Algebra Examples

$1 \frac{1}{4} c = 30$

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

Convert $1 \frac{1}{4}$ 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.

$(1 + \frac{1}{4}) c = 30$

Step 1.1.1.2

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

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{4}{4} + \frac{1}{4}) c = 30$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{4 + 1}{4} c = 30$

Step 1.1.1.2.3

Add $4$ and $1$ .

$\frac{5}{4} c = 30$

Step 1.1.2

Combine $\frac{5}{4}$ and $c$ .

$\frac{5 c}{4} = 30$

Step 2

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 c}{4} = \frac{4}{5} \cdot 30$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{4}{5} \cdot \frac{5 c}{4}$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 c}{4} = \frac{4}{5} \cdot 30$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 c) = \frac{4}{5} \cdot 30$

Step 3.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.2.1

Factor $5$ out of $5 c$ .

$\frac{1}{5} (5 (c)) = \frac{4}{5} \cdot 30$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 c) = \frac{4}{5} \cdot 30$

Step 3.1.1.2.3

Rewrite the expression.

$c = \frac{4}{5} \cdot 30$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{4}{5} \cdot 30$ .

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Step 3.2.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1

Factor $5$ out of $30$ .

$c = \frac{4}{5} \cdot (5 (6))$

Step 3.2.1.1.2

Cancel the common factor.

$c = \frac{4}{5} \cdot (5 \cdot 6)$

Step 3.2.1.1.3

Rewrite the expression.

$c = 4 \cdot 6$

Step 3.2.1.2

Multiply $4$ by $6$ .

$c = 24$