Basic Math Examples

$\frac{3}{4} r + \frac{3}{2} r = \frac{9}{4}$

Step 1

Simplify $\frac{3}{4} r + \frac{3}{2} r$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{3 r}{4} + \frac{3}{2} r = \frac{9}{4}$

Step 1.1.2

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

$\frac{3 r}{4} + \frac{3 r}{2} = \frac{9}{4}$

Step 1.2

To write $\frac{3 r}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 r}{4} + \frac{3 r}{2} \cdot \frac{2}{2} = \frac{9}{4}$

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3 r}{2}$ by $\frac{2}{2}$ .

$\frac{3 r}{4} + \frac{3 r \cdot 2}{2 \cdot 2} = \frac{9}{4}$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{3 r}{4} + \frac{3 r \cdot 2}{4} = \frac{9}{4}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 r + 3 r \cdot 2}{4} = \frac{9}{4}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $3 r$ out of $3 r + 3 r \cdot 2$ .

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Step 1.5.1.1

Factor $3 r$ out of $3 r$ .

$\frac{3 r (1) + 3 r \cdot 2}{4} = \frac{9}{4}$

Step 1.5.1.2

Factor $3 r$ out of $3 r \cdot 2$ .

$\frac{3 r (1) + 3 r (2)}{4} = \frac{9}{4}$

Step 1.5.1.3

Factor $3 r$ out of $3 r (1) + 3 r (2)$ .

$\frac{3 r (1 + 2)}{4} = \frac{9}{4}$

Step 1.5.2

Add $1$ and $2$ .

$\frac{3 r \cdot 3}{4} = \frac{9}{4}$

Step 1.5.3

Multiply $3$ by $3$ .

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

Step 2

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

$9 r = 9$

Step 3

Divide each term in $9 r = 9$ by $9$ and simplify.

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Step 3.1

Divide each term in $9 r = 9$ by $9$ .

$\frac{9 r}{9} = \frac{9}{9}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $9$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{9 r}{9} = \frac{9}{9}$

Step 3.2.1.2

Divide $r$ by $1$ .

$r = \frac{9}{9}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $9$ by $9$ .

$r = 1$