Basic Math Examples

\frac{3}{5} + \frac{6}{11}

$\frac{3}{5} + \frac{6}{11}$

Step 1

To write

\frac{3}{5}

$\frac{3}{5}$ as a fraction with a common denominator, multiply by

\frac{11}{11}

$\frac{11}{11}$ .

\frac{3}{5} \cdot \frac{11}{11} + \frac{6}{11}

$\frac{3}{5} \cdot \frac{11}{11} + \frac{6}{11}$

Step 2

To write

\frac{6}{11}

$\frac{6}{11}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3}{5} \cdot \frac{11}{11} + \frac{6}{11} \cdot \frac{5}{5}

$\frac{3}{5} \cdot \frac{11}{11} + \frac{6}{11} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of

55

$55$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{11}{11}

$\frac{11}{11}$ .

\frac{3 \cdot 11}{5 \cdot 11} + \frac{6}{11} \cdot \frac{5}{5}

$\frac{3 \cdot 11}{5 \cdot 11} + \frac{6}{11} \cdot \frac{5}{5}$

Step 3.2

Multiply

5

$5$ by

11

$11$ .

\frac{3 \cdot 11}{55} + \frac{6}{11} \cdot \frac{5}{5}

$\frac{3 \cdot 11}{55} + \frac{6}{11} \cdot \frac{5}{5}$

Step 3.3

Multiply

\frac{6}{11}

$\frac{6}{11}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3 \cdot 11}{55} + \frac{6 \cdot 5}{11 \cdot 5}

$\frac{3 \cdot 11}{55} + \frac{6 \cdot 5}{11 \cdot 5}$

Step 3.4

Multiply

11

$11$ by

5

$5$ .

\frac{3 \cdot 11}{55} + \frac{6 \cdot 5}{55}

$\frac{3 \cdot 11}{55} + \frac{6 \cdot 5}{55}$

\frac{3 \cdot 11}{55} + \frac{6 \cdot 5}{55}

$\frac{3 \cdot 11}{55} + \frac{6 \cdot 5}{55}$

Step 4

Combine the numerators over the common denominator.

\frac{3 \cdot 11 + 6 \cdot 5}{55}

$\frac{3 \cdot 11 + 6 \cdot 5}{55}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

3

$3$ by

11

$11$ .

\frac{33 + 6 \cdot 5}{55}

$\frac{33 + 6 \cdot 5}{55}$

Step 5.2

Multiply

6

$6$ by

5

$5$ .

\frac{33 + 30}{55}

$\frac{33 + 30}{55}$

Step 5.3

Add

33

$33$ and

30

$30$ .

\frac{63}{55}

$\frac{63}{55}$

\frac{63}{55}

$\frac{63}{55}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{63}{55}

$\frac{63}{55}$

Decimal Form:

1.1 ¯ ¯¯ ¯ 45

$1.1\overline{45}$

Mixed Number Form:

1 \frac{8}{55}

$1 \frac{8}{55}$