Basic Math Examples

2 \frac{4}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$2 \frac{4}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

Step 1

Simplify the left side.

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Step 1.1

Simplify

2 \frac{4}{7} \cdot n + 4 \frac{1}{2}

$2 \frac{4}{7} \cdot n + 4 \frac{1}{2}$ .

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Step 1.1.1

Convert

2 \frac{4}{7}

$2 \frac{4}{7}$ to an improper fraction.

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Step 1.1.1.1

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

(2 + \frac{4}{7}) \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$(2 + \frac{4}{7}) \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

Step 1.1.1.2

Add

2

$2$ and

\frac{4}{7}

$\frac{4}{7}$ .

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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{4}{7}) \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$(2 \cdot \frac{7}{7} + \frac{4}{7}) \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

Step 1.1.1.2.2

Combine

2

$2$ and

\frac{7}{7}

$\frac{7}{7}$ .

(\frac{2 \cdot 7}{7} + \frac{4}{7}) \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$(\frac{2 \cdot 7}{7} + \frac{4}{7}) \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 7 + 4}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$\frac{2 \cdot 7 + 4}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply

2

$2$ by

7

$7$ .

\frac{14 + 4}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$\frac{14 + 4}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

Step 1.1.1.2.4.2

Add

14

$14$ and

4

$4$ .

\frac{18}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

\frac{18}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

\frac{18}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

\frac{18}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + 4 \frac{1}{2} = 1 \frac{5}{22}$

Step 1.1.2

Convert

4 \frac{1}{2}

$4 \frac{1}{2}$ to an improper fraction.

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Step 1.1.2.1

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

\frac{18}{7} \cdot n + 4 + \frac{1}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + 4 + \frac{1}{2} = 1 \frac{5}{22}$

Step 1.1.2.2

Add

4

$4$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.1.2.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{18}{7} \cdot n + 4 \cdot \frac{2}{2} + \frac{1}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + 4 \cdot \frac{2}{2} + \frac{1}{2} = 1 \frac{5}{22}$

Step 1.1.2.2.2

Combine

4

$4$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{18}{7} \cdot n + \frac{4 \cdot 2}{2} + \frac{1}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + \frac{4 \cdot 2}{2} + \frac{1}{2} = 1 \frac{5}{22}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

\frac{18}{7} \cdot n + \frac{4 \cdot 2 + 1}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + \frac{4 \cdot 2 + 1}{2} = 1 \frac{5}{22}$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply

4

$4$ by

2

$2$ .

\frac{18}{7} \cdot n + \frac{8 + 1}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + \frac{8 + 1}{2} = 1 \frac{5}{22}$

Step 1.1.2.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{18}{7} \cdot n + \frac{9}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + \frac{9}{2} = 1 \frac{5}{22}$

\frac{18}{7} \cdot n + \frac{9}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + \frac{9}{2} = 1 \frac{5}{22}$

\frac{18}{7} \cdot n + \frac{9}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + \frac{9}{2} = 1 \frac{5}{22}$

\frac{18}{7} \cdot n + \frac{9}{2} = 1 \frac{5}{22}

$\frac{18}{7} \cdot n + \frac{9}{2} = 1 \frac{5}{22}$

Step 1.1.3

Combine

\frac{18}{7}

$\frac{18}{7}$ and

n

$n$ .

\frac{18 n}{7} + \frac{9}{2} = 1 \frac{5}{22}

$\frac{18 n}{7} + \frac{9}{2} = 1 \frac{5}{22}$

\frac{18 n}{7} + \frac{9}{2} = 1 \frac{5}{22}

$\frac{18 n}{7} + \frac{9}{2} = 1 \frac{5}{22}$

\frac{18 n}{7} + \frac{9}{2} = 1 \frac{5}{22}

$\frac{18 n}{7} + \frac{9}{2} = 1 \frac{5}{22}$

Step 2

Simplify the right side.

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Step 2.1

Convert

1 \frac{5}{22}

$1 \frac{5}{22}$ to an improper fraction.

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Step 2.1.1

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

\frac{18 n}{7} + \frac{9}{2} = 1 + \frac{5}{22}

$\frac{18 n}{7} + \frac{9}{2} = 1 + \frac{5}{22}$

Step 2.1.2

Add

1

$1$ and

\frac{5}{22}

$\frac{5}{22}$ .

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Step 2.1.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{18 n}{7} + \frac{9}{2} = \frac{22}{22} + \frac{5}{22}

$\frac{18 n}{7} + \frac{9}{2} = \frac{22}{22} + \frac{5}{22}$

Step 2.1.2.2

Combine the numerators over the common denominator.

\frac{18 n}{7} + \frac{9}{2} = \frac{22 + 5}{22}

$\frac{18 n}{7} + \frac{9}{2} = \frac{22 + 5}{22}$

Step 2.1.2.3

Add

22

$22$ and

5

$5$ .

\frac{18 n}{7} + \frac{9}{2} = \frac{27}{22}

$\frac{18 n}{7} + \frac{9}{2} = \frac{27}{22}$

\frac{18 n}{7} + \frac{9}{2} = \frac{27}{22}

$\frac{18 n}{7} + \frac{9}{2} = \frac{27}{22}$

\frac{18 n}{7} + \frac{9}{2} = \frac{27}{22}

$\frac{18 n}{7} + \frac{9}{2} = \frac{27}{22}$

\frac{18 n}{7} + \frac{9}{2} = \frac{27}{22}

$\frac{18 n}{7} + \frac{9}{2} = \frac{27}{22}$

Step 3

Move all terms not containing

n

$n$ to the right side of the equation.

