Solve (5/6)(1/12*1/4+frac{3/4x)}{frac{3}{4}}

$$\frac { ( \frac { 5 } { 6 } ) ( \frac { 1 } { 12 } \cdot \frac { 1 } { 4 } + \frac { 3 } { 4 } x ) } { \frac { 3 } { 4 } }$$

Evaluate

$$\frac{5x}{6}+\frac{5}{216}$$

Solution Steps

Multiply \frac{1}{12} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{6}\left(\frac{1\times 1}{12\times 4}+\frac{3}{4}x\right)}{\frac{3}{4}}$$

Do the multiplications in the fraction \frac{1\times 1}{12\times 4}.

$$\frac{\frac{5}{6}\left(\frac{1}{48}+\frac{3}{4}x\right)}{\frac{3}{4}}$$

Divide \frac{5}{6}\left(\frac{1}{48}+\frac{3}{4}x\right) by \frac{3}{4} to get \frac{10}{9}\left(\frac{1}{48}+\frac{3}{4}x\right).

$$\frac{10}{9}\left(\frac{1}{48}+\frac{3}{4}x\right)$$

Use the distributive property to multiply \frac{10}{9} by \frac{1}{48}+\frac{3}{4}x.

$$\frac{10}{9}\times \frac{1}{48}+\frac{10}{9}\times \frac{3}{4}x$$

Multiply \frac{10}{9} times \frac{1}{48} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 1}{9\times 48}+\frac{10}{9}\times \frac{3}{4}x$$

Do the multiplications in the fraction \frac{10\times 1}{9\times 48}.

$$\frac{10}{432}+\frac{10}{9}\times \frac{3}{4}x$$

Reduce the fraction \frac{10}{432} to lowest terms by extracting and canceling out 2.

$$\frac{5}{216}+\frac{10}{9}\times \frac{3}{4}x$$

Multiply \frac{10}{9} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{216}+\frac{10\times 3}{9\times 4}x$$

Do the multiplications in the fraction \frac{10\times 3}{9\times 4}.

$$\frac{5}{216}+\frac{30}{36}x$$

Reduce the fraction \frac{30}{36} to lowest terms by extracting and canceling out 6.

$$\frac{5}{216}+\frac{5}{6}x$$

Expand

$$\frac{5x}{6}+\frac{5}{216}$$

Solution Steps

Multiply \frac{1}{12} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{6}\left(\frac{1\times 1}{12\times 4}+\frac{3}{4}x\right)}{\frac{3}{4}}$$

Do the multiplications in the fraction \frac{1\times 1}{12\times 4}.

$$\frac{\frac{5}{6}\left(\frac{1}{48}+\frac{3}{4}x\right)}{\frac{3}{4}}$$

Divide \frac{5}{6}\left(\frac{1}{48}+\frac{3}{4}x\right) by \frac{3}{4} to get \frac{10}{9}\left(\frac{1}{48}+\frac{3}{4}x\right).

$$\frac{10}{9}\left(\frac{1}{48}+\frac{3}{4}x\right)$$

Use the distributive property to multiply \frac{10}{9} by \frac{1}{48}+\frac{3}{4}x.

$$\frac{10}{9}\times \frac{1}{48}+\frac{10}{9}\times \frac{3}{4}x$$

Multiply \frac{10}{9} times \frac{1}{48} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 1}{9\times 48}+\frac{10}{9}\times \frac{3}{4}x$$

Do the multiplications in the fraction \frac{10\times 1}{9\times 48}.

$$\frac{10}{432}+\frac{10}{9}\times \frac{3}{4}x$$

Reduce the fraction \frac{10}{432} to lowest terms by extracting and canceling out 2.

$$\frac{5}{216}+\frac{10}{9}\times \frac{3}{4}x$$

Multiply \frac{10}{9} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{216}+\frac{10\times 3}{9\times 4}x$$

Do the multiplications in the fraction \frac{10\times 3}{9\times 4}.

$$\frac{5}{216}+\frac{30}{36}x$$

Reduce the fraction \frac{30}{36} to lowest terms by extracting and canceling out 6.

$$\frac{5}{216}+\frac{5}{6}x$$