Basic Math Examples

$2 \frac{1}{4} \cdot c = 6 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $2 \frac{1}{4} \cdot c$ .

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Step 1.1.1

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

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Step 1.1.1.1

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

$(2 + \frac{1}{4}) \cdot c = 6 \frac{1}{2}$

Step 1.1.1.2

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

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Step 1.1.1.2.1

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

$(2 \cdot \frac{4}{4} + \frac{1}{4}) \cdot c = 6 \frac{1}{2}$

Step 1.1.1.2.2

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

$(\frac{2 \cdot 4}{4} + \frac{1}{4}) \cdot c = 6 \frac{1}{2}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 1}{4} \cdot c = 6 \frac{1}{2}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 1}{4} \cdot c = 6 \frac{1}{2}$

Step 1.1.1.2.4.2

Add $8$ and $1$ .

$\frac{9}{4} \cdot c = 6 \frac{1}{2}$

Step 1.1.2

Combine $\frac{9}{4}$ and $c$ .

$\frac{9 c}{4} = 6 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Convert $6 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

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

$\frac{9 c}{4} = 6 + \frac{1}{2}$

Step 2.1.2

Add $6$ and $\frac{1}{2}$ .

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Step 2.1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 c}{4} = 6 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.1.2.2

Combine $6$ and $\frac{2}{2}$ .

$\frac{9 c}{4} = \frac{6 \cdot 2}{2} + \frac{1}{2}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{9 c}{4} = \frac{6 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $6$ by $2$ .

$\frac{9 c}{4} = \frac{12 + 1}{2}$

Step 2.1.2.4.2

Add $12$ and $1$ .

$\frac{9 c}{4} = \frac{13}{2}$

Step 3

Multiply both sides of the equation by $\frac{4}{9}$ .

$\frac{4}{9} \cdot \frac{9 c}{4} = \frac{4}{9} \cdot \frac{13}{2}$

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 $\frac{4}{9} \cdot \frac{9 c}{4}$ .

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{9} \cdot \frac{9 c}{4} = \frac{4}{9} \cdot \frac{13}{2}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 c) = \frac{4}{9} \cdot \frac{13}{2}$

Step 4.1.1.2

Cancel the common factor of $9$ .

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Step 4.1.1.2.1

Factor $9$ out of $9 c$ .

$\frac{1}{9} (9 (c)) = \frac{4}{9} \cdot \frac{13}{2}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 c) = \frac{4}{9} \cdot \frac{13}{2}$

Step 4.1.1.2.3

Rewrite the expression.

$c = \frac{4}{9} \cdot \frac{13}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{9} \cdot \frac{13}{2}$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $4$ .

$c = \frac{2 (2)}{9} \cdot \frac{13}{2}$

Step 4.2.1.1.2

Cancel the common factor.

$c = \frac{2 \cdot 2}{9} \cdot \frac{13}{2}$

Step 4.2.1.1.3

Rewrite the expression.

$c = \frac{2}{9} \cdot 13$

Step 4.2.1.2

Combine $\frac{2}{9}$ and $13$ .

$c = \frac{2 \cdot 13}{9}$

Step 4.2.1.3

Multiply $2$ by $13$ .

$c = \frac{26}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = \frac{26}{9}$

Decimal Form:

$c = 2.\overline{8}$

Mixed Number Form:

$c = 2 \frac{8}{9}$