Basic Math Examples

$2 \frac{1}{2} + f = 3 \frac{1}{4}$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Convert $2 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 1.1.1

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

$2 + \frac{1}{2} + f = 3 \frac{1}{4}$

Step 1.1.2

Add $2$ and $\frac{1}{2}$ .

Tap for more steps...

Step 1.1.2.1

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

$2 \cdot \frac{2}{2} + \frac{1}{2} + f = 3 \frac{1}{4}$

Step 1.1.2.2

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

$\frac{2 \cdot 2}{2} + \frac{1}{2} + f = 3 \frac{1}{4}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} + f = 3 \frac{1}{4}$

Step 1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.2.4.1

Multiply $2$ by $2$ .

$\frac{4 + 1}{2} + f = 3 \frac{1}{4}$

Step 1.1.2.4.2

Add $4$ and $1$ .

$\frac{5}{2} + f = 3 \frac{1}{4}$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Convert $3 \frac{1}{4}$ to an improper fraction.

Tap for more steps...

Step 2.1.1

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

$\frac{5}{2} + f = 3 + \frac{1}{4}$

Step 2.1.2

Add $3$ and $\frac{1}{4}$ .

Tap for more steps...

Step 2.1.2.1

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

$\frac{5}{2} + f = 3 \cdot \frac{4}{4} + \frac{1}{4}$

Step 2.1.2.2

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

$\frac{5}{2} + f = \frac{3 \cdot 4}{4} + \frac{1}{4}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{5}{2} + f = \frac{3 \cdot 4 + 1}{4}$

Step 2.1.2.4

Simplify the numerator.

Tap for more steps...

Step 2.1.2.4.1

Multiply $3$ by $4$ .

$\frac{5}{2} + f = \frac{12 + 1}{4}$

Step 2.1.2.4.2

Add $12$ and $1$ .

$\frac{5}{2} + f = \frac{13}{4}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{5}{2}$ from both sides of the equation.

$f = \frac{13}{4} - \frac{5}{2}$

Step 3.2

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

$f = \frac{13}{4} - \frac{5}{2} \cdot \frac{2}{2}$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

Multiply $\frac{5}{2}$ by $\frac{2}{2}$ .

$f = \frac{13}{4} - \frac{5 \cdot 2}{2 \cdot 2}$

Step 3.3.2

Multiply $2$ by $2$ .

$f = \frac{13}{4} - \frac{5 \cdot 2}{4}$

Step 3.4

Combine the numerators over the common denominator.

$f = \frac{13 - 5 \cdot 2}{4}$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Multiply $- 5$ by $2$ .

$f = \frac{13 - 10}{4}$

Step 3.5.2

Subtract $10$ from $13$ .

$f = \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$f = \frac{3}{4}$

Decimal Form:

$f = 0.75$