Basic Math Examples

$1 \frac{2}{3} \cdot j = 15$

Step 1

Simplify the left side.

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Step 1.1

Simplify $1 \frac{2}{3} \cdot j$ .

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Step 1.1.1

Convert $1 \frac{2}{3}$ 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.

$(1 + \frac{2}{3}) \cdot j = 15$

Step 1.1.1.2

Add $1$ and $\frac{2}{3}$ .

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Step 1.1.1.2.1

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

$(\frac{3}{3} + \frac{2}{3}) \cdot j = 15$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{3 + 2}{3} \cdot j = 15$

Step 1.1.1.2.3

Add $3$ and $2$ .

$\frac{5}{3} \cdot j = 15$

Step 1.1.2

Combine $\frac{5}{3}$ and $j$ .

$\frac{5 j}{3} = 15$

Step 2

Multiply both sides of the equation by $\frac{3}{5}$ .

$\frac{3}{5} \cdot \frac{5 j}{3} = \frac{3}{5} \cdot 15$

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 $\frac{3}{5} \cdot \frac{5 j}{3}$ .

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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.

$\frac{3}{5} \cdot \frac{5 j}{3} = \frac{3}{5} \cdot 15$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 j) = \frac{3}{5} \cdot 15$

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 $5 j$ .

$\frac{1}{5} (5 (j)) = \frac{3}{5} \cdot 15$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 j) = \frac{3}{5} \cdot 15$

Step 3.1.1.2.3

Rewrite the expression.

$j = \frac{3}{5} \cdot 15$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{3}{5} \cdot 15$ .

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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 $15$ .

$j = \frac{3}{5} \cdot (5 (3))$

Step 3.2.1.1.2

Cancel the common factor.

$j = \frac{3}{5} \cdot (5 \cdot 3)$

Step 3.2.1.1.3

Rewrite the expression.

$j = 3 \cdot 3$

Step 3.2.1.2

Multiply $3$ by $3$ .

$j = 9$