Basic Math Examples

$111 + \frac{1000 - \frac{1121}{10}}{1000 + \frac{1121}{2}}$

Step 1

To write $1000$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$111 + \frac{1000 \cdot \frac{10}{10} - \frac{1121}{10}}{1000 + \frac{1121}{2}}$

Step 2

Combine $1000$ and $\frac{10}{10}$ .

$111 + \frac{\frac{1000 \cdot 10}{10} - \frac{1121}{10}}{1000 + \frac{1121}{2}}$

Step 3

Combine the numerators over the common denominator.

$111 + \frac{\frac{1000 \cdot 10 - 1121}{10}}{1000 + \frac{1121}{2}}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $1000$ by $10$ .

$111 + \frac{\frac{10000 - 1121}{10}}{1000 + \frac{1121}{2}}$

Step 4.2

Subtract $1121$ from $10000$ .

$111 + \frac{\frac{8879}{10}}{1000 + \frac{1121}{2}}$

Step 5

Simplify each term.

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Step 5.1

Multiply the numerator by the reciprocal of the denominator.

$111 + \frac{8879}{10} \cdot \frac{1}{1000 + \frac{1121}{2}}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

To write $1000$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$111 + \frac{8879}{10} \cdot \frac{1}{1000 \cdot \frac{2}{2} + \frac{1121}{2}}$

Step 5.2.2

Combine $1000$ and $\frac{2}{2}$ .

$111 + \frac{8879}{10} \cdot \frac{1}{\frac{1000 \cdot 2}{2} + \frac{1121}{2}}$

Step 5.2.3

Combine the numerators over the common denominator.

$111 + \frac{8879}{10} \cdot \frac{1}{\frac{1000 \cdot 2 + 1121}{2}}$

Step 5.2.4

Simplify the numerator.

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Step 5.2.4.1

Multiply $1000$ by $2$ .

$111 + \frac{8879}{10} \cdot \frac{1}{\frac{2000 + 1121}{2}}$

Step 5.2.4.2

Add $2000$ and $1121$ .

$111 + \frac{8879}{10} \cdot \frac{1}{\frac{3121}{2}}$

Step 5.3

Multiply the numerator by the reciprocal of the denominator.

$111 + \frac{8879}{10} (1 (\frac{2}{3121}))$

Step 5.4

Multiply $\frac{2}{3121}$ by $1$ .

$111 + \frac{8879}{10} \cdot \frac{2}{3121}$

Step 5.5

Cancel the common factor of $2$ .

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Step 5.5.1

Factor $2$ out of $10$ .

$111 + \frac{8879}{2 (5)} \cdot \frac{2}{3121}$

Step 5.5.2

Cancel the common factor.

$111 + \frac{8879}{2 \cdot 5} \cdot \frac{2}{3121}$

Step 5.5.3

Rewrite the expression.

$111 + \frac{8879}{5} \cdot \frac{1}{3121}$

Step 5.6

Multiply $\frac{8879}{5}$ by $\frac{1}{3121}$ .

$111 + \frac{8879}{5 \cdot 3121}$

Step 5.7

Multiply $5$ by $3121$ .

$111 + \frac{8879}{15605}$

Step 6

To write $111$ as a fraction with a common denominator, multiply by $\frac{15605}{15605}$ .

$111 \cdot \frac{15605}{15605} + \frac{8879}{15605}$

Step 7

Combine $111$ and $\frac{15605}{15605}$ .

$\frac{111 \cdot 15605}{15605} + \frac{8879}{15605}$

Step 8

Combine the numerators over the common denominator.

$\frac{111 \cdot 15605 + 8879}{15605}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $111$ by $15605$ .

$\frac{1732155 + 8879}{15605}$

Step 9.2

Add $1732155$ and $8879$ .

$\frac{1741034}{15605}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{1741034}{15605}$

Decimal Form:

$111.56898429 \dots$

Mixed Number Form:

$111 \frac{8879}{15605}$