Basic Math Examples

$\frac{2}{5} r - \frac{3}{4} = \frac{7}{4}$

Step 1

Combine $\frac{2}{5}$ and $r$ .

$\frac{2 r}{5} - \frac{3}{4} = \frac{7}{4}$

Step 2

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

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Step 2.1

Add $\frac{3}{4}$ to both sides of the equation.

$\frac{2 r}{5} = \frac{7}{4} + \frac{3}{4}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{2 r}{5} = \frac{7 + 3}{4}$

Step 2.3

Add $7$ and $3$ .

$\frac{2 r}{5} = \frac{10}{4}$

Step 2.4

Cancel the common factor of $10$ and $4$ .

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Step 2.4.1

Factor $2$ out of $10$ .

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

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

$\frac{2 r}{5} = \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.4.2.2

Cancel the common factor.

$\frac{2 r}{5} = \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.4.2.3

Rewrite the expression.

$\frac{2 r}{5} = \frac{5}{2}$

Step 3

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 r}{5} = \frac{5}{2} \cdot \frac{5}{2}$

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 $\frac{5}{2} \cdot \frac{2 r}{5}$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 r}{5} = \frac{5}{2} \cdot \frac{5}{2}$

Step 4.1.1.1.2

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $2 r$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

$r = \frac{5}{2} \cdot \frac{5}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{5}{2} \cdot \frac{5}{2}$ .

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Step 4.2.1.1

Multiply $\frac{5}{2}$ by $\frac{5}{2}$ .

$r = \frac{5 \cdot 5}{2 \cdot 2}$

Step 4.2.1.2

Multiply $5$ by $5$ .

$r = \frac{25}{2 \cdot 2}$

Step 4.2.1.3

Multiply $2$ by $2$ .

$r = \frac{25}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$r = \frac{25}{4}$

Decimal Form:

$r = 6.25$

Mixed Number Form:

$r = 6 \frac{1}{4}$