Basic Math Examples

$\frac{13}{10} + \frac{5}{6} + 1 \frac{11}{12}$

Step 1

Convert $1 \frac{11}{12}$ to an improper fraction.

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Step 1.1

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

$\frac{13}{10} + \frac{5}{6} + 1 + \frac{11}{12}$

Step 1.2

Add $1$ and $\frac{11}{12}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{13}{10} + \frac{5}{6} + \frac{12}{12} + \frac{11}{12}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{13}{10} + \frac{5}{6} + \frac{12 + 11}{12}$

Step 1.2.3

Add $12$ and $11$ .

$\frac{13}{10} + \frac{5}{6} + \frac{23}{12}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{13}{10}$ by $\frac{6}{6}$ .

$\frac{13}{10} \cdot \frac{6}{6} + \frac{5}{6} + \frac{23}{12}$

Step 2.2

Multiply $\frac{13}{10}$ by $\frac{6}{6}$ .

$\frac{13 \cdot 6}{10 \cdot 6} + \frac{5}{6} + \frac{23}{12}$

Step 2.3

Multiply $\frac{5}{6}$ by $\frac{10}{10}$ .

$\frac{13 \cdot 6}{10 \cdot 6} + \frac{5}{6} \cdot \frac{10}{10} + \frac{23}{12}$

Step 2.4

Multiply $\frac{5}{6}$ by $\frac{10}{10}$ .

$\frac{13 \cdot 6}{10 \cdot 6} + \frac{5 \cdot 10}{6 \cdot 10} + \frac{23}{12}$

Step 2.5

Multiply $\frac{23}{12}$ by $\frac{5}{5}$ .

$\frac{13 \cdot 6}{10 \cdot 6} + \frac{5 \cdot 10}{6 \cdot 10} + \frac{23}{12} \cdot \frac{5}{5}$

Step 2.6

Multiply $\frac{23}{12}$ by $\frac{5}{5}$ .

$\frac{13 \cdot 6}{10 \cdot 6} + \frac{5 \cdot 10}{6 \cdot 10} + \frac{23 \cdot 5}{12 \cdot 5}$

Step 2.7

Reorder the factors of $10 \cdot 6$ .

$\frac{13 \cdot 6}{6 \cdot 10} + \frac{5 \cdot 10}{6 \cdot 10} + \frac{23 \cdot 5}{12 \cdot 5}$

Step 2.8

Multiply $6$ by $10$ .

$\frac{13 \cdot 6}{60} + \frac{5 \cdot 10}{6 \cdot 10} + \frac{23 \cdot 5}{12 \cdot 5}$

Step 2.9

Multiply $6$ by $10$ .

$\frac{13 \cdot 6}{60} + \frac{5 \cdot 10}{60} + \frac{23 \cdot 5}{12 \cdot 5}$

Step 2.10

Reorder the factors of $12 \cdot 5$ .

$\frac{13 \cdot 6}{60} + \frac{5 \cdot 10}{60} + \frac{23 \cdot 5}{5 \cdot 12}$

Step 2.11

Multiply $5$ by $12$ .

$\frac{13 \cdot 6}{60} + \frac{5 \cdot 10}{60} + \frac{23 \cdot 5}{60}$

Step 3

Combine the numerators over the common denominator.

$\frac{13 \cdot 6 + 5 \cdot 10 + 23 \cdot 5}{60}$

Step 4

Simplify each term.

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Step 4.1

Multiply $13$ by $6$ .

$\frac{78 + 5 \cdot 10 + 23 \cdot 5}{60}$

Step 4.2

Multiply $5$ by $10$ .

$\frac{78 + 50 + 23 \cdot 5}{60}$

Step 4.3

Multiply $23$ by $5$ .

$\frac{78 + 50 + 115}{60}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Add $78$ and $50$ .

$\frac{128 + 115}{60}$

Step 5.2

Add $128$ and $115$ .

$\frac{243}{60}$

Step 5.3

Cancel the common factor of $243$ and $60$ .

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Step 5.3.1

Factor $3$ out of $243$ .

$\frac{3 (81)}{60}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $3$ out of $60$ .

$\frac{3 \cdot 81}{3 \cdot 20}$

Step 5.3.2.2

Cancel the common factor.

$\frac{3 \cdot 81}{3 \cdot 20}$

Step 5.3.2.3

Rewrite the expression.

$\frac{81}{20}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{20}$

Decimal Form:

$4.05$

Mixed Number Form:

$4 \frac{1}{20}$