Pre-Algebra Examples

$2 \frac{3}{5} \cdot x + 3 - \frac{2}{3} x - 1$

Step 1

Convert $2 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

$(2 + \frac{3}{5}) \cdot x + 3 - \frac{2}{3} x - 1$

Step 1.2

Add $2$ and $\frac{3}{5}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(2 \cdot \frac{5}{5} + \frac{3}{5}) \cdot x + 3 - \frac{2}{3} x - 1$

Step 1.2.2

Combine $2$ and $\frac{5}{5}$ .

$(\frac{2 \cdot 5}{5} + \frac{3}{5}) \cdot x + 3 - \frac{2}{3} x - 1$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 3}{5} \cdot x + 3 - \frac{2}{3} x - 1$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

$\frac{10 + 3}{5} \cdot x + 3 - \frac{2}{3} x - 1$

Step 1.2.4.2

Add $10$ and $3$ .

$\frac{13}{5} \cdot x + 3 - \frac{2}{3} x - 1$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{13}{5}$ and $x$ .

$\frac{13 x}{5} + 3 - \frac{2}{3} x - 1$

Step 2.2

Combine $x$ and $\frac{2}{3}$ .

$\frac{13 x}{5} + 3 - \frac{x \cdot 2}{3} - 1$

Step 2.3

Move $2$ to the left of $x$ .

$\frac{13 x}{5} + 3 - \frac{2 x}{3} - 1$

Step 3

To write $\frac{13 x}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{13 x}{5} \cdot \frac{3}{3} - \frac{2 x}{3} + 3 - 1$

Step 4

To write $- \frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{13 x}{5} \cdot \frac{3}{3} - \frac{2 x}{3} \cdot \frac{5}{5} + 3 - 1$

Step 5

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{13 x}{5}$ by $\frac{3}{3}$ .

$\frac{13 x \cdot 3}{5 \cdot 3} - \frac{2 x}{3} \cdot \frac{5}{5} + 3 - 1$

Step 5.2

Multiply $5$ by $3$ .

$\frac{13 x \cdot 3}{15} - \frac{2 x}{3} \cdot \frac{5}{5} + 3 - 1$

Step 5.3

Multiply $\frac{2 x}{3}$ by $\frac{5}{5}$ .

$\frac{13 x \cdot 3}{15} - \frac{2 x \cdot 5}{3 \cdot 5} + 3 - 1$

Step 5.4

Multiply $3$ by $5$ .

$\frac{13 x \cdot 3}{15} - \frac{2 x \cdot 5}{15} + 3 - 1$

Step 6

Combine the numerators over the common denominator.

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + 3 - 1$

Step 7

Find the common denominator.

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Step 7.1

Write $3$ as a fraction with denominator $1$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3}{1} - 1$

Step 7.2

Multiply $\frac{3}{1}$ by $\frac{15}{15}$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3}{1} \cdot \frac{15}{15} - 1$

Step 7.3

Multiply $\frac{3}{1}$ by $\frac{15}{15}$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3 \cdot 15}{15} - 1$

Step 7.4

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

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3 \cdot 15}{15} + \frac{- 1}{1}$

Step 7.5

Multiply $\frac{- 1}{1}$ by $\frac{15}{15}$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3 \cdot 15}{15} + \frac{- 1}{1} \cdot \frac{15}{15}$

Step 7.6

Multiply $\frac{- 1}{1}$ by $\frac{15}{15}$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3 \cdot 15}{15} + \frac{- 1 \cdot 15}{15}$

Step 8

Combine the numerators over the common denominator.

$\frac{13 x \cdot 3 - 2 x \cdot 5 + 3 \cdot 15 - 1 \cdot 15}{15}$

Step 9

Simplify each term.

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Step 9.1

Multiply $3$ by $13$ .

$\frac{39 x - 2 x \cdot 5 + 3 \cdot 15 - 1 \cdot 15}{15}$

Step 9.2

Multiply $5$ by $- 2$ .

$\frac{39 x - 10 x + 3 \cdot 15 - 1 \cdot 15}{15}$

Step 9.3

Multiply $3$ by $15$ .

$\frac{39 x - 10 x + 45 - 1 \cdot 15}{15}$

Step 9.4

Multiply $- 1$ by $15$ .

$\frac{39 x - 10 x + 45 - 15}{15}$

Step 10

Simplify by adding terms.

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Step 10.1

Subtract $10 x$ from $39 x$ .

$\frac{29 x + 45 - 15}{15}$

Step 10.2

Subtract $15$ from $45$ .

$\frac{29 x + 30}{15}$