Algebra Examples

$\frac{48}{y} = \frac{6}{\frac{1}{8}}$

Step 1

Factor each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{48}{y} = 6 \cdot 8$

Step 1.2

Multiply $6$ by $8$ .

$\frac{48}{y} = 48$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$y, 1$

Step 2.2

The LCM of one and any expression is the expression.

$y$

Step 3

Multiply each term in $\frac{48}{y} = 48$ by $y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{48}{y} = 48$ by $y$ .

$\frac{48}{y} y = 48 y$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{48}{y} y = 48 y$

Step 3.2.1.2

Rewrite the expression.

$48 = 48 y$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $48 y = 48$ .

$48 y = 48$

Step 4.2

Divide each term in $48 y = 48$ by $48$ and simplify.

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Step 4.2.1

Divide each term in $48 y = 48$ by $48$ .

$\frac{48 y}{48} = \frac{48}{48}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $48$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{48 y}{48} = \frac{48}{48}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{48}{48}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $48$ by $48$ .

$y = 1$