Basic Math Examples

- 2 \frac{3}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- 2 \frac{3}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Simplify

- 2 \frac{3}{7} \div a

$- 2 \frac{3}{7} \div a$ .

Tap for more steps...

Step 1.1.1

Convert

2 \frac{3}{7}

$2 \frac{3}{7}$ to an improper fraction.

Tap for more steps...

Step 1.1.1.1

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

- (2 + \frac{3}{7}) \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- (2 + \frac{3}{7}) \div a = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1.1.1.2

Add

2

$2$ and

\frac{3}{7}

$\frac{3}{7}$ .

Tap for more steps...

Step 1.1.1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

- (2 \cdot \frac{7}{7} + \frac{3}{7}) \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- (2 \cdot \frac{7}{7} + \frac{3}{7}) \div a = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1.1.1.2.2

Combine

2

$2$ and

\frac{7}{7}

$\frac{7}{7}$ .

- (\frac{2 \cdot 7}{7} + \frac{3}{7}) \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- (\frac{2 \cdot 7}{7} + \frac{3}{7}) \div a = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

- \frac{2 \cdot 7 + 3}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{2 \cdot 7 + 3}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1.1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.1.2.4.1

Multiply

2

$2$ by

7

$7$ .

- \frac{14 + 3}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{14 + 3}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1.1.1.2.4.2

Add

14

$14$ and

3

$3$ .

- \frac{17}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{17}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}$

- \frac{17}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{17}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}$

- \frac{17}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{17}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}$

- \frac{17}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{17}{7} \div a = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1.1.2

Rewrite the division as a fraction.

\frac{- \frac{17}{7}}{a} = 1 \frac{13}{14} \div \frac{6}{17}

$\frac{- \frac{17}{7}}{a} = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1.1.3

Multiply the numerator by the reciprocal of the denominator.

- \frac{17}{7} \cdot \frac{1}{a} = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{17}{7} \cdot \frac{1}{a} = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1.1.4

Multiply

\frac{1}{a}

$\frac{1}{a}$ by

\frac{17}{7}

$\frac{17}{7}$ .

- \frac{17}{a \cdot 7} = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{17}{a \cdot 7} = 1 \frac{13}{14} \div \frac{6}{17}$

Step 1.1.5

Move

7

$7$ to the left of

a

$a$ .

- \frac{17}{7 a} = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{17}{7 a} = 1 \frac{13}{14} \div \frac{6}{17}$

- \frac{17}{7 a} = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{17}{7 a} = 1 \frac{13}{14} \div \frac{6}{17}$

- \frac{17}{7 a} = 1 \frac{13}{14} \div \frac{6}{17}

$- \frac{17}{7 a} = 1 \frac{13}{14} \div \frac{6}{17}$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Simplify

1 \frac{13}{14} \div \frac{6}{17}

$1 \frac{13}{14} \div \frac{6}{17}$ .

Tap for more steps...

Step 2.1.1

Convert

1 \frac{13}{14}

$1 \frac{13}{14}$ to an improper fraction.

Tap for more steps...

Step 2.1.1.1

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

- \frac{17}{7 a} = (1 + \frac{13}{14}) \div \frac{6}{17}

$- \frac{17}{7 a} = (1 + \frac{13}{14}) \div \frac{6}{17}$

Step 2.1.1.2

Add

1

$1$ and

\frac{13}{14}

$\frac{13}{14}$ .

Tap for more steps...

Step 2.1.1.2.1

Write

1

$1$ as a fraction with a common denominator.

- \frac{17}{7 a} = (\frac{14}{14} + \frac{13}{14}) \div \frac{6}{17}

$- \frac{17}{7 a} = (\frac{14}{14} + \frac{13}{14}) \div \frac{6}{17}$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

- \frac{17}{7 a} = \frac{14 + 13}{14} \div \frac{6}{17}

$- \frac{17}{7 a} = \frac{14 + 13}{14} \div \frac{6}{17}$

Step 2.1.1.2.3

Add

14

$14$ and

13

$13$ .

- \frac{17}{7 a} = \frac{27}{14} \div \frac{6}{17}

$- \frac{17}{7 a} = \frac{27}{14} \div \frac{6}{17}$

Step 2.1.2

To divide by a fraction, multiply by its reciprocal.

$- \frac{17}{7 a} = \frac{27}{14} \cdot \frac{17}{6}$

Step 2.1.3

Cancel the common factor of

$3$ .

Tap for more steps...

Step 2.1.3.1

Factor

$3$ out of

$27$ .

$- \frac{17}{7 a} = \frac{3 (9)}{14} \cdot \frac{17}{6}$

Step 2.1.3.2

Factor

$3$ out of

$6$ .

$- \frac{17}{7 a} = \frac{3 \cdot 9}{14} \cdot \frac{17}{3 \cdot 2}$

Step 2.1.3.3

Cancel the common factor.

$- \frac{17}{7 a} = \frac{3 \cdot 9}{14} \cdot \frac{17}{3 \cdot 2}$

Step 2.1.3.4

Rewrite the expression.

$- \frac{17}{7 a} = \frac{9}{14} \cdot \frac{17}{2}$

Step 2.1.4

Multiply

$\frac{9}{14}$ by

$\frac{17}{2}$ .

$- \frac{17}{7 a} = \frac{9 \cdot 17}{14 \cdot 2}$

Step 2.1.5

Multiply.

Tap for more steps...

Step 2.1.5.1

Multiply

$9$ by

$17$ .

$- \frac{17}{7 a} = \frac{153}{14 \cdot 2}$

Step 2.1.5.2

Multiply

$14$ by

$2$ .

$- \frac{17}{7 a} = \frac{153}{28}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$- 17 \cdot 28 = 7 a \cdot 153$

Step 4

Solve the equation for

$a$ .

Tap for more steps...

Step 4.1

Rewrite the equation as

$7 a \cdot 153 = - 17 \cdot 28$ .

$7 a \cdot 153 = - 17 \cdot 28$

Step 4.2

Simplify.

Tap for more steps...

Step 4.2.1

Multiply

$153$ by

$7$ .

$1071 a = - 17 \cdot 28$

Step 4.2.2

Multiply

$- 17$ by

$28$ .

$1071 a = - 476$

Step 4.3

Divide each term in

$1071 a = - 476$ by

$1071$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in

$1071 a = - 476$ by

$1071$ .

$\frac{1071 a}{1071} = \frac{- 476}{1071}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of

$1071$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{1071 a}{1071} = \frac{- 476}{1071}$

Step 4.3.2.1.2

Divide

$a$ by

$1$ .

$a = \frac{- 476}{1071}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Cancel the common factor of

$- 476$ and

$1071$ .

Tap for more steps...

Step 4.3.3.1.1

Factor

$119$ out of

$- 476$ .

$a = \frac{119 (- 4)}{1071}$

Step 4.3.3.1.2

Cancel the common factors.

Tap for more steps...

Step 4.3.3.1.2.1

Factor

$119$ out of

$1071$ .

$a = \frac{119 \cdot - 4}{119 \cdot 9}$

Step 4.3.3.1.2.2

Cancel the common factor.

$a = \frac{119 \cdot - 4}{119 \cdot 9}$

Step 4.3.3.1.2.3

Rewrite the expression.

$a = \frac{- 4}{9}$

Step 4.3.3.2

Move the negative in front of the fraction.

$a = - \frac{4}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{4}{9}$

Decimal Form:

$a = - 0.\overline{4}$