Solve for a a+5 3/16=83/16

$a + 5 \frac{3}{16} = \frac{83}{16}$

Step 1

Simplify the left side.

Convert $5 \frac{3}{16}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$a + 5 + \frac{3}{16} = \frac{83}{16}$

Add $5$ and $\frac{3}{16}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$a + 5 \cdot \frac{16}{16} + \frac{3}{16} = \frac{83}{16}$

Combine $5$ and $\frac{16}{16}$ .

$a + \frac{5 \cdot 16}{16} + \frac{3}{16} = \frac{83}{16}$

Combine the numerators over the common denominator.

$a + \frac{5 \cdot 16 + 3}{16} = \frac{83}{16}$

Simplify the numerator.

Multiply $5$ by $16$ .

$a + \frac{80 + 3}{16} = \frac{83}{16}$

Add $80$ and $3$ .

$a + \frac{83}{16} = \frac{83}{16}$

Step 2

Move all terms not containing $a$ to the right side of the equation.

Subtract $\frac{83}{16}$ from both sides of the equation.

$a = \frac{83}{16} - \frac{83}{16}$

Combine the numerators over the common denominator.

$a = \frac{83 - 83}{16}$

Subtract $83$ from $83$ .

$a = \frac{0}{16}$

Divide $0$ by $16$ .

$a = 0$