Basic Math Examples

14 \frac{1}{3} + 13 \frac{3}{4}

$14 \frac{1}{3} + 13 \frac{3}{4}$

Step 1

Convert

14 \frac{1}{3}

$14 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

14 + \frac{1}{3} + 13 \frac{3}{4}

$14 + \frac{1}{3} + 13 \frac{3}{4}$

Step 1.2

Add

14

$14$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

14

$14$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

14 \cdot \frac{3}{3} + \frac{1}{3} + 13 \frac{3}{4}

$14 \cdot \frac{3}{3} + \frac{1}{3} + 13 \frac{3}{4}$

Step 1.2.2

Combine

14

$14$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{14 \cdot 3}{3} + \frac{1}{3} + 13 \frac{3}{4}

$\frac{14 \cdot 3}{3} + \frac{1}{3} + 13 \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{14 \cdot 3 + 1}{3} + 13 \frac{3}{4}

$\frac{14 \cdot 3 + 1}{3} + 13 \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

14

$14$ by

3

$3$ .

\frac{42 + 1}{3} + 13 \frac{3}{4}

$\frac{42 + 1}{3} + 13 \frac{3}{4}$

Step 1.2.4.2

Add

42

$42$ and

1

$1$ .

\frac{43}{3} + 13 \frac{3}{4}

$\frac{43}{3} + 13 \frac{3}{4}$

\frac{43}{3} + 13 \frac{3}{4}

$\frac{43}{3} + 13 \frac{3}{4}$

\frac{43}{3} + 13 \frac{3}{4}

$\frac{43}{3} + 13 \frac{3}{4}$

\frac{43}{3} + 13 \frac{3}{4}

$\frac{43}{3} + 13 \frac{3}{4}$

Step 2

Convert

13 \frac{3}{4}

$13 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

\frac{43}{3} + 13 + \frac{3}{4}

$\frac{43}{3} + 13 + \frac{3}{4}$

Step 2.2

Add

13

$13$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 2.2.1

To write

13

$13$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{43}{3} + 13 \cdot \frac{4}{4} + \frac{3}{4}

$\frac{43}{3} + 13 \cdot \frac{4}{4} + \frac{3}{4}$

Step 2.2.2

Combine

13

$13$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{43}{3} + \frac{13 \cdot 4}{4} + \frac{3}{4}

$\frac{43}{3} + \frac{13 \cdot 4}{4} + \frac{3}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{43}{3} + \frac{13 \cdot 4 + 3}{4}

$\frac{43}{3} + \frac{13 \cdot 4 + 3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

13

$13$ by

4

$4$ .

\frac{43}{3} + \frac{52 + 3}{4}

$\frac{43}{3} + \frac{52 + 3}{4}$

Step 2.2.4.2

Add

52

$52$ and

3

$3$ .

\frac{43}{3} + \frac{55}{4}

$\frac{43}{3} + \frac{55}{4}$

\frac{43}{3} + \frac{55}{4}

$\frac{43}{3} + \frac{55}{4}$

\frac{43}{3} + \frac{55}{4}

$\frac{43}{3} + \frac{55}{4}$

\frac{43}{3} + \frac{55}{4}

$\frac{43}{3} + \frac{55}{4}$

Step 3

To write

\frac{43}{3}

$\frac{43}{3}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{43}{3} \cdot \frac{4}{4} + \frac{55}{4}

$\frac{43}{3} \cdot \frac{4}{4} + \frac{55}{4}$

Step 4

To write

\frac{55}{4}

$\frac{55}{4}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{43}{3} \cdot \frac{4}{4} + \frac{55}{4} \cdot \frac{3}{3}

$\frac{43}{3} \cdot \frac{4}{4} + \frac{55}{4} \cdot \frac{3}{3}$

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

$\frac{43}{3}$ by

$\frac{4}{4}$ .

$\frac{43 \cdot 4}{3 \cdot 4} + \frac{55}{4} \cdot \frac{3}{3}$

Step 5.2

Multiply

$3$ by

$4$ .

$\frac{43 \cdot 4}{12} + \frac{55}{4} \cdot \frac{3}{3}$

Step 5.3

Multiply

$\frac{55}{4}$ by

$\frac{3}{3}$ .

$\frac{43 \cdot 4}{12} + \frac{55 \cdot 3}{4 \cdot 3}$

Step 5.4

Multiply

$4$ by

$3$ .

$\frac{43 \cdot 4}{12} + \frac{55 \cdot 3}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{43 \cdot 4 + 55 \cdot 3}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$43$ by

$4$ .

$\frac{172 + 55 \cdot 3}{12}$

Step 7.2

Multiply

$55$ by

$3$ .

$\frac{172 + 165}{12}$

Step 7.3

Add

$172$ and

$165$ .

$\frac{337}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{337}{12}$

Decimal Form:

$28.08\overline{3}$

Mixed Number Form:

$28 \frac{1}{12}$