Solve 13x/13+16/19+21/8+16/16=

$$1 \frac { 3 x } { 13 } + \frac { 16 } { 19 } + \frac { 21 } { 8 } + \frac { 16 } { 16 } =$$

Evaluate

$$\frac{3x}{13}+\frac{679}{152}$$

Short Solution Steps

Divide 16 by 16 to get 1.

$$1\times \frac{3x}{13}+\frac{16}{19}+\frac{21}{8}+1$$

Express 1\times \frac{3x}{13} as a single fraction.

$$\frac{3x}{13}+\frac{16}{19}+\frac{21}{8}+1$$

Least common multiple of 19 and 8 is 152. Convert \frac{16}{19} and \frac{21}{8} to fractions with denominator 152.

$$\frac{3x}{13}+\frac{128}{152}+\frac{399}{152}+1$$

Since \frac{128}{152} and \frac{399}{152} have the same denominator, add them by adding their numerators.

$$\frac{3x}{13}+\frac{128+399}{152}+1$$

Add 128 and 399 to get 527.

$$\frac{3x}{13}+\frac{527}{152}+1$$

Convert 1 to fraction \frac{152}{152}.

$$\frac{3x}{13}+\frac{527}{152}+\frac{152}{152}$$

Since \frac{527}{152} and \frac{152}{152} have the same denominator, add them by adding their numerators.

$$\frac{3x}{13}+\frac{527+152}{152}$$

Add 527 and 152 to get 679.

$$\frac{3x}{13}+\frac{679}{152}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 13 and 152 is 1976. Multiply \frac{3x}{13} times \frac{152}{152}. Multiply \frac{679}{152} times \frac{13}{13}.

$$\frac{152\times 3x}{1976}+\frac{679\times 13}{1976}$$

Since \frac{152\times 3x}{1976} and \frac{679\times 13}{1976} have the same denominator, add them by adding their numerators.

$$\frac{152\times 3x+679\times 13}{1976}$$

Do the multiplications in 152\times 3x+679\times 13.

$$\frac{456x+8827}{1976}$$

Factor

$$\frac{456x+8827}{1976}$$

Solution Steps

Factor out \frac{1}{1976}.

$$\frac{456x+8827}{1976}$$

Consider 456x+1664+5187+1976. Multiply and combine like terms.

$$456x+8827$$

Rewrite the complete factored expression.

$$\frac{456x+8827}{1976}$$