Basic Math Examples

$y \cdot \frac{9}{12} \cdot \frac{12}{100} = 3815000 - y$

Step 1

Simplify $y \cdot \frac{9}{12} \cdot \frac{12}{100}$ .

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Step 1.1

Rewrite.

$0 + 0 + y \cdot \frac{9}{12} \cdot \frac{12}{100} = 3815000 - y$

Step 1.2

Simplify by adding zeros.

$y \cdot \frac{9}{12} \cdot \frac{12}{100} = 3815000 - y$

Step 1.3

Cancel the common factor of $9$ and $12$ .

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Step 1.3.1

Factor $3$ out of $9$ .

$y \cdot \frac{3 (3)}{12} \cdot \frac{12}{100} = 3815000 - y$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $3$ out of $12$ .

$y \cdot \frac{3 \cdot 3}{3 \cdot 4} \cdot \frac{12}{100} = 3815000 - y$

Step 1.3.2.2

Cancel the common factor.

$y \cdot \frac{3 \cdot 3}{3 \cdot 4} \cdot \frac{12}{100} = 3815000 - y$

Step 1.3.2.3

Rewrite the expression.

$y \cdot \frac{3}{4} \cdot \frac{12}{100} = 3815000 - y$

Step 1.4

Combine $y$ and $\frac{3}{4}$ .

$\frac{y \cdot 3}{4} \cdot \frac{12}{100} = 3815000 - y$

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Factor $4$ out of $12$ .

$\frac{y \cdot 3}{4} \cdot \frac{4 (3)}{100} = 3815000 - y$

Step 1.5.2

Cancel the common factor.

$\frac{y \cdot 3}{4} \cdot \frac{4 \cdot 3}{100} = 3815000 - y$

Step 1.5.3

Rewrite the expression.

$y \cdot 3 \cdot \frac{3}{100} = 3815000 - y$

Step 1.6

Combine $y$ and $\frac{3}{100}$ .

$\frac{3 (y \cdot 3)}{100} = 3815000 - y$

Step 1.7

Multiply $3$ by $3$ .

$\frac{9 y}{100} = 3815000 - y$

Step 2

Move all terms containing $y$ to the left side of the equation.

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Step 2.1

Add $y$ to both sides of the equation.

$\frac{9 y}{100} + y = 3815000$

Step 2.2

To write $y$ as a fraction with a common denominator, multiply by $\frac{100}{100}$ .

$\frac{9 y}{100} + y \cdot \frac{100}{100} = 3815000$

Step 2.3

Combine $y$ and $\frac{100}{100}$ .

$\frac{9 y}{100} + \frac{y \cdot 100}{100} = 3815000$

Step 2.4

Combine the numerators over the common denominator.

$\frac{9 y + y \cdot 100}{100} = 3815000$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Move $100$ to the left of $y$ .

$\frac{9 y + 100 \cdot y}{100} = 3815000$

Step 2.5.2

Add $9 y$ and $100 y$ .

$\frac{109 y}{100} = 3815000$

Step 3

Multiply both sides of the equation by $\frac{100}{109}$ .

$\frac{100}{109} \cdot \frac{109 y}{100} = \frac{100}{109} \cdot 3815000$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{100}{109} \cdot \frac{109 y}{100}$ .

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Step 4.1.1.1

Cancel the common factor of $100$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{100}{109} \cdot \frac{109 y}{100} = \frac{100}{109} \cdot 3815000$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{109} (109 y) = \frac{100}{109} \cdot 3815000$

Step 4.1.1.2

Cancel the common factor of $109$ .

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Step 4.1.1.2.1

Factor $109$ out of $109 y$ .

$\frac{1}{109} (109 (y)) = \frac{100}{109} \cdot 3815000$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{109} (109 y) = \frac{100}{109} \cdot 3815000$

Step 4.1.1.2.3

Rewrite the expression.

$y = \frac{100}{109} \cdot 3815000$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{100}{109} \cdot 3815000$ .

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Step 4.2.1.1

Cancel the common factor of $109$ .

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Step 4.2.1.1.1

Factor $109$ out of $3815000$ .

$y = \frac{100}{109} \cdot (109 (35000))$

Step 4.2.1.1.2

Cancel the common factor.

$y = \frac{100}{109} \cdot (109 \cdot 35000)$

Step 4.2.1.1.3

Rewrite the expression.

$y = 100 \cdot 35000$

Step 4.2.1.2

Multiply $100$ by $35000$ .

$y = 3500000$