Basic Math Examples

$\frac{y - 1}{3} + \frac{y}{90} - \frac{1 - y}{270} = \frac{1}{5}$

Step 1

Simplify $\frac{y - 1}{3} + \frac{y}{90} - \frac{1 - y}{270}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{y - 1}{3}$ by $\frac{90}{90}$ .

$\frac{y - 1}{3} \cdot \frac{90}{90} + \frac{y}{90} - \frac{1 - y}{270} = \frac{1}{5}$

Step 1.1.2

Multiply $\frac{y - 1}{3}$ by $\frac{90}{90}$ .

$\frac{(y - 1) \cdot 90}{3 \cdot 90} + \frac{y}{90} - \frac{1 - y}{270} = \frac{1}{5}$

Step 1.1.3

Multiply $\frac{y}{90}$ by $\frac{3}{3}$ .

$\frac{(y - 1) \cdot 90}{3 \cdot 90} + \frac{y}{90} \cdot \frac{3}{3} - \frac{1 - y}{270} = \frac{1}{5}$

Step 1.1.4

Multiply $\frac{y}{90}$ by $\frac{3}{3}$ .

$\frac{(y - 1) \cdot 90}{3 \cdot 90} + \frac{y \cdot 3}{90 \cdot 3} - \frac{1 - y}{270} = \frac{1}{5}$

Step 1.1.5

Multiply $3$ by $90$ .

$\frac{(y - 1) \cdot 90}{270} + \frac{y \cdot 3}{90 \cdot 3} - \frac{1 - y}{270} = \frac{1}{5}$

Step 1.1.6

Reorder the factors of $90 \cdot 3$ .

$\frac{(y - 1) \cdot 90}{270} + \frac{y \cdot 3}{3 \cdot 90} - \frac{1 - y}{270} = \frac{1}{5}$

Step 1.1.7

Multiply $3$ by $90$ .

$\frac{(y - 1) \cdot 90}{270} + \frac{y \cdot 3}{270} - \frac{1 - y}{270} = \frac{1}{5}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{(y - 1) \cdot 90 + y \cdot 3 - (1 - y)}{270} = \frac{1}{5}$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{y \cdot 90 - 1 \cdot 90 + y \cdot 3 - (1 - y)}{270} = \frac{1}{5}$

Step 1.3.2

Move $90$ to the left of $y$ .

$\frac{90 \cdot y - 1 \cdot 90 + y \cdot 3 - (1 - y)}{270} = \frac{1}{5}$

Step 1.3.3

Multiply $- 1$ by $90$ .

$\frac{90 \cdot y - 90 + y \cdot 3 - (1 - y)}{270} = \frac{1}{5}$

Step 1.3.4

Move $3$ to the left of $y$ .

$\frac{90 y - 90 + 3 \cdot y - (1 - y)}{270} = \frac{1}{5}$

Step 1.3.5

Apply the distributive property.

$\frac{90 y - 90 + 3 y - 1 \cdot 1 - - y}{270} = \frac{1}{5}$

Step 1.3.6

Multiply $- 1$ by $1$ .

$\frac{90 y - 90 + 3 y - 1 - - y}{270} = \frac{1}{5}$

Step 1.3.7

Multiply $- - y$ .

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Step 1.3.7.1

Multiply $- 1$ by $- 1$ .

$\frac{90 y - 90 + 3 y - 1 + 1 y}{270} = \frac{1}{5}$

Step 1.3.7.2

Multiply $y$ by $1$ .

$\frac{90 y - 90 + 3 y - 1 + y}{270} = \frac{1}{5}$

Step 1.4

Simplify by adding terms.

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Step 1.4.1

Add $90 y$ and $3 y$ .

$\frac{93 y - 90 - 1 + y}{270} = \frac{1}{5}$

Step 1.4.2

Add $93 y$ and $y$ .

$\frac{94 y - 90 - 1}{270} = \frac{1}{5}$

Step 1.4.3

Subtract $1$ from $- 90$ .

$\frac{94 y - 91}{270} = \frac{1}{5}$

Step 2

Multiply both sides by $270$ .

$\frac{94 y - 91}{270} \cdot 270 = \frac{1}{5} \cdot 270$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $270$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{94 y - 91}{270} \cdot 270 = \frac{1}{5} \cdot 270$

Step 3.1.1.2

Rewrite the expression.

$94 y - 91 = \frac{1}{5} \cdot 270$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Factor $5$ out of $270$ .

$94 y - 91 = \frac{1}{5} \cdot (5 (54))$

Step 3.2.1.2

Cancel the common factor.

$94 y - 91 = \frac{1}{5} \cdot (5 \cdot 54)$

Step 3.2.1.3

Rewrite the expression.

$94 y - 91 = 54$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Add $91$ to both sides of the equation.

$94 y = 54 + 91$

Step 4.1.2

Add $54$ and $91$ .

$94 y = 145$

Step 4.2

Divide each term in $94 y = 145$ by $94$ and simplify.

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Step 4.2.1

Divide each term in $94 y = 145$ by $94$ .

$\frac{94 y}{94} = \frac{145}{94}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $94$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{94 y}{94} = \frac{145}{94}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{145}{94}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{145}{94}$

Decimal Form:

$y = 1.54255319 \dots$

Mixed Number Form:

$y = 1 \frac{51}{94}$