Finite Math Examples

7 \frac{4}{9} - 3 \frac{1}{8}

$7 \frac{4}{9} - 3 \frac{1}{8}$

Step 1

Set

7 \frac{4}{9} - 3 \frac{1}{8}

$7 \frac{4}{9} - 3 \frac{1}{8}$ equal to

0

$0$ .

7 \frac{4}{9} - 3 \frac{1}{8} = 0

$7 \frac{4}{9} - 3 \frac{1}{8} = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify

7 \frac{4}{9} - 3 \frac{1}{8}

$7 \frac{4}{9} - 3 \frac{1}{8}$ .

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Step 2.1.1.1

Convert

7 \frac{4}{9}

$7 \frac{4}{9}$ to an improper fraction.

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Step 2.1.1.1.1

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

7 + \frac{4}{9} - 3 \frac{1}{8} = 0

$7 + \frac{4}{9} - 3 \frac{1}{8} = 0$

Step 2.1.1.1.2

Add

7

$7$ and

\frac{4}{9}

$\frac{4}{9}$ .

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Step 2.1.1.1.2.1

To write

7

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

\frac{9}{9}

$\frac{9}{9}$ .

7 \cdot \frac{9}{9} + \frac{4}{9} - 3 \frac{1}{8} = 0

$7 \cdot \frac{9}{9} + \frac{4}{9} - 3 \frac{1}{8} = 0$

Step 2.1.1.1.2.2

Combine

7

$7$ and

\frac{9}{9}

$\frac{9}{9}$ .

\frac{7 \cdot 9}{9} + \frac{4}{9} - 3 \frac{1}{8} = 0

$\frac{7 \cdot 9}{9} + \frac{4}{9} - 3 \frac{1}{8} = 0$

Step 2.1.1.1.2.3

Combine the numerators over the common denominator.

\frac{7 \cdot 9 + 4}{9} - 3 \frac{1}{8} = 0

$\frac{7 \cdot 9 + 4}{9} - 3 \frac{1}{8} = 0$

Step 2.1.1.1.2.4

Simplify the numerator.

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Step 2.1.1.1.2.4.1

Multiply

7

$7$ by

9

$9$ .

\frac{63 + 4}{9} - 3 \frac{1}{8} = 0

$\frac{63 + 4}{9} - 3 \frac{1}{8} = 0$

Step 2.1.1.1.2.4.2

Add

63

$63$ and

4

$4$ .

\frac{67}{9} - 3 \frac{1}{8} = 0

$\frac{67}{9} - 3 \frac{1}{8} = 0$

\frac{67}{9} - 3 \frac{1}{8} = 0

$\frac{67}{9} - 3 \frac{1}{8} = 0$

\frac{67}{9} - 3 \frac{1}{8} = 0

$\frac{67}{9} - 3 \frac{1}{8} = 0$

\frac{67}{9} - 3 \frac{1}{8} = 0

$\frac{67}{9} - 3 \frac{1}{8} = 0$

Step 2.1.1.2

Convert

3 \frac{1}{8}

$3 \frac{1}{8}$ to an improper fraction.

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Step 2.1.1.2.1

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

\frac{67}{9} - (3 + \frac{1}{8}) = 0

$\frac{67}{9} - (3 + \frac{1}{8}) = 0$

Step 2.1.1.2.2

Add

3

$3$ and

\frac{1}{8}

$\frac{1}{8}$ .

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Step 2.1.1.2.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{67}{9} - (3 \cdot \frac{8}{8} + \frac{1}{8}) = 0

$\frac{67}{9} - (3 \cdot \frac{8}{8} + \frac{1}{8}) = 0$

Step 2.1.1.2.2.2

Combine

3

$3$ and

\frac{8}{8}

$\frac{8}{8}$ .

\frac{67}{9} - (\frac{3 \cdot 8}{8} + \frac{1}{8}) = 0

$\frac{67}{9} - (\frac{3 \cdot 8}{8} + \frac{1}{8}) = 0$

Step 2.1.1.2.2.3

Combine the numerators over the common denominator.

