Basic Math Examples

$2 \frac{3}{4} + 3 \frac{1}{8}$

Step 1

Convert

$2 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$2 + \frac{3}{4} + 3 \frac{1}{8}$

Step 1.2

Add

$2$ and

$\frac{3}{4}$ .

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Step 1.2.1

To write

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

$\frac{4}{4}$ .

$2 \cdot \frac{4}{4} + \frac{3}{4} + 3 \frac{1}{8}$

Step 1.2.2

Combine

$2$ and

$\frac{4}{4}$ .

$\frac{2 \cdot 4}{4} + \frac{3}{4} + 3 \frac{1}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 3}{4} + 3 \frac{1}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$4$ .

$\frac{8 + 3}{4} + 3 \frac{1}{8}$

Step 1.2.4.2

Add

$8$ and

$3$ .

$\frac{11}{4} + 3 \frac{1}{8}$

Step 2

Convert

$3 \frac{1}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{11}{4} + 3 + \frac{1}{8}$

Step 2.2

Add

$3$ and

$\frac{1}{8}$ .

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Step 2.2.1

To write

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

$\frac{8}{8}$ .

$\frac{11}{4} + 3 \cdot \frac{8}{8} + \frac{1}{8}$

Step 2.2.2

Combine

$3$ and

$\frac{8}{8}$ .

$\frac{11}{4} + \frac{3 \cdot 8}{8} + \frac{1}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{11}{4} + \frac{3 \cdot 8 + 1}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$8$ .

$\frac{11}{4} + \frac{24 + 1}{8}$

Step 2.2.4.2

Add

$24$ and

$1$ .

$\frac{11}{4} + \frac{25}{8}$

Step 3

To write

$\frac{11}{4}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{11}{4} \cdot \frac{2}{2} + \frac{25}{8}$

Step 4

Write each expression with a common denominator of

$8$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{11}{4}$ by

$\frac{2}{2}$ .

$\frac{11 \cdot 2}{4 \cdot 2} + \frac{25}{8}$

Step 4.2

Multiply

$4$ by

$2$ .

$\frac{11 \cdot 2}{8} + \frac{25}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{11 \cdot 2 + 25}{8}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$11$ by

$2$ .

$\frac{22 + 25}{8}$

Step 6.2

Add

$22$ and

$25$ .

$\frac{47}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{47}{8}$

Decimal Form:

$5.875$

Mixed Number Form:

$5 \frac{7}{8}$