Basic Math Examples

$6 z - 1 \frac{3}{4} = - 6 \frac{1}{4}$

Step 1

Simplify the left side.

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Step 1.1

Convert $1 \frac{3}{4}$ to an improper fraction.

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Step 1.1.1

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

$6 z - (1 + \frac{3}{4}) = - 6 \frac{1}{4}$

Step 1.1.2

Add $1$ and $\frac{3}{4}$ .

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Step 1.1.2.1

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

$6 z - (\frac{4}{4} + \frac{3}{4}) = - 6 \frac{1}{4}$

Step 1.1.2.2

Combine the numerators over the common denominator.

$6 z - \frac{4 + 3}{4} = - 6 \frac{1}{4}$

Step 1.1.2.3

Add $4$ and $3$ .

$6 z - \frac{7}{4} = - 6 \frac{1}{4}$

Step 2

Simplify the right side.

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Step 2.1

Convert $6 \frac{1}{4}$ to an improper fraction.

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Step 2.1.1

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

$6 z - \frac{7}{4} = - (6 + \frac{1}{4})$

Step 2.1.2

Add $6$ and $\frac{1}{4}$ .

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Step 2.1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$6 z - \frac{7}{4} = - (6 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.1.2.2

Combine $6$ and $\frac{4}{4}$ .

$6 z - \frac{7}{4} = - (\frac{6 \cdot 4}{4} + \frac{1}{4})$

Step 2.1.2.3

Combine the numerators over the common denominator.

$6 z - \frac{7}{4} = - \frac{6 \cdot 4 + 1}{4}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $6$ by $4$ .

$6 z - \frac{7}{4} = - \frac{24 + 1}{4}$

Step 2.1.2.4.2

Add $24$ and $1$ .

$6 z - \frac{7}{4} = - \frac{25}{4}$

Step 3

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

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Step 3.1

Add $\frac{7}{4}$ to both sides of the equation.

$6 z = - \frac{25}{4} + \frac{7}{4}$

Step 3.2

Combine the numerators over the common denominator.

$6 z = \frac{- 25 + 7}{4}$

Step 3.3

Add $- 25$ and $7$ .

$6 z = \frac{- 18}{4}$

Step 3.4

Cancel the common factor of $- 18$ and $4$ .

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Step 3.4.1

Factor $2$ out of $- 18$ .

$6 z = \frac{2 (- 9)}{4}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $4$ .

$6 z = \frac{2 \cdot - 9}{2 \cdot 2}$

Step 3.4.2.2

Cancel the common factor.

$6 z = \frac{2 \cdot - 9}{2 \cdot 2}$

Step 3.4.2.3

Rewrite the expression.

$6 z = \frac{- 9}{2}$

Step 3.5

Move the negative in front of the fraction.

$6 z = - \frac{9}{2}$

Step 4

Divide each term in $6 z = - \frac{9}{2}$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 z = - \frac{9}{2}$ by $6$ .

$\frac{6 z}{6} = \frac{- \frac{9}{2}}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 z}{6} = \frac{- \frac{9}{2}}{6}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z = \frac{- \frac{9}{2}}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$z = - \frac{9}{2} \cdot \frac{1}{6}$

Step 4.3.2

Cancel the common factor of $3$ .

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Step 4.3.2.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$z = \frac{- 9}{2} \cdot \frac{1}{6}$

Step 4.3.2.2

Factor $3$ out of $- 9$ .

$z = \frac{3 (- 3)}{2} \cdot \frac{1}{6}$

Step 4.3.2.3

Factor $3$ out of $6$ .

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

Step 4.3.2.4

Cancel the common factor.

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

Step 4.3.2.5

Rewrite the expression.

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

Step 4.3.3

Multiply $\frac{- 3}{2}$ by $\frac{1}{2}$ .

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

Step 4.3.4

Simplify the expression.

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Step 4.3.4.1

Multiply $2$ by $2$ .

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

Step 4.3.4.2

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$z = - 0.75$