Basic Math Examples

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

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.1.2

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

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Step 1.1.1.2.1

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

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

Step 1.1.1.2.2

Combine the numerators over the common denominator.

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

Step 1.1.1.2.3

Add $3$ and $1$ .

$\frac{4}{3} \cdot p = 3 \frac{1}{3} \cdot c$

Step 1.1.2

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

$\frac{4 p}{3} = 3 \frac{1}{3} \cdot c$

Step 2

Simplify the right side.

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Step 2.1

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

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Step 2.1.1

Convert $3 \frac{1}{3}$ to an improper fraction.

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Step 2.1.1.1

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

$\frac{4 p}{3} = (3 + \frac{1}{3}) \cdot c$

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

$\frac{4 p}{3} = (3 \cdot \frac{3}{3} + \frac{1}{3}) \cdot c$

Step 2.1.1.2.2

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

$\frac{4 p}{3} = (\frac{3 \cdot 3}{3} + \frac{1}{3}) \cdot c$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{4 p}{3} = \frac{3 \cdot 3 + 1}{3} \cdot c$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $3$ by $3$ .

$\frac{4 p}{3} = \frac{9 + 1}{3} \cdot c$

Step 2.1.1.2.4.2

Add $9$ and $1$ .

$\frac{4 p}{3} = \frac{10}{3} \cdot c$

Step 2.1.2

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

$\frac{4 p}{3} = \frac{10 c}{3}$

Step 3

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

$4 p = 10 c$

Step 4

Divide each term in $4 p = 10 c$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 p = 10 c$ by $4$ .

$\frac{4 p}{4} = \frac{10 c}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 p}{4} = \frac{10 c}{4}$

Step 4.2.1.2

Divide $p$ by $1$ .

$p = \frac{10 c}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $10$ and $4$ .

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Step 4.3.1.1

Factor $2$ out of $10 c$ .

$p = \frac{2 (5 c)}{4}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $4$ .

$p = \frac{2 (5 c)}{2 (2)}$

Step 4.3.1.2.2

Cancel the common factor.

$p = \frac{2 (5 c)}{2 \cdot 2}$

Step 4.3.1.2.3

Rewrite the expression.

$p = \frac{5 c}{2}$