Solve 993/4+1993/4+29993/4

$$99 \frac { 3 } { 4 } + 199 \frac { 3 } { 4 } + 2999 \frac { 3 } { 4 }$$

Evaluate

$$\frac{12369}{4}=3092.25$$

Solution Steps

Multiply 99 and 4 to get 396.

$$\frac{396+3}{4}+1\times \frac{99\times 4+3}{4}+29\times \frac{99\times 4+3}{4}$$

Add 396 and 3 to get 399.

$$\frac{399}{4}+1\times \frac{99\times 4+3}{4}+29\times \frac{99\times 4+3}{4}$$

Multiply 99 and 4 to get 396.

$$\frac{399}{4}+1\times \frac{396+3}{4}+29\times \frac{99\times 4+3}{4}$$

Add 396 and 3 to get 399.

$$\frac{399}{4}+1\times \frac{399}{4}+29\times \frac{99\times 4+3}{4}$$

Multiply 1 and \frac{399}{4} to get \frac{399}{4}.

$$\frac{399}{4}+\frac{399}{4}+29\times \frac{99\times 4+3}{4}$$

Since \frac{399}{4} and \frac{399}{4} have the same denominator, add them by adding their numerators.

$$\frac{399+399}{4}+29\times \frac{99\times 4+3}{4}$$

Add 399 and 399 to get 798.

$$\frac{798}{4}+29\times \frac{99\times 4+3}{4}$$

Reduce the fraction \frac{798}{4} to lowest terms by extracting and canceling out 2.

$$\frac{399}{2}+29\times \frac{99\times 4+3}{4}$$

Multiply 99 and 4 to get 396.

$$\frac{399}{2}+29\times \frac{396+3}{4}$$

Add 396 and 3 to get 399.

$$\frac{399}{2}+29\times \frac{399}{4}$$

Express 29\times \frac{399}{4} as a single fraction.

$$\frac{399}{2}+\frac{29\times 399}{4}$$

Multiply 29 and 399 to get 11571.

$$\frac{399}{2}+\frac{11571}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{399}{2} and \frac{11571}{4} to fractions with denominator 4.

$$\frac{798}{4}+\frac{11571}{4}$$

Since \frac{798}{4} and \frac{11571}{4} have the same denominator, add them by adding their numerators.

$$\frac{798+11571}{4}$$

Add 798 and 11571 to get 12369.

$$\frac{12369}{4}$$

Factor

$$\frac{3 \cdot 7 \cdot 19 \cdot 31}{2 ^ {2}} = 3092\frac{1}{4} = 3092.25$$