Basic Math Examples

$2 \frac{1}{4} = 7 c$

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.

$2 + \frac{1}{4} = 7 c$

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 $\frac{4}{4}$ .

$2 \cdot \frac{4}{4} + \frac{1}{4} = 7 c$

Step 1.1.2.2

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

$\frac{2 \cdot 4}{4} + \frac{1}{4} = 7 c$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 1}{4} = 7 c$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 1}{4} = 7 c$

Step 1.1.2.4.2

Add $8$ and $1$ .

$\frac{9}{4} = 7 c$

Step 2

Rewrite the equation as $7 c = \frac{9}{4}$ .

$7 c = \frac{9}{4}$

Step 3

Divide each term in $7 c = \frac{9}{4}$ by $7$ and simplify.

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Step 3.1

Divide each term in $7 c = \frac{9}{4}$ by $7$ .

$\frac{7 c}{7} = \frac{\frac{9}{4}}{7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 c}{7} = \frac{\frac{9}{4}}{7}$

Step 3.2.1.2

Divide $c$ by $1$ .

$c = \frac{\frac{9}{4}}{7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$c = \frac{9}{4} \cdot \frac{1}{7}$

Step 3.3.2

Multiply $\frac{9}{4} \cdot \frac{1}{7}$ .

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Step 3.3.2.1

Multiply $\frac{9}{4}$ by $\frac{1}{7}$ .

$c = \frac{9}{4 \cdot 7}$

Step 3.3.2.2

Multiply $4$ by $7$ .

$c = \frac{9}{28}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = \frac{9}{28}$

Decimal Form:

$c = 0.32142857 \dots$