Basic Math Examples

\frac{4}{5} k + \frac{7}{10} = \frac{13}{15} k - \frac{3}{5}

$\frac{4}{5} k + \frac{7}{10} = \frac{13}{15} k - \frac{3}{5}$

Step 1

Combine

\frac{4}{5}

$\frac{4}{5}$ and

k

$k$ .

\frac{4 k}{5} + \frac{7}{10} = \frac{13}{15} k - \frac{3}{5}

$\frac{4 k}{5} + \frac{7}{10} = \frac{13}{15} k - \frac{3}{5}$

Step 2

Combine

\frac{13}{15}

$\frac{13}{15}$ and

k

$k$ .

\frac{4 k}{5} + \frac{7}{10} = \frac{13 k}{15} - \frac{3}{5}

$\frac{4 k}{5} + \frac{7}{10} = \frac{13 k}{15} - \frac{3}{5}$

Step 3

Move all terms containing

k

$k$ to the left side of the equation.

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Step 3.1

Subtract

\frac{13 k}{15}

$\frac{13 k}{15}$ from both sides of the equation.

\frac{4 k}{5} + \frac{7}{10} - \frac{13 k}{15} = - \frac{3}{5}

$\frac{4 k}{5} + \frac{7}{10} - \frac{13 k}{15} = - \frac{3}{5}$

Step 3.2

To write

\frac{4 k}{5}

$\frac{4 k}{5}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{4 k}{5} \cdot \frac{3}{3} - \frac{13 k}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{4 k}{5} \cdot \frac{3}{3} - \frac{13 k}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.3

Write each expression with a common denominator of

15

$15$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.3.1

Multiply

\frac{4 k}{5}

$\frac{4 k}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{4 k \cdot 3}{5 \cdot 3} - \frac{13 k}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{4 k \cdot 3}{5 \cdot 3} - \frac{13 k}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.3.2

Multiply

5

$5$ by

3

$3$ .

\frac{4 k \cdot 3}{15} - \frac{13 k}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{4 k \cdot 3}{15} - \frac{13 k}{15} + \frac{7}{10} = - \frac{3}{5}$

\frac{4 k \cdot 3}{15} - \frac{13 k}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{4 k \cdot 3}{15} - \frac{13 k}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.4

Combine the numerators over the common denominator.

\frac{4 k \cdot 3 - 13 k}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{4 k \cdot 3 - 13 k}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor

k

$k$ out of

4 k \cdot 3 - 13 k

$4 k \cdot 3 - 13 k$ .

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Step 3.5.1.1.1

Factor

k

$k$ out of

4 k \cdot 3

$4 k \cdot 3$ .

\frac{k (4 \cdot 3) - 13 k}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{k (4 \cdot 3) - 13 k}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.5.1.1.2

Factor

k

$k$ out of

- 13 k

$- 13 k$ .

\frac{k (4 \cdot 3) + k \cdot - 13}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{k (4 \cdot 3) + k \cdot - 13}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.5.1.1.3

Factor

k

$k$ out of

k (4 \cdot 3) + k \cdot - 13

$k (4 \cdot 3) + k \cdot - 13$ .

\frac{k (4 \cdot 3 - 13)}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{k (4 \cdot 3 - 13)}{15} + \frac{7}{10} = - \frac{3}{5}$

\frac{k (4 \cdot 3 - 13)}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{k (4 \cdot 3 - 13)}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.5.1.2

Multiply

4

$4$ by

3

$3$ .

\frac{k (12 - 13)}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{k (12 - 13)}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.5.1.3

Subtract

13

$13$ from

12

$12$ .

\frac{k \cdot - 1}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{k \cdot - 1}{15} + \frac{7}{10} = - \frac{3}{5}$

\frac{k \cdot - 1}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{k \cdot - 1}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.5.2

Move

- 1

$- 1$ to the left of

k

$k$ .

\frac{- 1 \cdot k}{15} + \frac{7}{10} = - \frac{3}{5}

$\frac{- 1 \cdot k}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 3.5.3

Move the negative in front of the fraction.

- \frac{k}{15} + \frac{7}{10} = - \frac{3}{5}

$- \frac{k}{15} + \frac{7}{10} = - \frac{3}{5}$

- \frac{k}{15} + \frac{7}{10} = - \frac{3}{5}

$- \frac{k}{15} + \frac{7}{10} = - \frac{3}{5}$

- \frac{k}{15} + \frac{7}{10} = - \frac{3}{5}

$- \frac{k}{15} + \frac{7}{10} = - \frac{3}{5}$

Step 4

Move all terms not containing

k

$k$ to the right side of the equation.

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Step 4.1

Subtract

\frac{7}{10}

$\frac{7}{10}$ from both sides of the equation.

