Basic Math Examples

$a - 2 \frac{3}{5} = \frac{1}{3}$

Step 1

Simplify the left side.

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Step 1.1

Convert $2 \frac{3}{5}$ to an improper fraction.

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Step 1.1.1

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

$a - (2 + \frac{3}{5}) = \frac{1}{3}$

Step 1.1.2

Add $2$ and $\frac{3}{5}$ .

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Step 1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$a - (2 \cdot \frac{5}{5} + \frac{3}{5}) = \frac{1}{3}$

Step 1.1.2.2

Combine $2$ and $\frac{5}{5}$ .

$a - (\frac{2 \cdot 5}{5} + \frac{3}{5}) = \frac{1}{3}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$a - \frac{2 \cdot 5 + 3}{5} = \frac{1}{3}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $5$ .

$a - \frac{10 + 3}{5} = \frac{1}{3}$

Step 1.1.2.4.2

Add $10$ and $3$ .

$a - \frac{13}{5} = \frac{1}{3}$

Step 2

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

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Step 2.1

Add $\frac{13}{5}$ to both sides of the equation.

$a = \frac{1}{3} + \frac{13}{5}$

Step 2.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$a = \frac{1}{3} \cdot \frac{5}{5} + \frac{13}{5}$

Step 2.3

To write $\frac{13}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$a = \frac{1}{3} \cdot \frac{5}{5} + \frac{13}{5} \cdot \frac{3}{3}$

Step 2.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$a = \frac{5}{3 \cdot 5} + \frac{13}{5} \cdot \frac{3}{3}$

Step 2.4.2

Multiply $3$ by $5$ .

$a = \frac{5}{15} + \frac{13}{5} \cdot \frac{3}{3}$

Step 2.4.3

Multiply $\frac{13}{5}$ by $\frac{3}{3}$ .

$a = \frac{5}{15} + \frac{13 \cdot 3}{5 \cdot 3}$

Step 2.4.4

Multiply $5$ by $3$ .

$a = \frac{5}{15} + \frac{13 \cdot 3}{15}$

Step 2.5

Combine the numerators over the common denominator.

$a = \frac{5 + 13 \cdot 3}{15}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $13$ by $3$ .

$a = \frac{5 + 39}{15}$

Step 2.6.2

Add $5$ and $39$ .

$a = \frac{44}{15}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a = \frac{44}{15}$

Decimal Form:

$a = 2.9\overline{3}$

Mixed Number Form:

$a = 2 \frac{14}{15}$