\frac{67}{9} - \frac{3 \cdot 8 + 1}{8} = 0

$\frac{67}{9} - \frac{3 \cdot 8 + 1}{8} = 0$

Step 2.1.1.2.2.4

Simplify the numerator.

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Step 2.1.1.2.2.4.1

Multiply

3

$3$ by

8

$8$ .

\frac{67}{9} - \frac{24 + 1}{8} = 0

$\frac{67}{9} - \frac{24 + 1}{8} = 0$

Step 2.1.1.2.2.4.2

Add

24

$24$ and

1

$1$ .

\frac{67}{9} - \frac{25}{8} = 0

$\frac{67}{9} - \frac{25}{8} = 0$

\frac{67}{9} - \frac{25}{8} = 0

$\frac{67}{9} - \frac{25}{8} = 0$

\frac{67}{9} - \frac{25}{8} = 0

$\frac{67}{9} - \frac{25}{8} = 0$

\frac{67}{9} - \frac{25}{8} = 0

$\frac{67}{9} - \frac{25}{8} = 0$

Step 2.1.1.3

To write

\frac{67}{9}

$\frac{67}{9}$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{67}{9} \cdot \frac{8}{8} - \frac{25}{8} = 0

$\frac{67}{9} \cdot \frac{8}{8} - \frac{25}{8} = 0$

Step 2.1.1.4

To write

- \frac{25}{8}

$- \frac{25}{8}$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

\frac{67}{9} \cdot \frac{8}{8} - \frac{25}{8} \cdot \frac{9}{9} = 0

$\frac{67}{9} \cdot \frac{8}{8} - \frac{25}{8} \cdot \frac{9}{9} = 0$

Step 2.1.1.5

Write each expression with a common denominator of

72

$72$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 2.1.1.5.1

Multiply

\frac{67}{9}

$\frac{67}{9}$ by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{67 \cdot 8}{9 \cdot 8} - \frac{25}{8} \cdot \frac{9}{9} = 0

$\frac{67 \cdot 8}{9 \cdot 8} - \frac{25}{8} \cdot \frac{9}{9} = 0$

Step 2.1.1.5.2

Multiply

9

$9$ by

8

$8$ .

\frac{67 \cdot 8}{72} - \frac{25}{8} \cdot \frac{9}{9} = 0

$\frac{67 \cdot 8}{72} - \frac{25}{8} \cdot \frac{9}{9} = 0$

Step 2.1.1.5.3

Multiply

\frac{25}{8}

$\frac{25}{8}$ by

\frac{9}{9}

$\frac{9}{9}$ .

\frac{67 \cdot 8}{72} - \frac{25 \cdot 9}{8 \cdot 9} = 0

$\frac{67 \cdot 8}{72} - \frac{25 \cdot 9}{8 \cdot 9} = 0$

Step 2.1.1.5.4

Multiply

8

$8$ by

9

$9$ .

\frac{67 \cdot 8}{72} - \frac{25 \cdot 9}{72} = 0

$\frac{67 \cdot 8}{72} - \frac{25 \cdot 9}{72} = 0$

\frac{67 \cdot 8}{72} - \frac{25 \cdot 9}{72} = 0

$\frac{67 \cdot 8}{72} - \frac{25 \cdot 9}{72} = 0$

Step 2.1.1.6

Combine the numerators over the common denominator.

\frac{67 \cdot 8 - 25 \cdot 9}{72} = 0

$\frac{67 \cdot 8 - 25 \cdot 9}{72} = 0$

Step 2.1.1.7

Simplify the numerator.

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Step 2.1.1.7.1

Multiply

67

$67$ by

8

$8$ .

\frac{536 - 25 \cdot 9}{72} = 0

$\frac{536 - 25 \cdot 9}{72} = 0$

Step 2.1.1.7.2

Multiply

- 25

$- 25$ by

9

$9$ .

\frac{536 - 225}{72} = 0

$\frac{536 - 225}{72} = 0$

Step 2.1.1.7.3

Subtract

225

$225$ from

536

$536$ .

\frac{311}{72} = 0

$\frac{311}{72} = 0$

Step 2.2

Set the numerator equal to zero.

$311 = 0$

Step 2.3

Since

$311 \neq 0$ , there are no solutions.

No solution