Basic Math Examples

1 \frac{1}{2} + \frac{3}{4}

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

Step 1

Convert

1 \frac{1}{2}

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

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Step 1.1

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

1 + \frac{1}{2} + \frac{3}{4}

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

Step 1.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{2}{2} + \frac{1}{2} + \frac{3}{4}

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

Step 1.2.2

Combine the numerators over the common denominator.

\frac{2 + 1}{2} + \frac{3}{4}

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

Step 1.2.3

Add

2

$2$ and

1

$1$ .

\frac{3}{2} + \frac{3}{4}

$\frac{3}{2} + \frac{3}{4}$

\frac{3}{2} + \frac{3}{4}

$\frac{3}{2} + \frac{3}{4}$

\frac{3}{2} + \frac{3}{4}

$\frac{3}{2} + \frac{3}{4}$

Step 2

To write

\frac{3}{2}

$\frac{3}{2}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3}{2} \cdot \frac{2}{2} + \frac{3}{4}

$\frac{3}{2} \cdot \frac{2}{2} + \frac{3}{4}$

Step 3

Write each expression with a common denominator of

4

$4$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3 \cdot 2}{2 \cdot 2} + \frac{3}{4}

$\frac{3 \cdot 2}{2 \cdot 2} + \frac{3}{4}$

Step 3.2

Multiply

2

$2$ by

2

$2$ .

\frac{3 \cdot 2}{4} + \frac{3}{4}

$\frac{3 \cdot 2}{4} + \frac{3}{4}$

\frac{3 \cdot 2}{4} + \frac{3}{4}

$\frac{3 \cdot 2}{4} + \frac{3}{4}$

Step 4

Combine the numerators over the common denominator.

\frac{3 \cdot 2 + 3}{4}

$\frac{3 \cdot 2 + 3}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

3

$3$ by

2

$2$ .

\frac{6 + 3}{4}

$\frac{6 + 3}{4}$

Step 5.2

Add

6

$6$ and

3

$3$ .

\frac{9}{4}

$\frac{9}{4}$

\frac{9}{4}

$\frac{9}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{9}{4}

$\frac{9}{4}$

Decimal Form:

2.25

$2.25$

Mixed Number Form:

2 \frac{1}{4}

$2 \frac{1}{4}$