Basic Math Examples

- 10 \frac{1}{9} + 9 \frac{9}{45}

$- 10 \frac{1}{9} + 9 \frac{9}{45}$

Step 1

Convert

10 \frac{1}{9}

$10 \frac{1}{9}$ to an improper fraction.

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Step 1.1

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

- (10 + \frac{1}{9}) + 9 \frac{9}{45}

$- (10 + \frac{1}{9}) + 9 \frac{9}{45}$

Step 1.2

Add

10

$10$ and

\frac{1}{9}

$\frac{1}{9}$ .

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Step 1.2.1

To write

10

$10$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

- (10 \cdot \frac{9}{9} + \frac{1}{9}) + 9 \frac{9}{45}

$- (10 \cdot \frac{9}{9} + \frac{1}{9}) + 9 \frac{9}{45}$

Step 1.2.2

Combine

10

$10$ and

\frac{9}{9}

$\frac{9}{9}$ .

- (\frac{10 \cdot 9}{9} + \frac{1}{9}) + 9 \frac{9}{45}

$- (\frac{10 \cdot 9}{9} + \frac{1}{9}) + 9 \frac{9}{45}$

Step 1.2.3

Combine the numerators over the common denominator.

- \frac{10 \cdot 9 + 1}{9} + 9 \frac{9}{45}

$- \frac{10 \cdot 9 + 1}{9} + 9 \frac{9}{45}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

10

$10$ by

9

$9$ .

- \frac{90 + 1}{9} + 9 \frac{9}{45}

$- \frac{90 + 1}{9} + 9 \frac{9}{45}$

Step 1.2.4.2

Add

90

$90$ and

1

$1$ .

- \frac{91}{9} + 9 \frac{9}{45}

$- \frac{91}{9} + 9 \frac{9}{45}$

- \frac{91}{9} + 9 \frac{9}{45}

$- \frac{91}{9} + 9 \frac{9}{45}$

- \frac{91}{9} + 9 \frac{9}{45}

$- \frac{91}{9} + 9 \frac{9}{45}$

- \frac{91}{9} + 9 \frac{9}{45}

$- \frac{91}{9} + 9 \frac{9}{45}$

Step 2

Convert

9 \frac{9}{45}

$9 \frac{9}{45}$ to an improper fraction.

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Step 2.1

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

- \frac{91}{9} + 9 + \frac{9}{45}

$- \frac{91}{9} + 9 + \frac{9}{45}$

Step 2.2

Add

9

$9$ and

\frac{9}{45}

$\frac{9}{45}$ .

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Step 2.2.1

To write

9

$9$ as a fraction with a common denominator, multiply by

\frac{45}{45}

$\frac{45}{45}$ .

- \frac{91}{9} + 9 \cdot \frac{45}{45} + \frac{9}{45}

$- \frac{91}{9} + 9 \cdot \frac{45}{45} + \frac{9}{45}$

Step 2.2.2

Combine

9

$9$ and

\frac{45}{45}

$\frac{45}{45}$ .

- \frac{91}{9} + \frac{9 \cdot 45}{45} + \frac{9}{45}

$- \frac{91}{9} + \frac{9 \cdot 45}{45} + \frac{9}{45}$

Step 2.2.3

Combine the numerators over the common denominator.

- \frac{91}{9} + \frac{9 \cdot 45 + 9}{45}

$- \frac{91}{9} + \frac{9 \cdot 45 + 9}{45}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

9

$9$ by

45

$45$ .

- \frac{91}{9} + \frac{405 + 9}{45}

$- \frac{91}{9} + \frac{405 + 9}{45}$

Step 2.2.4.2

Add

405

$405$ and

9

$9$ .

- \frac{91}{9} + \frac{414}{45}

$- \frac{91}{9} + \frac{414}{45}$

- \frac{91}{9} + \frac{414}{45}

$- \frac{91}{9} + \frac{414}{45}$

- \frac{91}{9} + \frac{414}{45}

$- \frac{91}{9} + \frac{414}{45}$

- \frac{91}{9} + \frac{414}{45}

$- \frac{91}{9} + \frac{414}{45}$

Step 3

Cancel the common factor of

414

$414$ and

45

$45$ .

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Step 3.1

Factor

9

$9$ out of

414

$414$ .

- \frac{91}{9} + \frac{9 (46)}{45}

$- \frac{91}{9} + \frac{9 (46)}{45}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

9

$9$ out of

45

$45$ .

- \frac{91}{9} + \frac{9 \cdot 46}{9 \cdot 5}

$- \frac{91}{9} + \frac{9 \cdot 46}{9 \cdot 5}$

Step 3.2.2

Cancel the common factor.

$- \frac{91}{9} + \frac{9 \cdot 46}{9 \cdot 5}$

Step 3.2.3

Rewrite the expression.

$- \frac{91}{9} + \frac{46}{5}$

Step 4

To write

$- \frac{91}{9}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$- \frac{91}{9} \cdot \frac{5}{5} + \frac{46}{5}$

Step 5

To write

$\frac{46}{5}$ as a fraction with a common denominator, multiply by

$\frac{9}{9}$ .

$- \frac{91}{9} \cdot \frac{5}{5} + \frac{46}{5} \cdot \frac{9}{9}$

Step 6

Write each expression with a common denominator of

$45$ , by multiplying each by an appropriate factor of

$1$ .

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Step 6.1

Multiply

$\frac{91}{9}$ by

$\frac{5}{5}$ .

$- \frac{91 \cdot 5}{9 \cdot 5} + \frac{46}{5} \cdot \frac{9}{9}$

Step 6.2

Multiply

$9$ by

$5$ .

$- \frac{91 \cdot 5}{45} + \frac{46}{5} \cdot \frac{9}{9}$

Step 6.3

Multiply

$\frac{46}{5}$ by

$\frac{9}{9}$ .

$- \frac{91 \cdot 5}{45} + \frac{46 \cdot 9}{5 \cdot 9}$

Step 6.4

Multiply

$5$ by

$9$ .

$- \frac{91 \cdot 5}{45} + \frac{46 \cdot 9}{45}$

Step 7

Combine the numerators over the common denominator.

$\frac{- 91 \cdot 5 + 46 \cdot 9}{45}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply

$- 91$ by

$5$ .

$\frac{- 455 + 46 \cdot 9}{45}$

Step 8.2

Multiply

$46$ by

$9$ .

$\frac{- 455 + 414}{45}$

Step 8.3

Add

$- 455$ and

$414$ .

$\frac{- 41}{45}$

Step 9

Move the negative in front of the fraction.

$- \frac{41}{45}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{41}{45}$

Decimal Form:

$- 0.9\overline{1}$