Basic Math Examples

$\frac{3}{4} - \frac{1}{3} z = \frac{1}{4}$

Step 1

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

$\frac{3}{4} - \frac{z}{3} = \frac{1}{4}$

Step 2

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

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Step 2.1

Subtract $\frac{3}{4}$ from both sides of the equation.

$- \frac{z}{3} = \frac{1}{4} - \frac{3}{4}$

Step 2.2

Combine the numerators over the common denominator.

$- \frac{z}{3} = \frac{1 - 3}{4}$

Step 2.3

Subtract $3$ from $1$ .

$- \frac{z}{3} = \frac{- 2}{4}$

Step 2.4

Cancel the common factor of $- 2$ and $4$ .

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Step 2.4.1

Factor $2$ out of $- 2$ .

$- \frac{z}{3} = \frac{2 (- 1)}{4}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

$- \frac{z}{3} = \frac{2 \cdot - 1}{2 \cdot 2}$

Step 2.4.2.2

Cancel the common factor.

$- \frac{z}{3} = \frac{2 \cdot - 1}{2 \cdot 2}$

Step 2.4.2.3

Rewrite the expression.

$- \frac{z}{3} = \frac{- 1}{2}$

Step 2.5

Move the negative in front of the fraction.

$- \frac{z}{3} = - \frac{1}{2}$

Step 3

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{z}{3}) = - 3 (- \frac{1}{2})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 3 (- \frac{z}{3})$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{z}{3}$ into the numerator.

$- 3 \frac{- z}{3} = - 3 (- \frac{1}{2})$

Step 4.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- z}{3} = - 3 (- \frac{1}{2})$

Step 4.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- z}{3} = - 3 (- \frac{1}{2})$

Step 4.1.1.1.4

Rewrite the expression.

$- - z = - 3 (- \frac{1}{2})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 z = - 3 (- \frac{1}{2})$

Step 4.1.1.2.2

Multiply $z$ by $1$ .

$z = - 3 (- \frac{1}{2})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 3 (- \frac{1}{2})$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 3$ .

$z = 3 (\frac{1}{2})$

Step 4.2.1.2

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

$z = \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{3}{2}$

Decimal Form:

$z = 1.5$

Mixed Number Form:

$z = 1 \frac{1}{2}$