Basic Math Examples

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

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

Step 1

Convert

2 \frac{1}{4}

$2 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{8 + 1}{4} + 1 \frac{1}{2}

$\frac{8 + 1}{4} + 1 \frac{1}{2}$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{9}{4} + 1 \frac{1}{2}

$\frac{9}{4} + 1 \frac{1}{2}$

\frac{9}{4} + 1 \frac{1}{2}

$\frac{9}{4} + 1 \frac{1}{2}$

\frac{9}{4} + 1 \frac{1}{2}

$\frac{9}{4} + 1 \frac{1}{2}$

\frac{9}{4} + 1 \frac{1}{2}

$\frac{9}{4} + 1 \frac{1}{2}$

Step 2

Convert

1 \frac{1}{2}

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

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Step 2.1

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

\frac{9}{4} + 1 + \frac{1}{2}

$\frac{9}{4} + 1 + \frac{1}{2}$

Step 2.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{9}{4} + \frac{2}{2} + \frac{1}{2}

$\frac{9}{4} + \frac{2}{2} + \frac{1}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{9}{4} + \frac{2 + 1}{2}

$\frac{9}{4} + \frac{2 + 1}{2}$

Step 2.2.3

Add

2

$2$ and

1

$1$ .

\frac{9}{4} + \frac{3}{2}

$\frac{9}{4} + \frac{3}{2}$

\frac{9}{4} + \frac{3}{2}

$\frac{9}{4} + \frac{3}{2}$

\frac{9}{4} + \frac{3}{2}

$\frac{9}{4} + \frac{3}{2}$

Step 3

To write

\frac{3}{2}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{9}{4} + \frac{3}{2} \cdot \frac{2}{2}

$\frac{9}{4} + \frac{3}{2} \cdot \frac{2}{2}$

Step 4

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 4.1

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{9}{4} + \frac{3 \cdot 2}{2 \cdot 2}

$\frac{9}{4} + \frac{3 \cdot 2}{2 \cdot 2}$

Step 4.2

Multiply

2

$2$ by

2

$2$ .

\frac{9}{4} + \frac{3 \cdot 2}{4}

$\frac{9}{4} + \frac{3 \cdot 2}{4}$

\frac{9}{4} + \frac{3 \cdot 2}{4}

$\frac{9}{4} + \frac{3 \cdot 2}{4}$

Step 5

Combine the numerators over the common denominator.

\frac{9 + 3 \cdot 2}{4}

$\frac{9 + 3 \cdot 2}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

3

$3$ by

2

$2$ .

\frac{9 + 6}{4}

$\frac{9 + 6}{4}$

Step 6.2

Add

9

$9$ and

6

$6$ .

\frac{15}{4}

$\frac{15}{4}$

\frac{15}{4}

$\frac{15}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{15}{4}

$\frac{15}{4}$

Decimal Form:

3.75

$3.75$

Mixed Number Form:

3 \frac{3}{4}

$3 \frac{3}{4}$