Basic Math Examples

$8 \cdot k - \frac{8 \cdot k}{3} - 0.8 \cdot k - \frac{0.001 \cdot k}{3} = 1$

Step 1

Simplify $8 \cdot k - \frac{8 \cdot k}{3} - 0.8 \cdot k - \frac{0.001 \cdot k}{3}$ .

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Step 1.1

Combine the numerators over the common denominator.

$8 \cdot k - 0.8 \cdot k + \frac{- 8 \cdot k - 0.001 \cdot k}{3} = 1$

Step 1.2

Multiply $- 0.001$ by $k$ .

$8 \cdot k - 0.8 \cdot k + \frac{- 8 k - 0.001 k}{3} = 1$

Step 1.3

Subtract $0.001 k$ from $- 8 k$ .

$8 \cdot k - 0.8 \cdot k + \frac{- 8.001 k}{3} = 1$

Step 1.4

Find the common denominator.

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Step 1.4.1

Write $8 \cdot k$ as a fraction with denominator $1$ .

$\frac{8 \cdot k}{1} - 0.8 \cdot k + \frac{- 8.001 k}{3} = 1$

Step 1.4.2

Multiply $\frac{8 \cdot k}{1}$ by $\frac{3}{3}$ .

$\frac{8 \cdot k}{1} \cdot \frac{3}{3} - 0.8 \cdot k + \frac{- 8.001 k}{3} = 1$

Step 1.4.3

Multiply $\frac{8 \cdot k}{1}$ by $\frac{3}{3}$ .

$\frac{8 \cdot k \cdot 3}{3} - 0.8 \cdot k + \frac{- 8.001 k}{3} = 1$

Step 1.4.4

Write $- 0.8 \cdot k$ as a fraction with denominator $1$ .

$\frac{8 \cdot k \cdot 3}{3} + \frac{- 0.8 \cdot k}{1} + \frac{- 8.001 k}{3} = 1$

Step 1.4.5

Multiply $\frac{- 0.8 \cdot k}{1}$ by $\frac{3}{3}$ .

$\frac{8 \cdot k \cdot 3}{3} + \frac{- 0.8 \cdot k}{1} \cdot \frac{3}{3} + \frac{- 8.001 k}{3} = 1$

Step 1.4.6

Multiply $\frac{- 0.8 \cdot k}{1}$ by $\frac{3}{3}$ .

$\frac{8 \cdot k \cdot 3}{3} + \frac{- 0.8 \cdot k \cdot 3}{3} + \frac{- 8.001 k}{3} = 1$

Step 1.5

Combine the numerators over the common denominator.

$\frac{8 \cdot k \cdot 3 - 0.8 \cdot k \cdot 3 - 8.001 k}{3} = 1$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $3$ by $8$ .

$\frac{24 k - 0.8 \cdot k \cdot 3 - 8.001 k}{3} = 1$

Step 1.6.2

Multiply $3$ by $- 0.8$ .

$\frac{24 k - 2.4 k - 8.001 k}{3} = 1$

Step 1.7

Simplify terms.

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Step 1.7.1

Subtract $2.4 k$ from $24 k$ .

$\frac{21.6 k - 8.001 k}{3} = 1$

Step 1.7.2

Subtract $8.001 k$ from $21.6 k$ .

$\frac{13.599 k}{3} = 1$

Step 1.7.3

Factor $13.599$ out of $13.599 k$ .

$\frac{13.599 (k)}{3} = 1$

Step 1.7.4

Factor $3$ out of $3$ .

$\frac{13.599 (k)}{3 (1)} = 1$

Step 1.8

Separate fractions.

$\frac{13.599}{3} \cdot \frac{k}{1} = 1$

Step 1.9

Divide $13.599$ by $3$ .

$4.533 \frac{k}{1} = 1$

Step 1.10

Divide $k$ by $1$ .

$4.533 k = 1$

Step 2

Divide each term in $4.533 k = 1$ by $4.533$ and simplify.

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Step 2.1

Divide each term in $4.533 k = 1$ by $4.533$ .

$\frac{4.533 k}{4.533} = \frac{1}{4.533}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4.533$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4.533 k}{4.533} = \frac{1}{4.533}$

Step 2.2.1.2

Divide $k$ by $1$ .

$k = \frac{1}{4.533}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $1$ by $4.533$ .

$k = 0.22060445$