Basic Math Examples

\frac{1}{3 y} = - 10

$\frac{1}{3 y} = - 10$

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, 1

$3 y, 1$

Step 1.2

The LCM of one and any expression is the expression.

3 y

$3 y$

3 y

$3 y$

Step 2

Multiply each term in

\frac{1}{3 y} = - 10

$\frac{1}{3 y} = - 10$ by

3 y

$3 y$ to eliminate the fractions.

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Step 2.1

Multiply each term in

\frac{1}{3 y} = - 10

$\frac{1}{3 y} = - 10$ by

3 y

$3 y$ .

\frac{1}{3 y} (3 y) = - 10 (3 y)

$\frac{1}{3 y} (3 y) = - 10 (3 y)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

3 \frac{1}{3 y} y = - 10 (3 y)

$3 \frac{1}{3 y} y = - 10 (3 y)$

Step 2.2.2

Cancel the common factor of

3

$3$ .

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Step 2.2.2.1

Factor

3

$3$ out of

3 y

$3 y$ .

3 \frac{1}{3 (y)} y = - 10 (3 y)

$3 \frac{1}{3 (y)} y = - 10 (3 y)$

Step 2.2.2.2

Cancel the common factor.

$3 \frac{1}{3 y} y = - 10 (3 y)$

Step 2.2.2.3

Rewrite the expression.

$\frac{1}{y} y = - 10 (3 y)$

Step 2.2.3

Cancel the common factor of

$y$ .

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Step 2.2.3.1

Cancel the common factor.

$\frac{1}{y} y = - 10 (3 y)$

Step 2.2.3.2

Rewrite the expression.

$1 = - 10 (3 y)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply

$3$ by

$- 10$ .

$1 = - 30 y$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as

$- 30 y = 1$ .

$- 30 y = 1$

Step 3.2

Divide each term in

$- 30 y = 1$ by

$- 30$ and simplify.

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Step 3.2.1

Divide each term in

$- 30 y = 1$ by

$- 30$ .

$\frac{- 30 y}{- 30} = \frac{1}{- 30}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of

$- 30$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 30 y}{- 30} = \frac{1}{- 30}$

Step 3.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{1}{- 30}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$y = - \frac{1}{30}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{1}{30}$

Decimal Form:

$y = - 0.0\overline{3}$