Basic Math Examples

$\frac{2}{3 (y + 57)} = 178$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

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

$3 (y + 57), 1$

Step 1.2

The LCM of one and any expression is the expression.

$3 (y + 57)$

Step 2

Multiply each term in $\frac{2}{3 (y + 57)} = 178$ by $3 (y + 57)$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2}{3 (y + 57)} = 178$ by $3 (y + 57)$ .

$\frac{2}{3 (y + 57)} (3 (y + 57)) = 178 (3 (y + 57))$

Step 2.2

Simplify the left side.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$3 \frac{2}{3 (y + 57)} (y + 57) = 178 (3 (y + 57))$

Step 2.2.2

Cancel the common factor of $3$ .

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Step 2.2.2.1

Cancel the common factor.

$3 \frac{2}{3 (y + 57)} (y + 57) = 178 (3 (y + 57))$

Step 2.2.2.2

Rewrite the expression.

$\frac{2}{y + 57} (y + 57) = 178 (3 (y + 57))$

Step 2.2.3

Cancel the common factor of $y + 57$ .

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Step 2.2.3.1

Cancel the common factor.

$\frac{2}{y + 57} (y + 57) = 178 (3 (y + 57))$

Step 2.2.3.2

Rewrite the expression.

$2 = 178 (3 (y + 57))$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$2 = 178 (3 y + 3 \cdot 57)$

Step 2.3.2

Multiply $3$ by $57$ .

$2 = 178 (3 y + 171)$

Step 2.3.3

Apply the distributive property.

$2 = 178 (3 y) + 178 \cdot 171$

Step 2.3.4

Multiply.

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Step 2.3.4.1

Multiply $3$ by $178$ .

$2 = 534 y + 178 \cdot 171$

Step 2.3.4.2

Multiply $178$ by $171$ .

$2 = 534 y + 30438$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $534 y + 30438 = 2$ .

$534 y + 30438 = 2$

Step 3.2

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

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Step 3.2.1

Subtract $30438$ from both sides of the equation.

$534 y = 2 - 30438$

Step 3.2.2

Subtract $30438$ from $2$ .

$534 y = - 30436$

Step 3.3

Divide each term in $534 y = - 30436$ by $534$ and simplify.

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Step 3.3.1

Divide each term in $534 y = - 30436$ by $534$ .

$\frac{534 y}{534} = \frac{- 30436}{534}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $534$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{534 y}{534} = \frac{- 30436}{534}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 30436}{534}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Cancel the common factor of $- 30436$ and $534$ .

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Step 3.3.3.1.1

Factor $2$ out of $- 30436$ .

$y = \frac{2 (- 15218)}{534}$

Step 3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.1.2.1

Factor $2$ out of $534$ .

$y = \frac{2 \cdot - 15218}{2 \cdot 267}$

Step 3.3.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot - 15218}{2 \cdot 267}$

Step 3.3.3.1.2.3

Rewrite the expression.

$y = \frac{- 15218}{267}$

Step 3.3.3.2

Move the negative in front of the fraction.

$y = - \frac{15218}{267}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{15218}{267}$

Decimal Form:

$y = - 56.99625468 \dots$

Mixed Number Form:

$y = - 56 \frac{266}{267}$