Basic Math Examples

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

Step 1

Convert

$3 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add

$3$ and

$\frac{1}{2}$ .

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Step 1.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

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

Step 1.2.2

Combine

$3$ and

$\frac{2}{2}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$3$ by

$2$ .

$\frac{6 + 1}{2} + 4 \frac{3}{4}$

Step 1.2.4.2

Add

$6$ and

$1$ .

$\frac{7}{2} + 4 \frac{3}{4}$

Step 2

Convert

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

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Step 2.1

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

$\frac{7}{2} + 4 + \frac{3}{4}$

Step 2.2

Add

$4$ and

$\frac{3}{4}$ .

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Step 2.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{7}{2} + 4 \cdot \frac{4}{4} + \frac{3}{4}$

Step 2.2.2

Combine

$4$ and

$\frac{4}{4}$ .

$\frac{7}{2} + \frac{4 \cdot 4}{4} + \frac{3}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{7}{2} + \frac{4 \cdot 4 + 3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$4$ by

$4$ .

$\frac{7}{2} + \frac{16 + 3}{4}$

Step 2.2.4.2

Add

$16$ and

$3$ .

$\frac{7}{2} + \frac{19}{4}$

Step 3

To write

$\frac{7}{2}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{7}{2} \cdot \frac{2}{2} + \frac{19}{4}$

Step 4

Write each expression with a common denominator of

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

$1$ .

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Step 4.1

Multiply

$\frac{7}{2}$ by

$\frac{2}{2}$ .

$\frac{7 \cdot 2}{2 \cdot 2} + \frac{19}{4}$

Step 4.2

Multiply

$2$ by

$2$ .

$\frac{7 \cdot 2}{4} + \frac{19}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 19}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$7$ by

$2$ .

$\frac{14 + 19}{4}$

Step 6.2

Add

$14$ and

$19$ .

$\frac{33}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{33}{4}$

Decimal Form:

$8.25$

Mixed Number Form:

$8 \frac{1}{4}$