Basic Math Examples

$\frac{z - 0.35}{0.4 - 0.35} = \frac{0.4211 - 0.3794}{0.4284 - 0.3794}$

Step 1

Multiply both sides of the equation by $0.4 - 0.35$ .

$(0.4 - 0.35) \frac{z - 0.35}{0.4 - 0.35} = (0.4 - 0.35) \frac{0.4211 - 0.3794}{0.4284 - 0.3794}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(0.4 - 0.35) \frac{z - 0.35}{0.4 - 0.35}$ .

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Step 2.1.1.1

Simplify by subtracting numbers.

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Step 2.1.1.1.1

Subtract $0.35$ from $0.4$ .

$(0.4 - 0.35) \frac{z - 0.35}{0.05} = (0.4 - 0.35) \frac{0.4211 - 0.3794}{0.4284 - 0.3794}$

Step 2.1.1.1.2

Subtract $0.35$ from $0.4$ .

$0.05 \frac{z - 0.35}{0.05} = (0.4 - 0.35) \frac{0.4211 - 0.3794}{0.4284 - 0.3794}$

Step 2.1.1.2

Cancel the common factor of $0.05$ .

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Step 2.1.1.2.1

Cancel the common factor.

$0.05 \frac{z - 0.35}{0.05} = (0.4 - 0.35) \frac{0.4211 - 0.3794}{0.4284 - 0.3794}$

Step 2.1.1.2.2

Rewrite the expression.

$z - 0.35 = (0.4 - 0.35) \frac{0.4211 - 0.3794}{0.4284 - 0.3794}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(0.4 - 0.35) \frac{0.4211 - 0.3794}{0.4284 - 0.3794}$ .

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Step 2.2.1.1

Subtract $0.3794$ from $0.4211$ .

$z - 0.35 = (0.4 - 0.35) \frac{0.0417}{0.4284 - 0.3794}$

Step 2.2.1.2

Subtract $0.3794$ from $0.4284$ .

$z - 0.35 = (0.4 - 0.35) \frac{0.0417}{0.049}$

Step 2.2.1.3

Subtract $0.35$ from $0.4$ .

$z - 0.35 = 0.05 (\frac{0.0417}{0.049})$

Step 2.2.1.4

Divide $0.0417$ by $0.049$ .

$z - 0.35 = 0.05 \cdot 0.8510204$

Step 2.2.1.5

Multiply $0.05$ by $0.8510204$ .

$z - 0.35 = 0.04255102$

Step 3

Move all terms not containing $z$ to the right side of the equation.

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Step 3.1

Add $0.35$ to both sides of the equation.

$z = 0.04255102 + 0.35$

Step 3.2

Add $0.04255102$ and $0.35$ .

$z = 0.39255102$