Basic Math Examples

\frac{0.8}{0.11}

$\frac{0.8}{0.11}$

Step 1

Create two equations where the only numbers to the right of the decimal place are the repeating part.

Step 2

Set up an equation with

0. ¯ ¯¯ ¯ 27

$0.\overline{27}$ .

x = 0. ¯ ¯¯ ¯ 27

$x = 0.\overline{27}$

Step 3

Multiply both sides of

x = 0. ¯ ¯¯ ¯ 27

$x = 0.\overline{27}$ by

100

$100$ to create the second equation.

100 x = 27. ¯ ¯¯ ¯ 27

$100 x = 27.\overline{27}$

Step 4

Subtract

x = 0. ¯ ¯¯ ¯ 27

$x = 0.\overline{27}$ from

100 x = 27. ¯ ¯¯ ¯ 27

$100 x = 27.\overline{27}$ to remove the repeating part.

99 x = 27

$99 x = 27$

Step 5

Divide each term in

99 x = 27

$99 x = 27$ by

99

$99$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in

99 x = 27

$99 x = 27$ by

99

$99$ .

\frac{99 x}{99} = \frac{27}{99}

$\frac{99 x}{99} = \frac{27}{99}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of

99

$99$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

\frac{99 x}{99} = \frac{27}{99}

$\frac{99 x}{99} = \frac{27}{99}$

Step 5.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{27}{99}

$x = \frac{27}{99}$

x = \frac{27}{99}

$x = \frac{27}{99}$

x = \frac{27}{99}

$x = \frac{27}{99}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Cancel the common factor of

27

$27$ and

99

$99$ .

Tap for more steps...

Step 5.3.1.1

Factor

9

$9$ out of

27

$27$ .

x = \frac{9 (3)}{99}

$x = \frac{9 (3)}{99}$

Step 5.3.1.2

Cancel the common factors.

Tap for more steps...

Step 5.3.1.2.1

Factor

9

$9$ out of

99

$99$ .

x = \frac{9 \cdot 3}{9 \cdot 11}

$x = \frac{9 \cdot 3}{9 \cdot 11}$

Step 5.3.1.2.2

Cancel the common factor.

x = \frac{9 \cdot 3}{9 \cdot 11}

$x = \frac{9 \cdot 3}{9 \cdot 11}$

Step 5.3.1.2.3

Rewrite the expression.

x = \frac{3}{11}

$x = \frac{3}{11}$

x = \frac{3}{11}

$x = \frac{3}{11}$

x = \frac{3}{11}

$x = \frac{3}{11}$

x = \frac{3}{11}

$x = \frac{3}{11}$

x = \frac{3}{11}

$x = \frac{3}{11}$

Step 6

Write as a mixed number by taking the whole number part along with the solution to the equation.

7 \frac{3}{11}

$7 \frac{3}{11}$

Step 7

Convert

7 \frac{3}{11}

$7 \frac{3}{11}$ to an improper fraction.

Tap for more steps...

Step 7.1

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

7 + \frac{3}{11}

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

Step 7.2

Add

7

$7$ and

\frac{3}{11}

$\frac{3}{11}$ .

Tap for more steps...

Step 7.2.1

To write

7

$7$ as a fraction with a common denominator, multiply by

\frac{11}{11}

$\frac{11}{11}$ .

7 \cdot \frac{11}{11} + \frac{3}{11}

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

Step 7.2.2

Combine

7

$7$ and

\frac{11}{11}

$\frac{11}{11}$ .

\frac{7 \cdot 11}{11} + \frac{3}{11}

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

Step 7.2.3

Combine the numerators over the common denominator.

\frac{7 \cdot 11 + 3}{11}

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

Step 7.2.4

Simplify the numerator.

Tap for more steps...

Step 7.2.4.1

Multiply

7

$7$ by

11

$11$ .

\frac{77 + 3}{11}

$\frac{77 + 3}{11}$

Step 7.2.4.2

Add

77

$77$ and

3

$3$ .

\frac{80}{11}

$\frac{80}{11}$

\frac{80}{11}

$\frac{80}{11}$

\frac{80}{11}

$\frac{80}{11}$

\frac{80}{11}

$\frac{80}{11}$