Solve (-1/2+1/6-3/8+5/12)*(-24)+0.25^10*4^3

$$( - \frac { 1 } { 2 } + \frac { 1 } { 6 } - \frac { 3 } { 8 } + \frac { 5 } { 12 } ) \times ( - 24 ) + 0.25 ^ { 10 } \times 4 ^ { 3 }$$

Evaluate

$$7.00006103515625$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert -\frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$\left(-\frac{3}{6}+\frac{1}{6}-\frac{3}{8}+\frac{5}{12}\right)\left(-24\right)+0.25^{10}\times 4^{3}$$

Since -\frac{3}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\left(\frac{-3+1}{6}-\frac{3}{8}+\frac{5}{12}\right)\left(-24\right)+0.25^{10}\times 4^{3}$$

Add -3 and 1 to get -2.

$$\left(\frac{-2}{6}-\frac{3}{8}+\frac{5}{12}\right)\left(-24\right)+0.25^{10}\times 4^{3}$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$\left(-\frac{1}{3}-\frac{3}{8}+\frac{5}{12}\right)\left(-24\right)+0.25^{10}\times 4^{3}$$

Least common multiple of 3 and 8 is 24. Convert -\frac{1}{3} and \frac{3}{8} to fractions with denominator 24.

$$\left(-\frac{8}{24}-\frac{9}{24}+\frac{5}{12}\right)\left(-24\right)+0.25^{10}\times 4^{3}$$

Since -\frac{8}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{-8-9}{24}+\frac{5}{12}\right)\left(-24\right)+0.25^{10}\times 4^{3}$$

Subtract 9 from -8 to get -17.

$$\left(-\frac{17}{24}+\frac{5}{12}\right)\left(-24\right)+0.25^{10}\times 4^{3}$$

Least common multiple of 24 and 12 is 24. Convert -\frac{17}{24} and \frac{5}{12} to fractions with denominator 24.

$$\left(-\frac{17}{24}+\frac{10}{24}\right)\left(-24\right)+0.25^{10}\times 4^{3}$$

Since -\frac{17}{24} and \frac{10}{24} have the same denominator, add them by adding their numerators.

$$\frac{-17+10}{24}\left(-24\right)+0.25^{10}\times 4^{3}$$

Add -17 and 10 to get -7.

$$-\frac{7}{24}\left(-24\right)+0.25^{10}\times 4^{3}$$

Express -\frac{7}{24}\left(-24\right) as a single fraction.

$$\frac{-7\left(-24\right)}{24}+0.25^{10}\times 4^{3}$$

Multiply -7 and -24 to get 168.

$$\frac{168}{24}+0.25^{10}\times 4^{3}$$

Divide 168 by 24 to get 7.

$$7+0.25^{10}\times 4^{3}$$

Calculate 0.25 to the power of 10 and get 0.00000095367431640625.

$$7+0.00000095367431640625\times 4^{3}$$

Calculate 4 to the power of 3 and get 64.

$$7+0.00000095367431640625\times 64$$

Multiply 0.00000095367431640625 and 64 to get 0.00006103515625.

$$7+0.00006103515625$$

Add 7 and 0.00006103515625 to get 7.00006103515625.

$$7.00006103515625$$

Factor

$$\frac{114689}{2 ^ {14}} = 7\frac{1}{16384} = 7.00006103515625$$