Basic Math Examples

1 \frac{1}{4} + \frac{11}{12}

$1 \frac{1}{4} + \frac{11}{12}$

Step 1

Convert

1 \frac{1}{4}

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

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Step 1.1

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

1 + \frac{1}{4} + \frac{11}{12}

$1 + \frac{1}{4} + \frac{11}{12}$

Step 1.2

Add

1

$1$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{4}{4} + \frac{1}{4} + \frac{11}{12}

$\frac{4}{4} + \frac{1}{4} + \frac{11}{12}$

Step 1.2.2

Combine the numerators over the common denominator.

\frac{4 + 1}{4} + \frac{11}{12}

$\frac{4 + 1}{4} + \frac{11}{12}$

Step 1.2.3

Add

4

$4$ and

1

$1$ .

\frac{5}{4} + \frac{11}{12}

$\frac{5}{4} + \frac{11}{12}$

\frac{5}{4} + \frac{11}{12}

$\frac{5}{4} + \frac{11}{12}$

\frac{5}{4} + \frac{11}{12}

$\frac{5}{4} + \frac{11}{12}$

Step 2

To write

\frac{5}{4}

$\frac{5}{4}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5}{4} \cdot \frac{3}{3} + \frac{11}{12}

$\frac{5}{4} \cdot \frac{3}{3} + \frac{11}{12}$

Step 3

Write each expression with a common denominator of

12

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

1

$1$ .

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Step 3.1

Multiply

\frac{5}{4}

$\frac{5}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5 \cdot 3}{4 \cdot 3} + \frac{11}{12}

$\frac{5 \cdot 3}{4 \cdot 3} + \frac{11}{12}$

Step 3.2

Multiply

4

$4$ by

3

$3$ .

\frac{5 \cdot 3}{12} + \frac{11}{12}

$\frac{5 \cdot 3}{12} + \frac{11}{12}$

\frac{5 \cdot 3}{12} + \frac{11}{12}

$\frac{5 \cdot 3}{12} + \frac{11}{12}$

Step 4

Combine the numerators over the common denominator.

\frac{5 \cdot 3 + 11}{12}

$\frac{5 \cdot 3 + 11}{12}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

3

$3$ .

\frac{15 + 11}{12}

$\frac{15 + 11}{12}$

Step 5.2

Add

15

$15$ and

11

$11$ .

\frac{26}{12}

$\frac{26}{12}$

\frac{26}{12}

$\frac{26}{12}$

Step 6

Cancel the common factor of

26

$26$ and

12

$12$ .

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Step 6.1

Factor

2

$2$ out of

26

$26$ .

\frac{2 (13)}{12}

$\frac{2 (13)}{12}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor

2

$2$ out of

12

$12$ .

\frac{2 \cdot 13}{2 \cdot 6}

$\frac{2 \cdot 13}{2 \cdot 6}$

Step 6.2.2

Cancel the common factor.

\frac{2 \cdot 13}{2 \cdot 6}

$\frac{2 \cdot 13}{2 \cdot 6}$

Step 6.2.3

Rewrite the expression.

\frac{13}{6}

$\frac{13}{6}$

\frac{13}{6}

$\frac{13}{6}$

\frac{13}{6}

$\frac{13}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{13}{6}

$\frac{13}{6}$

Decimal Form:

2.1\overline{6}

$2.1\overline{6}$

Mixed Number Form:

2 \frac{1}{6}

$2 \frac{1}{6}$