- \frac{k}{15} = - \frac{3}{5} - \frac{7}{10}

$- \frac{k}{15} = - \frac{3}{5} - \frac{7}{10}$

Step 4.2

To write

- \frac{3}{5}

$- \frac{3}{5}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

- \frac{k}{15} = - \frac{3}{5} \cdot \frac{2}{2} - \frac{7}{10}

$- \frac{k}{15} = - \frac{3}{5} \cdot \frac{2}{2} - \frac{7}{10}$

Step 4.3

Write each expression with a common denominator of

10

$10$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.3.1

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{2}{2}

$\frac{2}{2}$ .

- \frac{k}{15} = - \frac{3 \cdot 2}{5 \cdot 2} - \frac{7}{10}

$- \frac{k}{15} = - \frac{3 \cdot 2}{5 \cdot 2} - \frac{7}{10}$

Step 4.3.2

Multiply

5

$5$ by

2

$2$ .

- \frac{k}{15} = - \frac{3 \cdot 2}{10} - \frac{7}{10}

$- \frac{k}{15} = - \frac{3 \cdot 2}{10} - \frac{7}{10}$

- \frac{k}{15} = - \frac{3 \cdot 2}{10} - \frac{7}{10}

$- \frac{k}{15} = - \frac{3 \cdot 2}{10} - \frac{7}{10}$

Step 4.4

Combine the numerators over the common denominator.

- \frac{k}{15} = \frac{- 3 \cdot 2 - 7}{10}

$- \frac{k}{15} = \frac{- 3 \cdot 2 - 7}{10}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply

- 3

$- 3$ by

2

$2$ .

- \frac{k}{15} = \frac{- 6 - 7}{10}

$- \frac{k}{15} = \frac{- 6 - 7}{10}$

Step 4.5.2

Subtract

7

$7$ from

- 6

$- 6$ .

- \frac{k}{15} = \frac{- 13}{10}

$- \frac{k}{15} = \frac{- 13}{10}$

- \frac{k}{15} = \frac{- 13}{10}

$- \frac{k}{15} = \frac{- 13}{10}$

Step 4.6

Move the negative in front of the fraction.

- \frac{k}{15} = - \frac{13}{10}

$- \frac{k}{15} = - \frac{13}{10}$

- \frac{k}{15} = - \frac{13}{10}

$- \frac{k}{15} = - \frac{13}{10}$

Step 5

Multiply both sides of the equation by

- 15

$- 15$ .

- 15 (- \frac{k}{15}) = - 15 (- \frac{13}{10})

$- 15 (- \frac{k}{15}) = - 15 (- \frac{13}{10})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify

- 15 (- \frac{k}{15})

$- 15 (- \frac{k}{15})$ .

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Step 6.1.1.1

Cancel the common factor of

15

$15$ .

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Step 6.1.1.1.1

Move the leading negative in

$- \frac{k}{15}$ into the numerator.

$- 15 \frac{- k}{15} = - 15 (- \frac{13}{10})$

Step 6.1.1.1.2

Factor

$15$ out of

$- 15$ .

$15 (- 1) \frac{- k}{15} = - 15 (- \frac{13}{10})$

Step 6.1.1.1.3

Cancel the common factor.

$15 \cdot - 1 \frac{- k}{15} = - 15 (- \frac{13}{10})$

Step 6.1.1.1.4

Rewrite the expression.

$- - k = - 15 (- \frac{13}{10})$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply

$- 1$ by

$- 1$ .

$1 k = - 15 (- \frac{13}{10})$

Step 6.1.1.2.2

Multiply

$k$ by

$1$ .

$k = - 15 (- \frac{13}{10})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify

$- 15 (- \frac{13}{10})$ .

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Step 6.2.1.1

Cancel the common factor of

$5$ .

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Step 6.2.1.1.1

Move the leading negative in

$- \frac{13}{10}$ into the numerator.

$k = - 15 (\frac{- 13}{10})$

Step 6.2.1.1.2

Factor

$5$ out of

$- 15$ .

$k = 5 (- 3) \frac{- 13}{10}$

Step 6.2.1.1.3

Factor

$5$ out of

$10$ .

$k = 5 \cdot - 3 \frac{- 13}{5 \cdot 2}$

Step 6.2.1.1.4

Cancel the common factor.

$k = 5 \cdot - 3 \frac{- 13}{5 \cdot 2}$

Step 6.2.1.1.5

Rewrite the expression.

$k = - 3 (\frac{- 13}{2})$

Step 6.2.1.2

Combine

$- 3$ and

$\frac{- 13}{2}$ .

$k = \frac{- 3 \cdot - 13}{2}$

Step 6.2.1.3

Multiply

$- 3$ by

$- 13$ .

$k = \frac{39}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$k = \frac{39}{2}$

Decimal Form:

$k = 19.5$

Mixed Number Form:

$k = 19 \frac{1}{2}$