Algebra Examples

$\frac{740}{760} \cdot 8.9 = \frac{18.1}{k} \cdot 0.0821 \cdot 295$

Step 1

Rewrite the equation as $\frac{18.1}{k} \cdot 0.0821 \cdot 295 = \frac{740}{760} \cdot 8.9$ .

$\frac{18.1}{k} \cdot 0.0821 \cdot 295 = \frac{740}{760} \cdot 8.9$

Step 2

Simplify $\frac{18.1}{k} \cdot 0.0821 \cdot 295$ .

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Step 2.1

Multiply $\frac{18.1}{k} \cdot 0.0821$ .

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Step 2.1.1

Combine $\frac{18.1}{k}$ and $0.0821$ .

$\frac{18.1 \cdot 0.0821}{k} \cdot 295 = \frac{740}{760} \cdot 8.9$

Step 2.1.2

Multiply $18.1$ by $0.0821$ .

$\frac{1.48601}{k} \cdot 295 = \frac{740}{760} \cdot 8.9$

Step 2.2

Multiply $\frac{1.48601}{k} \cdot 295$ .

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Step 2.2.1

Combine $\frac{1.48601}{k}$ and $295$ .

$\frac{1.48601 \cdot 295}{k} = \frac{740}{760} \cdot 8.9$

Step 2.2.2

Multiply $1.48601$ by $295$ .

$\frac{438.37295}{k} = \frac{740}{760} \cdot 8.9$

Step 3

Simplify $\frac{740}{760} \cdot 8.9$ .

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Step 3.1

Cancel the common factor of $740$ and $760$ .

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Step 3.1.1

Factor $20$ out of $740$ .

$\frac{438.37295}{k} = \frac{20 (37)}{760} \cdot 8.9$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $20$ out of $760$ .

$\frac{438.37295}{k} = \frac{20 \cdot 37}{20 \cdot 38} \cdot 8.9$

Step 3.1.2.2

Cancel the common factor.

$\frac{438.37295}{k} = \frac{20 \cdot 37}{20 \cdot 38} \cdot 8.9$

Step 3.1.2.3

Rewrite the expression.

$\frac{438.37295}{k} = \frac{37}{38} \cdot 8.9$

Step 3.2

Multiply $\frac{37}{38} \cdot 8.9$ .

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Step 3.2.1

Combine $\frac{37}{38}$ and $8.9$ .

$\frac{438.37295}{k} = \frac{37 \cdot 8.9}{38}$

Step 3.2.2

Multiply $37$ by $8.9$ .

$\frac{438.37295}{k} = \frac{329.3}{38}$

Step 3.3

Divide $329.3$ by $38$ .

$\frac{438.37295}{k} = 8.66578947$

Step 4

Find the LCD of the terms in the equation.

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Step 4.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$k, 1$

Step 4.2

The LCM of one and any expression is the expression.

$k$

Step 5

Multiply each term in $\frac{438.37295}{k} = 8.66578947$ by $k$ to eliminate the fractions.

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Step 5.1

Multiply each term in $\frac{438.37295}{k} = 8.66578947$ by $k$ .

$\frac{438.37295}{k} k = 8.66578947 k$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $k$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{438.37295}{k} k = 8.66578947 k$

Step 5.2.1.2

Rewrite the expression.

$438.37295 = 8.66578947 k$

Step 6

Solve the equation.

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Step 6.1

Rewrite the equation as $8.66578947 k = 438.37295$ .

$8.66578947 k = 438.37295$

Step 6.2

Divide each term in $8.66578947 k = 438.37295$ by $8.66578947$ and simplify.

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Step 6.2.1

Divide each term in $8.66578947 k = 438.37295$ by $8.66578947$ .

$\frac{8.66578947 k}{8.66578947} = \frac{438.37295}{8.66578947}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $8.66578947$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{8.66578947 k}{8.66578947} = \frac{438.37295}{8.66578947}$

Step 6.2.2.1.2

Divide $k$ by $1$ .

$k = \frac{438.37295}{8.66578947}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $438.37295$ by $8.66578947$ .

$k = 50.58661433$