Basic Math Examples

$\frac{3}{4} n = - 1 \frac{3}{4} - 18$

Step 1

Simplify the left side.

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Step 1.1

Combine $\frac{3}{4}$ and $n$ .

$\frac{3 n}{4} = - 1 \frac{3}{4} - 18$

Step 2

Simplify the right side.

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Step 2.1

Simplify $- 1 \frac{3}{4} - 18$ .

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Step 2.1.1

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

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Step 2.1.1.1

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

$\frac{3 n}{4} = - (1 + \frac{3}{4}) - 18$

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

$\frac{3 n}{4} = - (\frac{4}{4} + \frac{3}{4}) - 18$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{3 n}{4} = - \frac{4 + 3}{4} - 18$

Step 2.1.1.2.3

Add $4$ and $3$ .

$\frac{3 n}{4} = - \frac{7}{4} - 18$

Step 2.1.2

To write $- 18$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 n}{4} = - \frac{7}{4} - 18 \cdot \frac{4}{4}$

Step 2.1.3

Combine $- 18$ and $\frac{4}{4}$ .

$\frac{3 n}{4} = - \frac{7}{4} + \frac{- 18 \cdot 4}{4}$

Step 2.1.4

Combine the numerators over the common denominator.

$\frac{3 n}{4} = \frac{- 7 - 18 \cdot 4}{4}$

Step 2.1.5

Simplify the numerator.

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Step 2.1.5.1

Multiply $- 18$ by $4$ .

$\frac{3 n}{4} = \frac{- 7 - 72}{4}$

Step 2.1.5.2

Subtract $72$ from $- 7$ .

$\frac{3 n}{4} = \frac{- 79}{4}$

Step 2.1.6

Move the negative in front of the fraction.

$\frac{3 n}{4} = - \frac{79}{4}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 n = - 79$

Step 4

Divide each term in $3 n = - 79$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 n = - 79$ by $3$ .

$\frac{3 n}{3} = \frac{- 79}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 n}{3} = \frac{- 79}{3}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 79}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$n = - \frac{79}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{79}{3}$

Decimal Form:

$n = - 26.\overline{3}$

Mixed Number Form:

$n = - 26 \frac{1}{3}$