Solve for a a+1/3=4 3/4

$a + \frac{1}{3} = 4 \frac{3}{4}$

Simplify the right side.

Convert $4 \frac{3}{4}$ to an improper fraction.

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

$a + \frac{1}{3} = 4 + \frac{3}{4}$

Add $4$ and $\frac{3}{4}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$a + \frac{1}{3} = 4 \cdot \frac{4}{4} + \frac{3}{4}$

Combine $4$ and $\frac{4}{4}$ .

$a + \frac{1}{3} = \frac{4 \cdot 4}{4} + \frac{3}{4}$

Combine the numerators over the common denominator.

$a + \frac{1}{3} = \frac{4 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply $4$ by $4$ .

$a + \frac{1}{3} = \frac{16 + 3}{4}$

Add $16$ and $3$ .

$a + \frac{1}{3} = \frac{19}{4}$

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

Subtract $\frac{1}{3}$ from both sides of the equation.

$a = \frac{19}{4} - \frac{1}{3}$

To write $\frac{19}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$a = \frac{19}{4} \cdot \frac{3}{3} - \frac{1}{3}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$a = \frac{19}{4} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{4}{4}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{19}{4}$ by $\frac{3}{3}$ .

$a = \frac{19 \cdot 3}{4 \cdot 3} - \frac{1}{3} \cdot \frac{4}{4}$

Multiply $4$ by $3$ .

$a = \frac{19 \cdot 3}{12} - \frac{1}{3} \cdot \frac{4}{4}$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$a = \frac{19 \cdot 3}{12} - \frac{4}{3 \cdot 4}$

Multiply $3$ by $4$ .

$a = \frac{19 \cdot 3}{12} - \frac{4}{12}$

Combine the numerators over the common denominator.

$a = \frac{19 \cdot 3 - 4}{12}$

Simplify the numerator.

Multiply $19$ by $3$ .

$a = \frac{57 - 4}{12}$

Subtract $4$ from $57$ .

$a = \frac{53}{12}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{53}{12}$

Decimal Form:

$a = 4.41\overline{6}$

Mixed Number Form:

$a = 4 \frac{5}{12}$

Solve for a a+1/3=4 3/4

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