Solve 3-(1/2+1/4*1/4)+2(3/4+frac{1}{6})

$$3-( \frac{ 1 }{ 2 } + \frac{ 1 }{ 4 } \times \frac{ 1 }{ 4 } )+2( \frac{ 3 }{ 4 } + \frac{ 1 }{ 6 } )$$

Evaluate

$$\frac{205}{48}\approx 4.270833333$$

Solution Steps

Multiply \frac{1}{4} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$3-\left(\frac{1}{2}+\frac{1\times 1}{4\times 4}\right)+2\left(\frac{3}{4}+\frac{1}{6}\right)$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 4}.

$$3-\left(\frac{1}{2}+\frac{1}{16}\right)+2\left(\frac{3}{4}+\frac{1}{6}\right)$$

Least common multiple of 2 and 16 is 16. Convert \frac{1}{2} and \frac{1}{16} to fractions with denominator 16.

$$3-\left(\frac{8}{16}+\frac{1}{16}\right)+2\left(\frac{3}{4}+\frac{1}{6}\right)$$

Since \frac{8}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$3-\frac{8+1}{16}+2\left(\frac{3}{4}+\frac{1}{6}\right)$$

Add 8 and 1 to get 9.

$$3-\frac{9}{16}+2\left(\frac{3}{4}+\frac{1}{6}\right)$$

Convert 3 to fraction \frac{48}{16}.

$$\frac{48}{16}-\frac{9}{16}+2\left(\frac{3}{4}+\frac{1}{6}\right)$$

Since \frac{48}{16} and \frac{9}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48-9}{16}+2\left(\frac{3}{4}+\frac{1}{6}\right)$$

Subtract 9 from 48 to get 39.

$$\frac{39}{16}+2\left(\frac{3}{4}+\frac{1}{6}\right)$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{39}{16}+2\left(\frac{9}{12}+\frac{2}{12}\right)$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{39}{16}+2\times \frac{9+2}{12}$$

Add 9 and 2 to get 11.

$$\frac{39}{16}+2\times \frac{11}{12}$$

Express 2\times \frac{11}{12} as a single fraction.

$$\frac{39}{16}+\frac{2\times 11}{12}$$

Multiply 2 and 11 to get 22.

$$\frac{39}{16}+\frac{22}{12}$$

Reduce the fraction \frac{22}{12} to lowest terms by extracting and canceling out 2.

$$\frac{39}{16}+\frac{11}{6}$$

Least common multiple of 16 and 6 is 48. Convert \frac{39}{16} and \frac{11}{6} to fractions with denominator 48.

$$\frac{117}{48}+\frac{88}{48}$$

Since \frac{117}{48} and \frac{88}{48} have the same denominator, add them by adding their numerators.

$$\frac{117+88}{48}$$

Add 117 and 88 to get 205.

$$\frac{205}{48}$$

Factor

$$\frac{5 \cdot 41}{2 ^ {4} \cdot 3} = 4\frac{13}{48} = 4.270833333333333$$