Basic Math Examples

$5 \frac{3}{4} + 3 \frac{1}{3}$

Step 1

Convert

$5 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$5 + \frac{3}{4} + 3 \frac{1}{3}$

Step 1.2

Add

$5$ and

$\frac{3}{4}$ .

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Step 1.2.1

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$5 \cdot \frac{4}{4} + \frac{3}{4} + 3 \frac{1}{3}$

Step 1.2.2

Combine

$5$ and

$\frac{4}{4}$ .

$\frac{5 \cdot 4}{4} + \frac{3}{4} + 3 \frac{1}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 + 3}{4} + 3 \frac{1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$5$ by

$4$ .

$\frac{20 + 3}{4} + 3 \frac{1}{3}$

Step 1.2.4.2

Add

$20$ and

$3$ .

$\frac{23}{4} + 3 \frac{1}{3}$

Step 2

Convert

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

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Step 2.1

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

$\frac{23}{4} + 3 + \frac{1}{3}$

Step 2.2

Add

$3$ and

$\frac{1}{3}$ .

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Step 2.2.1

To write

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

$\frac{3}{3}$ .

$\frac{23}{4} + 3 \cdot \frac{3}{3} + \frac{1}{3}$

Step 2.2.2

Combine

$3$ and

$\frac{3}{3}$ .

$\frac{23}{4} + \frac{3 \cdot 3}{3} + \frac{1}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{23}{4} + \frac{3 \cdot 3 + 1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$3$ .

$\frac{23}{4} + \frac{9 + 1}{3}$

Step 2.2.4.2

Add

$9$ and

$1$ .

$\frac{23}{4} + \frac{10}{3}$

Step 3

To write

$\frac{23}{4}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{23}{4} \cdot \frac{3}{3} + \frac{10}{3}$

Step 4

To write

$\frac{10}{3}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{23}{4} \cdot \frac{3}{3} + \frac{10}{3} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of

$12$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{23}{4}$ by

$\frac{3}{3}$ .

$\frac{23 \cdot 3}{4 \cdot 3} + \frac{10}{3} \cdot \frac{4}{4}$

Step 5.2

Multiply

$4$ by

$3$ .

$\frac{23 \cdot 3}{12} + \frac{10}{3} \cdot \frac{4}{4}$

Step 5.3

Multiply

$\frac{10}{3}$ by

$\frac{4}{4}$ .

$\frac{23 \cdot 3}{12} + \frac{10 \cdot 4}{3 \cdot 4}$

Step 5.4

Multiply

$3$ by

$4$ .

$\frac{23 \cdot 3}{12} + \frac{10 \cdot 4}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{23 \cdot 3 + 10 \cdot 4}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$23$ by

$3$ .

$\frac{69 + 10 \cdot 4}{12}$

Step 7.2

Multiply

$10$ by

$4$ .

$\frac{69 + 40}{12}$

Step 7.3

Add

$69$ and

$40$ .

$\frac{109}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{109}{12}$

Decimal Form:

$9.08\overline{3}$

Mixed Number Form:

$9 \frac{1}{12}$