Basic Math Examples

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

Step 1

Rewrite the equation as $\frac{2}{3} u + \frac{5}{3} u = \frac{5}{3} + \frac{5}{3}$ .

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

Step 2

Simplify $\frac{2}{3} u + \frac{5}{3} u$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

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

Step 2.2.2

Add $2 u$ and $5 u$ .

$\frac{7 u}{3} = \frac{5}{3} + \frac{5}{3}$

Step 3

Simplify $\frac{5}{3} + \frac{5}{3}$ .

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Step 3.1

Combine the numerators over the common denominator.

$\frac{7 u}{3} = \frac{5 + 5}{3}$

Step 3.2

Add $5$ and $5$ .

$\frac{7 u}{3} = \frac{10}{3}$

Step 4

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

$7 u = 10$

Step 5

Divide each term in $7 u = 10$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 u = 10$ by $7$ .

$\frac{7 u}{7} = \frac{10}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 u}{7} = \frac{10}{7}$

Step 5.2.1.2

Divide $u$ by $1$ .

$u = \frac{10}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$u = \frac{10}{7}$

Decimal Form:

$u = 1.\overline{428571}$

Mixed Number Form:

$u = 1 \frac{3}{7}$