Basic Math Examples

$(29 \frac{7}{12}) - (- 19 \frac{7}{9})$

Step 1

Convert $29 \frac{7}{12}$ to an improper fraction.

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Step 1.1

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

$29 + \frac{7}{12} - (- 19 \frac{7}{9})$

Step 1.2

Add $29$ and $\frac{7}{12}$ .

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Step 1.2.1

To write $29$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$29 \cdot \frac{12}{12} + \frac{7}{12} - (- 19 \frac{7}{9})$

Step 1.2.2

Combine $29$ and $\frac{12}{12}$ .

$\frac{29 \cdot 12}{12} + \frac{7}{12} - (- 19 \frac{7}{9})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{29 \cdot 12 + 7}{12} - (- 19 \frac{7}{9})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $29$ by $12$ .

$\frac{348 + 7}{12} - (- 19 \frac{7}{9})$

Step 1.2.4.2

Add $348$ and $7$ .

$\frac{355}{12} - (- 19 \frac{7}{9})$

Step 2

Convert $19 \frac{7}{9}$ to an improper fraction.

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Step 2.1

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

$\frac{355}{12} - - (19 + \frac{7}{9})$

Step 2.2

Add $19$ and $\frac{7}{9}$ .

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Step 2.2.1

To write $19$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{355}{12} - - (19 \cdot \frac{9}{9} + \frac{7}{9})$

Step 2.2.2

Combine $19$ and $\frac{9}{9}$ .

$\frac{355}{12} - - (\frac{19 \cdot 9}{9} + \frac{7}{9})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{355}{12} - - \frac{19 \cdot 9 + 7}{9}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $19$ by $9$ .

$\frac{355}{12} - - \frac{171 + 7}{9}$

Step 2.2.4.2

Add $171$ and $7$ .

$\frac{355}{12} - - \frac{178}{9}$

Step 3

Multiply $- - \frac{178}{9}$ .

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Step 3.1

Multiply $- 1$ by $- 1$ .

$\frac{355}{12} + 1 (\frac{178}{9})$

Step 3.2

Multiply $\frac{178}{9}$ by $1$ .

$\frac{355}{12} + \frac{178}{9}$

Step 4

To write $\frac{355}{12}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{355}{12} \cdot \frac{3}{3} + \frac{178}{9}$

Step 5

To write $\frac{178}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{355}{12} \cdot \frac{3}{3} + \frac{178}{9} \cdot \frac{4}{4}$

Step 6

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{355}{12}$ by $\frac{3}{3}$ .

$\frac{355 \cdot 3}{12 \cdot 3} + \frac{178}{9} \cdot \frac{4}{4}$

Step 6.2

Multiply $12$ by $3$ .

$\frac{355 \cdot 3}{36} + \frac{178}{9} \cdot \frac{4}{4}$

Step 6.3

Multiply $\frac{178}{9}$ by $\frac{4}{4}$ .

$\frac{355 \cdot 3}{36} + \frac{178 \cdot 4}{9 \cdot 4}$

Step 6.4

Multiply $9$ by $4$ .

$\frac{355 \cdot 3}{36} + \frac{178 \cdot 4}{36}$

Step 7

Combine the numerators over the common denominator.

$\frac{355 \cdot 3 + 178 \cdot 4}{36}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $355$ by $3$ .

$\frac{1065 + 178 \cdot 4}{36}$

Step 8.2

Multiply $178$ by $4$ .

$\frac{1065 + 712}{36}$

Step 8.3

Add $1065$ and $712$ .

$\frac{1777}{36}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{1777}{36}$

Decimal Form:

$49.36\overline{1}$

Mixed Number Form:

$49 \frac{13}{36}$