Basic Math Examples

$1000 = 900 + \frac{\frac{y}{100} \cdot 65 - 1}{12} \cdot 400$

Step 1

Rewrite the equation as $900 + \frac{\frac{y}{100} \cdot 65 - 1}{12} \cdot 400 = 1000$ .

$900 + \frac{\frac{y}{100} \cdot 65 - 1}{12} \cdot 400 = 1000$

Step 2

Simplify $900 + \frac{\frac{y}{100} \cdot 65 - 1}{12} \cdot 400$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify the numerator.

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Step 2.1.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1.1

Factor $5$ out of $100$ .

$900 + \frac{\frac{y}{5 (20)} \cdot 65 - 1}{12} \cdot 400 = 1000$

Step 2.1.1.1.2

Factor $5$ out of $65$ .

$900 + \frac{\frac{y}{5 \cdot 20} \cdot (5 \cdot 13) - 1}{12} \cdot 400 = 1000$

Step 2.1.1.1.3

Cancel the common factor.

$900 + \frac{\frac{y}{5 \cdot 20} \cdot (5 \cdot 13) - 1}{12} \cdot 400 = 1000$

Step 2.1.1.1.4

Rewrite the expression.

$900 + \frac{\frac{y}{20} \cdot 13 - 1}{12} \cdot 400 = 1000$

Step 2.1.1.2

Combine $\frac{y}{20}$ and $13$ .

$900 + \frac{\frac{y \cdot 13}{20} - 1}{12} \cdot 400 = 1000$

Step 2.1.1.3

Move $13$ to the left of $y$ .

$900 + \frac{\frac{13 \cdot y}{20} - 1}{12} \cdot 400 = 1000$

Step 2.1.1.4

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$900 + \frac{\frac{13 y}{20} - 1 \cdot \frac{20}{20}}{12} \cdot 400 = 1000$

Step 2.1.1.5

Combine $- 1$ and $\frac{20}{20}$ .

$900 + \frac{\frac{13 y}{20} + \frac{- 1 \cdot 20}{20}}{12} \cdot 400 = 1000$

Step 2.1.1.6

Combine the numerators over the common denominator.

$900 + \frac{\frac{13 y - 1 \cdot 20}{20}}{12} \cdot 400 = 1000$

Step 2.1.1.7

Multiply $- 1$ by $20$ .

$900 + \frac{\frac{13 y - 20}{20}}{12} \cdot 400 = 1000$

Step 2.1.2

Cancel the common factor of $4$ .

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Step 2.1.2.1

Factor $4$ out of $12$ .

$900 + \frac{\frac{13 y - 20}{20}}{4 (3)} \cdot 400 = 1000$

Step 2.1.2.2

Factor $4$ out of $400$ .

$900 + \frac{\frac{13 y - 20}{20}}{4 \cdot 3} \cdot (4 \cdot 100) = 1000$

Step 2.1.2.3

Cancel the common factor.

$900 + \frac{\frac{13 y - 20}{20}}{4 \cdot 3} \cdot (4 \cdot 100) = 1000$

Step 2.1.2.4

Rewrite the expression.

$900 + \frac{\frac{13 y - 20}{20}}{3} \cdot 100 = 1000$

Step 2.1.3

Combine $\frac{\frac{13 y - 20}{20}}{3}$ and $100$ .

$900 + \frac{\frac{13 y - 20}{20} \cdot 100}{3} = 1000$

Step 2.1.4

Combine $\frac{13 y - 20}{20}$ and $100$ .

$900 + \frac{\frac{(13 y - 20) \cdot 100}{20}}{3} = 1000$

Step 2.1.5

Cancel the common factor of $100$ and $20$ .

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Step 2.1.5.1

Factor $20$ out of $(13 y - 20) \cdot 100$ .

$900 + \frac{\frac{20 ((13 y - 20) \cdot 5)}{20}}{3} = 1000$

Step 2.1.5.2

Cancel the common factors.

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Step 2.1.5.2.1

Factor $20$ out of $20$ .

$900 + \frac{\frac{20 ((13 y - 20) \cdot 5)}{20 (1)}}{3} = 1000$

Step 2.1.5.2.2

Cancel the common factor.

$900 + \frac{\frac{20 ((13 y - 20) \cdot 5)}{20 \cdot 1}}{3} = 1000$

Step 2.1.5.2.3

Rewrite the expression.

$900 + \frac{\frac{(13 y - 20) \cdot 5}{1}}{3} = 1000$

Step 2.1.5.2.4

Divide $(13 y - 20) \cdot 5$ by $1$ .

