Basic Math Examples

$6 \frac{1}{3} + 4 \frac{3}{4} + 3 \frac{7}{12}$

Step 1

Convert $6 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$6 + \frac{1}{3} + 4 \frac{3}{4} + 3 \frac{7}{12}$

Step 1.2

Add $6$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 \cdot \frac{3}{3} + \frac{1}{3} + 4 \frac{3}{4} + 3 \frac{7}{12}$

Step 1.2.2

Combine $6$ and $\frac{3}{3}$ .

$\frac{6 \cdot 3}{3} + \frac{1}{3} + 4 \frac{3}{4} + 3 \frac{7}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 3 + 1}{3} + 4 \frac{3}{4} + 3 \frac{7}{12}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $3$ .

$\frac{18 + 1}{3} + 4 \frac{3}{4} + 3 \frac{7}{12}$

Step 1.2.4.2

Add $18$ and $1$ .

$\frac{19}{3} + 4 \frac{3}{4} + 3 \frac{7}{12}$

Step 2

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

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Step 2.1

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

$\frac{19}{3} + 4 + \frac{3}{4} + 3 \frac{7}{12}$

Step 2.2

Add $4$ and $\frac{3}{4}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{19}{3} + 4 \cdot \frac{4}{4} + \frac{3}{4} + 3 \frac{7}{12}$

Step 2.2.2

Combine $4$ and $\frac{4}{4}$ .

$\frac{19}{3} + \frac{4 \cdot 4}{4} + \frac{3}{4} + 3 \frac{7}{12}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{19}{3} + \frac{4 \cdot 4 + 3}{4} + 3 \frac{7}{12}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $4$ .

$\frac{19}{3} + \frac{16 + 3}{4} + 3 \frac{7}{12}$

Step 2.2.4.2

Add $16$ and $3$ .

$\frac{19}{3} + \frac{19}{4} + 3 \frac{7}{12}$

Step 3

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

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Step 3.1

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

$\frac{19}{3} + \frac{19}{4} + 3 + \frac{7}{12}$

Step 3.2

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

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Step 3.2.1

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

$\frac{19}{3} + \frac{19}{4} + 3 \cdot \frac{12}{12} + \frac{7}{12}$

Step 3.2.2

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

$\frac{19}{3} + \frac{19}{4} + \frac{3 \cdot 12}{12} + \frac{7}{12}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{19}{3} + \frac{19}{4} + \frac{3 \cdot 12 + 7}{12}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $12$ .

$\frac{19}{3} + \frac{19}{4} + \frac{36 + 7}{12}$

Step 3.2.4.2

Add $36$ and $7$ .

$\frac{19}{3} + \frac{19}{4} + \frac{43}{12}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{19}{3}$ by $\frac{4}{4}$ .

$\frac{19}{3} \cdot \frac{4}{4} + \frac{19}{4} + \frac{43}{12}$

Step 4.2

Multiply $\frac{19}{3}$ by $\frac{4}{4}$ .

$\frac{19 \cdot 4}{3 \cdot 4} + \frac{19}{4} + \frac{43}{12}$

Step 4.3

Multiply $\frac{19}{4}$ by $\frac{3}{3}$ .

$\frac{19 \cdot 4}{3 \cdot 4} + \frac{19}{4} \cdot \frac{3}{3} + \frac{43}{12}$

Step 4.4

Multiply $\frac{19}{4}$ by $\frac{3}{3}$ .

$\frac{19 \cdot 4}{3 \cdot 4} + \frac{19 \cdot 3}{4 \cdot 3} + \frac{43}{12}$

Step 4.5

Multiply $3$ by $4$ .

$\frac{19 \cdot 4}{12} + \frac{19 \cdot 3}{4 \cdot 3} + \frac{43}{12}$

Step 4.6

Reorder the factors of $4 \cdot 3$ .

$\frac{19 \cdot 4}{12} + \frac{19 \cdot 3}{3 \cdot 4} + \frac{43}{12}$

Step 4.7

Multiply $3$ by $4$ .

$\frac{19 \cdot 4}{12} + \frac{19 \cdot 3}{12} + \frac{43}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{19 \cdot 4 + 19 \cdot 3 + 43}{12}$

Step 6

Simplify each term.

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Step 6.1

Multiply $19$ by $4$ .

$\frac{76 + 19 \cdot 3 + 43}{12}$

Step 6.2

Multiply $19$ by $3$ .

$\frac{76 + 57 + 43}{12}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Add $76$ and $57$ .

$\frac{133 + 43}{12}$

Step 7.2

Add $133$ and $43$ .

$\frac{176}{12}$

Step 7.3

Cancel the common factor of $176$ and $12$ .

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Step 7.3.1

Factor $4$ out of $176$ .

$\frac{4 (44)}{12}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $4$ out of $12$ .

$\frac{4 \cdot 44}{4 \cdot 3}$

Step 7.3.2.2

Cancel the common factor.

$\frac{4 \cdot 44}{4 \cdot 3}$

Step 7.3.2.3

Rewrite the expression.

$\frac{44}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{44}{3}$

Decimal Form:

$14.\overline{6}$

Mixed Number Form:

$14 \frac{2}{3}$