Basic Math Examples

$- \frac{1}{3} u - \frac{1}{2} = - \frac{6}{7}$

Step 1

Combine

$u$ and

$\frac{1}{3}$ .

$- \frac{u}{3} - \frac{1}{2} = - \frac{6}{7}$

Step 2

Move all terms not containing

$u$ to the right side of the equation.

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Step 2.1

Add

$\frac{1}{2}$ to both sides of the equation.

$- \frac{u}{3} = - \frac{6}{7} + \frac{1}{2}$

Step 2.2

To write

$- \frac{6}{7}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$- \frac{u}{3} = - \frac{6}{7} \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.3

To write

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

$\frac{7}{7}$ .

$- \frac{u}{3} = - \frac{6}{7} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{7}{7}$

Step 2.4

Write each expression with a common denominator of

$14$ , by multiplying each by an appropriate factor of

$1$ .

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Step 2.4.1

Multiply

$\frac{6}{7}$ by

$\frac{2}{2}$ .

$- \frac{u}{3} = - \frac{6 \cdot 2}{7 \cdot 2} + \frac{1}{2} \cdot \frac{7}{7}$

Step 2.4.2

Multiply

$7$ by

$2$ .

$- \frac{u}{3} = - \frac{6 \cdot 2}{14} + \frac{1}{2} \cdot \frac{7}{7}$

Step 2.4.3

Multiply

$\frac{1}{2}$ by

$\frac{7}{7}$ .

$- \frac{u}{3} = - \frac{6 \cdot 2}{14} + \frac{7}{2 \cdot 7}$

Step 2.4.4

Multiply

$2$ by

$7$ .

$- \frac{u}{3} = - \frac{6 \cdot 2}{14} + \frac{7}{14}$

Step 2.5

Combine the numerators over the common denominator.

$- \frac{u}{3} = \frac{- 6 \cdot 2 + 7}{14}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply

$- 6$ by

$2$ .

$- \frac{u}{3} = \frac{- 12 + 7}{14}$

Step 2.6.2

Add

$- 12$ and

$7$ .

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

Step 2.7

Move the negative in front of the fraction.

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

Step 3

Multiply both sides of the equation by

$- 3$ .

$- 3 (- \frac{u}{3}) = - 3 (- \frac{5}{14})$

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

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

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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

$- \frac{u}{3}$ into the numerator.

$- 3 \frac{- u}{3} = - 3 (- \frac{5}{14})$

Step 4.1.1.1.2

Factor

$3$ out of

$- 3$ .

$3 (- 1) \frac{- u}{3} = - 3 (- \frac{5}{14})$

Step 4.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- u}{3} = - 3 (- \frac{5}{14})$

Step 4.1.1.1.4

Rewrite the expression.

$- - u = - 3 (- \frac{5}{14})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply

$- 1$ by

$- 1$ .

$1 u = - 3 (- \frac{5}{14})$

Step 4.1.1.2.2

Multiply

$u$ by

$1$ .

$u = - 3 (- \frac{5}{14})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply

$- 3 (- \frac{5}{14})$ .

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Step 4.2.1.1

Multiply

$- 1$ by

$- 3$ .

$u = 3 (\frac{5}{14})$

Step 4.2.1.2

Combine

$3$ and

$\frac{5}{14}$ .

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

Step 4.2.1.3

Multiply

$3$ by

$5$ .

$u = \frac{15}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$u = \frac{15}{14}$

Decimal Form:

$u = 1.07142857 \dots$

Mixed Number Form:

$u = 1 \frac{1}{14}$