 1+1+2+2+1+2+2 }{ 365+371+385+395+412+418+430+435+440+445 } \times 1000$$

Evaluate

$$\frac{1375}{512}=2.685546875$$

Solution Steps

Add 1 and 1 to get 2.

$$\frac{2+2+2+1+2+2}{365+371+385+395+412+418+430+435+440+445}\times 1000$$

Add 2 and 2 to get 4.

$$\frac{4+2+1+2+2}{365+371+385+395+412+418+430+435+440+445}\times 1000$$

Add 4 and 2 to get 6.

$$\frac{6+1+2+2}{365+371+385+395+412+418+430+435+440+445}\times 1000$$

Add 6 and 1 to get 7.

$$\frac{7+2+2}{365+371+385+395+412+418+430+435+440+445}\times 1000$$

Add 7 and 2 to get 9.

$$\frac{9+2}{365+371+385+395+412+418+430+435+440+445}\times 1000$$

Add 9 and 2 to get 11.

$$\frac{11}{365+371+385+395+412+418+430+435+440+445}\times 1000$$

Add 365 and 371 to get 736.

$$\frac{11}{736+385+395+412+418+430+435+440+445}\times 1000$$

Add 736 and 385 to get 1121.

$$\frac{11}{1121+395+412+418+430+435+440+445}\times 1000$$

Add 1121 and 395 to get 1516.

$$\frac{11}{1516+412+418+430+435+440+445}\times 1000$$

Add 1516 and 412 to get 1928.

$$\frac{11}{1928+418+430+435+440+445}\times 1000$$

Add 1928 and 418 to get 2346.

$$\frac{11}{2346+430+435+440+445}\times 1000$$

Add 2346 and 430 to get 2776.

$$\frac{11}{2776+435+440+445}\times 1000$$

Add 2776 and 435 to get 3211.

$$\frac{11}{3211+440+445}\times 1000$$

Add 3211 and 440 to get 3651.

$$\frac{11}{3651+445}\times 1000$$

Add 3651 and 445 to get 4096.

$$\frac{11}{4096}\times 1000$$

Express \frac{11}{4096}\times 1000 as a single fraction.

$$\frac{11\times 1000}{4096}$$

Multiply 11 and 1000 to get 11000.

$$\frac{11000}{4096}$$

Reduce the fraction \frac{11000}{4096} to lowest terms by extracting and canceling out 8.

$$\frac{1375}{512}$$

Factor

$$\frac{5 ^ {3} \cdot 11}{2 ^ {9}} = 2\frac{351}{512} = 2.685546875$$