Solve 1/3*3/4*3quad(1/10+1/4)*4

$$\frac { 1 } { 3 } \times \frac { 3 } { 4 } \times 3 \quad ( \frac { 1 } { 10 } + \frac { 1 } { 4 } ) \times 4$$

Evaluate

$$\frac{21}{20}=1.05$$

Solution Steps

Multiply \frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{3\times 4}\times 3\left(\frac{1}{10}+\frac{1}{4}\right)\times 4$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{4}\times 3\left(\frac{1}{10}+\frac{1}{4}\right)\times 4$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$\frac{3}{4}\left(\frac{1}{10}+\frac{1}{4}\right)\times 4$$

Least common multiple of 10 and 4 is 20. Convert \frac{1}{10} and \frac{1}{4} to fractions with denominator 20.

$$\frac{3}{4}\left(\frac{2}{20}+\frac{5}{20}\right)\times 4$$

Since \frac{2}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}\times \frac{2+5}{20}\times 4$$

Add 2 and 5 to get 7.

$$\frac{3}{4}\times \frac{7}{20}\times 4$$

Multiply \frac{3}{4} times \frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 7}{4\times 20}\times 4$$

Do the multiplications in the fraction \frac{3\times 7}{4\times 20}.

$$\frac{21}{80}\times 4$$

Express \frac{21}{80}\times 4 as a single fraction.

$$\frac{21\times 4}{80}$$

Multiply 21 and 4 to get 84.

$$\frac{84}{80}$$

Reduce the fraction \frac{84}{80} to lowest terms by extracting and canceling out 4.

$$\frac{21}{20}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2} \cdot 5} = 1\frac{1}{20} = 1.05$$