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Step 3.1

Subtract

\frac{9}{2}

$\frac{9}{2}$ from both sides of the equation.

\frac{18 n}{7} = \frac{27}{22} - \frac{9}{2}

$\frac{18 n}{7} = \frac{27}{22} - \frac{9}{2}$

Step 3.2

To write

- \frac{9}{2}

$- \frac{9}{2}$ as a fraction with a common denominator, multiply by

\frac{11}{11}

$\frac{11}{11}$ .

\frac{18 n}{7} = \frac{27}{22} - \frac{9}{2} \cdot \frac{11}{11}

$\frac{18 n}{7} = \frac{27}{22} - \frac{9}{2} \cdot \frac{11}{11}$

Step 3.3

Write each expression with a common denominator of

22

$22$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.3.1

Multiply

\frac{9}{2}

$\frac{9}{2}$ by

\frac{11}{11}

$\frac{11}{11}$ .

\frac{18 n}{7} = \frac{27}{22} - \frac{9 \cdot 11}{2 \cdot 11}

$\frac{18 n}{7} = \frac{27}{22} - \frac{9 \cdot 11}{2 \cdot 11}$

Step 3.3.2

Multiply

2

$2$ by

11

$11$ .

\frac{18 n}{7} = \frac{27}{22} - \frac{9 \cdot 11}{22}

$\frac{18 n}{7} = \frac{27}{22} - \frac{9 \cdot 11}{22}$

\frac{18 n}{7} = \frac{27}{22} - \frac{9 \cdot 11}{22}

$\frac{18 n}{7} = \frac{27}{22} - \frac{9 \cdot 11}{22}$

Step 3.4

Combine the numerators over the common denominator.

\frac{18 n}{7} = \frac{27 - 9 \cdot 11}{22}

$\frac{18 n}{7} = \frac{27 - 9 \cdot 11}{22}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply

- 9

$- 9$ by

11

$11$ .

\frac{18 n}{7} = \frac{27 - 99}{22}

$\frac{18 n}{7} = \frac{27 - 99}{22}$

Step 3.5.2

Subtract

99

$99$ from

27

$27$ .

\frac{18 n}{7} = \frac{- 72}{22}

$\frac{18 n}{7} = \frac{- 72}{22}$

\frac{18 n}{7} = \frac{- 72}{22}

$\frac{18 n}{7} = \frac{- 72}{22}$

Step 3.6

Cancel the common factor of

- 72

$- 72$ and

22

$22$ .

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Step 3.6.1

Factor

2

$2$ out of

- 72

$- 72$ .

\frac{18 n}{7} = \frac{2 (- 36)}{22}

$\frac{18 n}{7} = \frac{2 (- 36)}{22}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor

2

$2$ out of

22

$22$ .

\frac{18 n}{7} = \frac{2 \cdot - 36}{2 \cdot 11}

$\frac{18 n}{7} = \frac{2 \cdot - 36}{2 \cdot 11}$

Step 3.6.2.2

Cancel the common factor.

$\frac{18 n}{7} = \frac{2 \cdot - 36}{2 \cdot 11}$

Step 3.6.2.3

Rewrite the expression.

$\frac{18 n}{7} = \frac{- 36}{11}$

Step 3.7

Move the negative in front of the fraction.

$\frac{18 n}{7} = - \frac{36}{11}$

Step 4

Multiply both sides of the equation by

$\frac{7}{18}$ .

$\frac{7}{18} \cdot \frac{18 n}{7} = \frac{7}{18} (- \frac{36}{11})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify

$\frac{7}{18} \cdot \frac{18 n}{7}$ .

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Step 5.1.1.1

Cancel the common factor of

$7$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{7}{18} \cdot \frac{18 n}{7} = \frac{7}{18} (- \frac{36}{11})$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{18} (18 n) = \frac{7}{18} (- \frac{36}{11})$

Step 5.1.1.2

Cancel the common factor of

$18$ .

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Step 5.1.1.2.1

Factor

$18$ out of

$18 n$ .

$\frac{1}{18} (18 (n)) = \frac{7}{18} (- \frac{36}{11})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{18} (18 n) = \frac{7}{18} (- \frac{36}{11})$

Step 5.1.1.2.3

Rewrite the expression.

$n = \frac{7}{18} (- \frac{36}{11})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify

$\frac{7}{18} (- \frac{36}{11})$ .

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Step 5.2.1.1

Cancel the common factor of

$18$ .

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Step 5.2.1.1.1

Move the leading negative in

$- \frac{36}{11}$ into the numerator.

$n = \frac{7}{18} \cdot \frac{- 36}{11}$

Step 5.2.1.1.2

Factor

$18$ out of

$- 36$ .

$n = \frac{7}{18} \cdot \frac{18 (- 2)}{11}$

Step 5.2.1.1.3

Cancel the common factor.

$n = \frac{7}{18} \cdot \frac{18 \cdot - 2}{11}$

Step 5.2.1.1.4

Rewrite the expression.

$n = 7 (\frac{- 2}{11})$

Step 5.2.1.2

Combine

$7$ and

$\frac{- 2}{11}$ .

$n = \frac{7 \cdot - 2}{11}$

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Multiply

$7$ by

$- 2$ .

$n = \frac{- 14}{11}$

Step 5.2.1.3.2

Move the negative in front of the fraction.

$n = - \frac{14}{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{14}{11}$

Decimal Form:

$n = - 1.\overline{27}$

Mixed Number Form:

$n = - 1 \frac{3}{11}$