$900 + \frac{(13 y - 20) \cdot 5}{3} = 1000$

Step 2.1.6

Move $5$ to the left of $13 y - 20$ .

$900 + \frac{5 (13 y - 20)}{3} = 1000$

Step 2.2

To write $900$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$900 \cdot \frac{3}{3} + \frac{5 (13 y - 20)}{3} = 1000$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine $900$ and $\frac{3}{3}$ .

$\frac{900 \cdot 3}{3} + \frac{5 (13 y - 20)}{3} = 1000$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{900 \cdot 3 + 5 (13 y - 20)}{3} = 1000$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Factor $5$ out of $900 \cdot 3 + 5 (13 y - 20)$ .

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Step 2.4.1.1

Factor $5$ out of $900 \cdot 3$ .

$\frac{5 (180 \cdot 3) + 5 (13 y - 20)}{3} = 1000$

Step 2.4.1.2

Factor $5$ out of $5 (180 \cdot 3) + 5 (13 y - 20)$ .

$\frac{5 (180 \cdot 3 + 13 y - 20)}{3} = 1000$

Step 2.4.2

Multiply $180$ by $3$ .

$\frac{5 (540 + 13 y - 20)}{3} = 1000$

Step 2.4.3

Subtract $20$ from $540$ .

$\frac{5 (13 y + 520)}{3} = 1000$

Step 2.4.4

Factor $13$ out of $13 y + 520$ .

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Step 2.4.4.1

Factor $13$ out of $13 y$ .

$\frac{5 (13 (y) + 520)}{3} = 1000$

Step 2.4.4.2

Factor $13$ out of $520$ .

$\frac{5 (13 y + 13 \cdot 40)}{3} = 1000$

Step 2.4.4.3

Factor $13$ out of $13 y + 13 \cdot 40$ .

$\frac{5 (13 (y + 40))}{3} = 1000$

$\frac{5 \cdot 13 (y + 40)}{3} = 1000$

Step 2.4.5

Multiply $5$ by $13$ .

$\frac{65 (y + 40)}{3} = 1000$

Step 3

Multiply both sides of the equation by $\frac{3}{65}$ .

$\frac{3}{65} \cdot \frac{65 (y + 40)}{3} = \frac{3}{65} \cdot 1000$

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 $\frac{3}{65} \cdot \frac{65 (y + 40)}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{65} \cdot \frac{65 (y + 40)}{3} = \frac{3}{65} \cdot 1000$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{65} (65 (y + 40)) = \frac{3}{65} \cdot 1000$

Step 4.1.1.2

Cancel the common factor of $65$ .

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Step 4.1.1.2.1

Cancel the common factor.

$\frac{1}{65} (65 (y + 40)) = \frac{3}{65} \cdot 1000$

Step 4.1.1.2.2

Rewrite the expression.

$y + 40 = \frac{3}{65} \cdot 1000$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{65} \cdot 1000$ .

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Step 4.2.1.1

Cancel the common factor of $5$ .

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Step 4.2.1.1.1

Factor $5$ out of $65$ .

$y + 40 = \frac{3}{5 (13)} \cdot 1000$

Step 4.2.1.1.2

Factor $5$ out of $1000$ .

$y + 40 = \frac{3}{5 \cdot 13} \cdot (5 \cdot 200)$

Step 4.2.1.1.3

Cancel the common factor.

$y + 40 = \frac{3}{5 \cdot 13} \cdot (5 \cdot 200)$

Step 4.2.1.1.4

Rewrite the expression.

$y + 40 = \frac{3}{13} \cdot 200$

Step 4.2.1.2

Combine $\frac{3}{13}$ and $200$ .

$y + 40 = \frac{3 \cdot 200}{13}$

Step 4.2.1.3

Multiply $3$ by $200$ .

$y + 40 = \frac{600}{13}$

Step 5

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

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Step 5.1

Subtract $40$ from both sides of the equation.

$y = \frac{600}{13} - 40$

Step 5.2

To write $- 40$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$y = \frac{600}{13} - 40 \cdot \frac{13}{13}$

Step 5.3

Combine $- 40$ and $\frac{13}{13}$ .

$y = \frac{600}{13} + \frac{- 40 \cdot 13}{13}$

Step 5.4

Combine the numerators over the common denominator.

$y = \frac{600 - 40 \cdot 13}{13}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $- 40$ by $13$ .

$y = \frac{600 - 520}{13}$

Step 5.5.2

Subtract $520$ from $600$ .

$y = \frac{80}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{80}{13}$

Decimal Form:

$y = 6.\overline{153846}$

Mixed Number Form:

$y = 6 \frac{2}{13}$