Basic Math Examples

$- \frac{4}{5} - \frac{4}{3} u = \frac{1}{2}$

Step 1

Simplify each term.

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Step 1.1

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

$- \frac{4}{5} - \frac{u \cdot 4}{3} = \frac{1}{2}$

Step 1.2

Move $4$ to the left of $u$ .

$- \frac{4}{5} - \frac{4 u}{3} = \frac{1}{2}$

Step 2

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

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Step 2.1

Add $\frac{4}{5}$ to both sides of the equation.

$- \frac{4 u}{3} = \frac{1}{2} + \frac{4}{5}$

Step 2.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{4 u}{3} = \frac{1}{2} \cdot \frac{5}{5} + \frac{4}{5}$

Step 2.3

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{4 u}{3} = \frac{1}{2} \cdot \frac{5}{5} + \frac{4}{5} \cdot \frac{2}{2}$

Step 2.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

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

Step 2.4.2

Multiply $2$ by $5$ .

$- \frac{4 u}{3} = \frac{5}{10} + \frac{4}{5} \cdot \frac{2}{2}$

Step 2.4.3

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

$- \frac{4 u}{3} = \frac{5}{10} + \frac{4 \cdot 2}{5 \cdot 2}$

Step 2.4.4

Multiply $5$ by $2$ .

$- \frac{4 u}{3} = \frac{5}{10} + \frac{4 \cdot 2}{10}$

Step 2.5

Combine the numerators over the common denominator.

$- \frac{4 u}{3} = \frac{5 + 4 \cdot 2}{10}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $4$ by $2$ .

$- \frac{4 u}{3} = \frac{5 + 8}{10}$

Step 2.6.2

Add $5$ and $8$ .

$- \frac{4 u}{3} = \frac{13}{10}$

Step 3

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} (- \frac{4 u}{3}) = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{3}{4} (- \frac{4 u}{3})$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 u}{3}) = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.1.1.1.2

Move the leading negative in $- \frac{4 u}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 u}{3} = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 u}{3} = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 u}{3} = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} (- 4 u) = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Factor $4$ out of $- 4 u$ .

$\frac{- 1}{4} (4 (- u)) = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} (4 (- u)) = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.1.1.2.3

Rewrite the expression.

$- - u = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 u = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.1.1.3.2

Multiply $u$ by $1$ .

$u = - \frac{3}{4} \cdot \frac{13}{10}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{3}{4} \cdot \frac{13}{10}$ .

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Step 4.2.1.1

Multiply $\frac{13}{10}$ by $\frac{3}{4}$ .

$u = - \frac{13 \cdot 3}{10 \cdot 4}$

Step 4.2.1.2

Multiply $13$ by $3$ .

$u = - \frac{39}{10 \cdot 4}$

Step 4.2.1.3

Multiply $10$ by $4$ .

$u = - \frac{39}{40}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$u = - \frac{39}{40}$

Decimal Form:

$u = - 0.975$