Basic Math Examples

$1 \frac{2}{3} \cdot z = \frac{5}{8}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $1 \frac{2}{3} \cdot z$ .

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Step 1.1.1

Convert $1 \frac{2}{3}$ 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.

$(1 + \frac{2}{3}) \cdot z = \frac{5}{8}$

Step 1.1.1.2

Add $1$ and $\frac{2}{3}$ .

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Step 1.1.1.2.1

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

$(\frac{3}{3} + \frac{2}{3}) \cdot z = \frac{5}{8}$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{3 + 2}{3} \cdot z = \frac{5}{8}$

Step 1.1.1.2.3

Add $3$ and $2$ .

$\frac{5}{3} \cdot z = \frac{5}{8}$

Step 1.1.2

Combine $\frac{5}{3}$ and $z$ .

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

Step 2

Multiply both sides of the equation by $\frac{3}{5}$ .

$\frac{3}{5} \cdot \frac{5 z}{3} = \frac{3}{5} \cdot \frac{5}{8}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{3}{5} \cdot \frac{5 z}{3}$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{3}{5} \cdot \frac{5 z}{3} = \frac{3}{5} \cdot \frac{5}{8}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 z) = \frac{3}{5} \cdot \frac{5}{8}$

Step 3.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.2.1

Factor $5$ out of $5 z$ .

$\frac{1}{5} (5 (z)) = \frac{3}{5} \cdot \frac{5}{8}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 z) = \frac{3}{5} \cdot \frac{5}{8}$

Step 3.1.1.2.3

Rewrite the expression.

$z = \frac{3}{5} \cdot \frac{5}{8}$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

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Step 3.2.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1

Cancel the common factor.

$z = \frac{3}{5} \cdot \frac{5}{8}$

Step 3.2.1.1.2

Rewrite the expression.

$z = 3 (\frac{1}{8})$

Step 3.2.1.2

Combine $3$ and $\frac{1}{8}$ .

$z = \frac{3}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{3}{8}$

Decimal Form:

$z = 0.375$