Basic Math Examples

$\frac{8}{1 \frac{3}{5}} = \frac{30}{z}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{8}{1 \frac{3}{5}}$ .

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Step 1.1.1

Convert $1 \frac{3}{5}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{8}{1 + \frac{3}{5}} = \frac{30}{z}$

Step 1.1.1.2

Add $1$ and $\frac{3}{5}$ .

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{8}{\frac{5}{5} + \frac{3}{5}} = \frac{30}{z}$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{8}{\frac{5 + 3}{5}} = \frac{30}{z}$

Step 1.1.1.2.3

Add $5$ and $3$ .

$\frac{8}{\frac{8}{5}} = \frac{30}{z}$

Step 1.1.2

Multiply the numerator by the reciprocal of the denominator.

$8 (\frac{5}{8}) = \frac{30}{z}$

Step 1.1.3

Cancel the common factor of $8$ .

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Step 1.1.3.1

Cancel the common factor.

$8 (\frac{5}{8}) = \frac{30}{z}$

Step 1.1.3.2

Rewrite the expression.

$5 = \frac{30}{z}$

Step 2

Rewrite the equation as $\frac{30}{z} = 5$ .

$\frac{30}{z} = 5$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$z, 1$

Step 3.2

The LCM of one and any expression is the expression.

$z$

Step 4

Multiply each term in $\frac{30}{z} = 5$ by $z$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{30}{z} = 5$ by $z$ .

$\frac{30}{z} z = 5 z$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $z$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{30}{z} z = 5 z$

Step 4.2.1.2

Rewrite the expression.

$30 = 5 z$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $5 z = 30$ .

$5 z = 30$

Step 5.2

Divide each term in $5 z = 30$ by $5$ and simplify.

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Step 5.2.1

Divide each term in $5 z = 30$ by $5$ .

$\frac{5 z}{5} = \frac{30}{5}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $5$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{5 z}{5} = \frac{30}{5}$

Step 5.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{30}{5}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $30$ by $5$ .

$z = 6$