Basic Math Examples

$- 2 \frac{1}{4} = r - \frac{4}{5}$

Step 1

Simplify the left side.

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Step 1.1

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 1.1.1

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

$- (2 + \frac{1}{4}) = r - \frac{4}{5}$

Step 1.1.2

Add $2$ and $\frac{1}{4}$ .

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Step 1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- (2 \cdot \frac{4}{4} + \frac{1}{4}) = r - \frac{4}{5}$

Step 1.1.2.2

Combine $2$ and $\frac{4}{4}$ .

$- (\frac{2 \cdot 4}{4} + \frac{1}{4}) = r - \frac{4}{5}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 4 + 1}{4} = r - \frac{4}{5}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $4$ .

$- \frac{8 + 1}{4} = r - \frac{4}{5}$

Step 1.1.2.4.2

Add $8$ and $1$ .

$- \frac{9}{4} = r - \frac{4}{5}$

Step 2

Rewrite the equation as $r - \frac{4}{5} = - \frac{9}{4}$ .

$r - \frac{4}{5} = - \frac{9}{4}$

Step 3

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

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Step 3.1

Add $\frac{4}{5}$ to both sides of the equation.

$r = - \frac{9}{4} + \frac{4}{5}$

Step 3.2

To write $- \frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$r = - \frac{9}{4} \cdot \frac{5}{5} + \frac{4}{5}$

Step 3.3

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$r = - \frac{9}{4} \cdot \frac{5}{5} + \frac{4}{5} \cdot \frac{4}{4}$

Step 3.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{9}{4}$ by $\frac{5}{5}$ .

$r = - \frac{9 \cdot 5}{4 \cdot 5} + \frac{4}{5} \cdot \frac{4}{4}$

Step 3.4.2

Multiply $4$ by $5$ .

$r = - \frac{9 \cdot 5}{20} + \frac{4}{5} \cdot \frac{4}{4}$

Step 3.4.3

Multiply $\frac{4}{5}$ by $\frac{4}{4}$ .

$r = - \frac{9 \cdot 5}{20} + \frac{4 \cdot 4}{5 \cdot 4}$

Step 3.4.4

Multiply $5$ by $4$ .

$r = - \frac{9 \cdot 5}{20} + \frac{4 \cdot 4}{20}$

Step 3.5

Combine the numerators over the common denominator.

$r = \frac{- 9 \cdot 5 + 4 \cdot 4}{20}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 9$ by $5$ .

$r = \frac{- 45 + 4 \cdot 4}{20}$

Step 3.6.2

Multiply $4$ by $4$ .

$r = \frac{- 45 + 16}{20}$

Step 3.6.3

Add $- 45$ and $16$ .

$r = \frac{- 29}{20}$

Step 3.7

Move the negative in front of the fraction.

$r = - \frac{29}{20}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{29}{20}$

Decimal Form:

$r = - 1.45$

Mixed Number Form:

$r = - 1 \frac{9}{20}$