Basic Math Examples

$3 \frac{1}{3} \cdot c = 80$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{1}{3} \cdot c$ .

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Step 1.1.1

Convert $3 \frac{1}{3}$ 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.

$(3 + \frac{1}{3}) \cdot c = 80$

Step 1.1.1.2

Add $3$ and $\frac{1}{3}$ .

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Step 1.1.1.2.1

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

$(3 \cdot \frac{3}{3} + \frac{1}{3}) \cdot c = 80$

Step 1.1.1.2.2

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

$(\frac{3 \cdot 3}{3} + \frac{1}{3}) \cdot c = 80$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 1}{3} \cdot c = 80$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $3$ .

$\frac{9 + 1}{3} \cdot c = 80$

Step 1.1.1.2.4.2

Add $9$ and $1$ .

$\frac{10}{3} \cdot c = 80$

Step 1.1.2

Combine $\frac{10}{3}$ and $c$ .

$\frac{10 c}{3} = 80$

Step 2

Multiply both sides of the equation by $\frac{3}{10}$ .

$\frac{3}{10} \cdot \frac{10 c}{3} = \frac{3}{10} \cdot 80$

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 $\frac{3}{10} \cdot \frac{10 c}{3}$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{3}{10} \cdot \frac{10 c}{3} = \frac{3}{10} \cdot 80$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{10} (10 c) = \frac{3}{10} \cdot 80$

Step 3.1.1.2

Cancel the common factor of $10$ .

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Step 3.1.1.2.1

Factor $10$ out of $10 c$ .

$\frac{1}{10} (10 (c)) = \frac{3}{10} \cdot 80$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{10} (10 c) = \frac{3}{10} \cdot 80$

Step 3.1.1.2.3

Rewrite the expression.

$c = \frac{3}{10} \cdot 80$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{3}{10} \cdot 80$ .

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Step 3.2.1.1

Cancel the common factor of $10$ .

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Step 3.2.1.1.1

Factor $10$ out of $80$ .

$c = \frac{3}{10} \cdot (10 (8))$

Step 3.2.1.1.2

Cancel the common factor.

$c = \frac{3}{10} \cdot (10 \cdot 8)$

Step 3.2.1.1.3

Rewrite the expression.

$c = 3 \cdot 8$

Step 3.2.1.2

Multiply $3$ by $8$ .

$c = 24$