Basic Math Examples

$3 \frac{7}{12} + 5 \frac{11}{12}$

Step 1

Convert $3 \frac{7}{12}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{7}{12} + 5 \frac{11}{12}$

Step 1.2

Add $3$ and $\frac{7}{12}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$3 \cdot \frac{12}{12} + \frac{7}{12} + 5 \frac{11}{12}$

Step 1.2.2

Combine $3$ and $\frac{12}{12}$ .

$\frac{3 \cdot 12}{12} + \frac{7}{12} + 5 \frac{11}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 12 + 7}{12} + 5 \frac{11}{12}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $12$ .

$\frac{36 + 7}{12} + 5 \frac{11}{12}$

Step 1.2.4.2

Add $36$ and $7$ .

$\frac{43}{12} + 5 \frac{11}{12}$

Step 2

Convert $5 \frac{11}{12}$ to an improper fraction.

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Step 2.1

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

$\frac{43}{12} + 5 + \frac{11}{12}$

Step 2.2

Add $5$ and $\frac{11}{12}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{43}{12} + 5 \cdot \frac{12}{12} + \frac{11}{12}$

Step 2.2.2

Combine $5$ and $\frac{12}{12}$ .

$\frac{43}{12} + \frac{5 \cdot 12}{12} + \frac{11}{12}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{43}{12} + \frac{5 \cdot 12 + 11}{12}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $12$ .

$\frac{43}{12} + \frac{60 + 11}{12}$

Step 2.2.4.2

Add $60$ and $11$ .

$\frac{43}{12} + \frac{71}{12}$

Step 3

Combine the numerators over the common denominator.

$\frac{43 + 71}{12}$

Step 4

Add $43$ and $71$ .

$\frac{114}{12}$

Step 5

Cancel the common factor of $114$ and $12$ .

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Step 5.1

Factor $6$ out of $114$ .

$\frac{6 (19)}{12}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $6$ out of $12$ .

$\frac{6 \cdot 19}{6 \cdot 2}$

Step 5.2.2

Cancel the common factor.

$\frac{6 \cdot 19}{6 \cdot 2}$

Step 5.2.3

Rewrite the expression.

$\frac{19}{2}$