Algebra Examples

$- 2 \frac{2}{5} + u = 1 \frac{1}{3}$

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

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

$- (2 + \frac{2}{5}) + u = 1 \frac{1}{3}$

Step 1.1.2

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

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Step 1.1.2.1

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

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $5$ .

$- \frac{10 + 2}{5} + u = 1 \frac{1}{3}$

Step 1.1.2.4.2

Add $10$ and $2$ .

$- \frac{12}{5} + u = 1 \frac{1}{3}$

Step 2

Simplify the right side.

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Step 2.1

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

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Step 2.1.1

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

$- \frac{12}{5} + u = 1 + \frac{1}{3}$

Step 2.1.2

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

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Step 2.1.2.1

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

$- \frac{12}{5} + u = \frac{3}{3} + \frac{1}{3}$

Step 2.1.2.2

Combine the numerators over the common denominator.

$- \frac{12}{5} + u = \frac{3 + 1}{3}$

Step 2.1.2.3

Add $3$ and $1$ .

$- \frac{12}{5} + u = \frac{4}{3}$

Step 3

Move all terms not containing $u$ to the right side of the equation.

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Step 3.1

Add $\frac{12}{5}$ to both sides of the equation.

$u = \frac{4}{3} + \frac{12}{5}$

Step 3.2

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$u = \frac{4}{3} \cdot \frac{5}{5} + \frac{12}{5}$

Step 3.3

To write $\frac{12}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$u = \frac{4}{3} \cdot \frac{5}{5} + \frac{12}{5} \cdot \frac{3}{3}$

Step 3.4

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

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Step 3.4.1

Multiply $\frac{4}{3}$ by $\frac{5}{5}$ .

$u = \frac{4 \cdot 5}{3 \cdot 5} + \frac{12}{5} \cdot \frac{3}{3}$

Step 3.4.2

Multiply $3$ by $5$ .

$u = \frac{4 \cdot 5}{15} + \frac{12}{5} \cdot \frac{3}{3}$

Step 3.4.3

Multiply $\frac{12}{5}$ by $\frac{3}{3}$ .

$u = \frac{4 \cdot 5}{15} + \frac{12 \cdot 3}{5 \cdot 3}$

Step 3.4.4

Multiply $5$ by $3$ .

$u = \frac{4 \cdot 5}{15} + \frac{12 \cdot 3}{15}$

Step 3.5

Combine the numerators over the common denominator.

$u = \frac{4 \cdot 5 + 12 \cdot 3}{15}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $4$ by $5$ .

$u = \frac{20 + 12 \cdot 3}{15}$

Step 3.6.2

Multiply $12$ by $3$ .

$u = \frac{20 + 36}{15}$

Step 3.6.3

Add $20$ and $36$ .

$u = \frac{56}{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$u = \frac{56}{15}$

Decimal Form:

$u = 3.7\overline{3}$

Mixed Number Form:

$u = 3 \frac{11}{15}$