Basic Math Examples

$u + \frac{4}{5} = 4 \frac{2}{3}$

Step 1

Simplify the right side.

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Step 1.1

Convert $4 \frac{2}{3}$ to an improper fraction.

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Step 1.1.1

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

$u + \frac{4}{5} = 4 + \frac{2}{3}$

Step 1.1.2

Add $4$ and $\frac{2}{3}$ .

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Step 1.1.2.1

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

$u + \frac{4}{5} = 4 \cdot \frac{3}{3} + \frac{2}{3}$

Step 1.1.2.2

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

$u + \frac{4}{5} = \frac{4 \cdot 3}{3} + \frac{2}{3}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$u + \frac{4}{5} = \frac{4 \cdot 3 + 2}{3}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $4$ by $3$ .

$u + \frac{4}{5} = \frac{12 + 2}{3}$

Step 1.1.2.4.2

Add $12$ and $2$ .

$u + \frac{4}{5} = \frac{14}{3}$

Step 2

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

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Step 2.1

Subtract $\frac{4}{5}$ from both sides of the equation.

$u = \frac{14}{3} - \frac{4}{5}$

Step 2.2

To write $\frac{14}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$u = \frac{14}{3} \cdot \frac{5}{5} - \frac{4}{5}$

Step 2.3

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

$u = \frac{14}{3} \cdot \frac{5}{5} - \frac{4}{5} \cdot \frac{3}{3}$

Step 2.4

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

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Step 2.4.1

Multiply $\frac{14}{3}$ by $\frac{5}{5}$ .

$u = \frac{14 \cdot 5}{3 \cdot 5} - \frac{4}{5} \cdot \frac{3}{3}$

Step 2.4.2

Multiply $3$ by $5$ .

$u = \frac{14 \cdot 5}{15} - \frac{4}{5} \cdot \frac{3}{3}$

Step 2.4.3

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

$u = \frac{14 \cdot 5}{15} - \frac{4 \cdot 3}{5 \cdot 3}$

Step 2.4.4

Multiply $5$ by $3$ .

$u = \frac{14 \cdot 5}{15} - \frac{4 \cdot 3}{15}$

Step 2.5

Combine the numerators over the common denominator.

$u = \frac{14 \cdot 5 - 4 \cdot 3}{15}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $14$ by $5$ .

$u = \frac{70 - 4 \cdot 3}{15}$

Step 2.6.2

Multiply $- 4$ by $3$ .

$u = \frac{70 - 12}{15}$

Step 2.6.3

Subtract $12$ from $70$ .

$u = \frac{58}{15}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$u = \frac{58}{15}$

Decimal Form:

$u = 3.8\overline{6}$

Mixed Number Form:

$u = 3 \frac{13}{15}$