Basic Math Examples

$\frac{q - 3}{2} - \frac{4 q - 7}{5} = 2 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{q - 3}{2} - \frac{4 q - 7}{5}$ .

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Step 1.1.1

To write $\frac{q - 3}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{q - 3}{2} \cdot \frac{5}{5} - \frac{4 q - 7}{5} = 2 \frac{1}{2}$

Step 1.1.2

To write $- \frac{4 q - 7}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{q - 3}{2} \cdot \frac{5}{5} - \frac{4 q - 7}{5} \cdot \frac{2}{2} = 2 \frac{1}{2}$

Step 1.1.3

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

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Step 1.1.3.1

Multiply $\frac{q - 3}{2}$ by $\frac{5}{5}$ .

$\frac{(q - 3) \cdot 5}{2 \cdot 5} - \frac{4 q - 7}{5} \cdot \frac{2}{2} = 2 \frac{1}{2}$

Step 1.1.3.2

Multiply $2$ by $5$ .

$\frac{(q - 3) \cdot 5}{10} - \frac{4 q - 7}{5} \cdot \frac{2}{2} = 2 \frac{1}{2}$

Step 1.1.3.3

Multiply $\frac{4 q - 7}{5}$ by $\frac{2}{2}$ .

$\frac{(q - 3) \cdot 5}{10} - \frac{(4 q - 7) \cdot 2}{5 \cdot 2} = 2 \frac{1}{2}$

Step 1.1.3.4

Multiply $5$ by $2$ .

$\frac{(q - 3) \cdot 5}{10} - \frac{(4 q - 7) \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.4

Combine the numerators over the common denominator.

$\frac{(q - 3) \cdot 5 - (4 q - 7) \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.5

Simplify the numerator.

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Step 1.1.5.1

Apply the distributive property.

$\frac{q \cdot 5 - 3 \cdot 5 - (4 q - 7) \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.5.2

Move $5$ to the left of $q$ .

$\frac{5 \cdot q - 3 \cdot 5 - (4 q - 7) \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.5.3

Multiply $- 3$ by $5$ .

$\frac{5 \cdot q - 15 - (4 q - 7) \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.5.4

Apply the distributive property.

$\frac{5 q - 15 + (- (4 q) - - 7) \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.5.5

Multiply $4$ by $- 1$ .

$\frac{5 q - 15 + (- 4 q - - 7) \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.5.6

Multiply $- 1$ by $- 7$ .

$\frac{5 q - 15 + (- 4 q + 7) \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.5.7

Apply the distributive property.

$\frac{5 q - 15 - 4 q \cdot 2 + 7 \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.5.8

Multiply $2$ by $- 4$ .

$\frac{5 q - 15 - 8 q + 7 \cdot 2}{10} = 2 \frac{1}{2}$

Step 1.1.5.9

Multiply $7$ by $2$ .

$\frac{5 q - 15 - 8 q + 14}{10} = 2 \frac{1}{2}$

Step 1.1.5.10

Subtract $8 q$ from $5 q$ .

$\frac{- 3 q - 15 + 14}{10} = 2 \frac{1}{2}$

Step 1.1.5.11

Add $- 15$ and $14$ .

$\frac{- 3 q - 1}{10} = 2 \frac{1}{2}$

Step 1.1.6

Simplify with factoring out.

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Step 1.1.6.1

Factor $- 1$ out of $- 3 q$ .

$\frac{- (3 q) - 1}{10} = 2 \frac{1}{2}$

Step 1.1.6.2

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- (3 q) - 1 (1)}{10} = 2 \frac{1}{2}$

Step 1.1.6.3

Factor $- 1$ out of $- (3 q) - 1 (1)$ .

$\frac{- (3 q + 1)}{10} = 2 \frac{1}{2}$

Step 1.1.6.4

Simplify the expression.

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Step 1.1.6.4.1

Rewrite $- (3 q + 1)$ as $- 1 (3 q + 1)$ .

$\frac{- 1 (3 q + 1)}{10} = 2 \frac{1}{2}$

Step 1.1.6.4.2

Move the negative in front of the fraction.

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

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

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

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

Step 2.1.2

Add $2$ and $\frac{1}{2}$ .

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Step 2.1.2.1

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

$- \frac{3 q + 1}{10} = 2 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.1.2.2

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

$- \frac{3 q + 1}{10} = \frac{2 \cdot 2}{2} + \frac{1}{2}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$- \frac{3 q + 1}{10} = \frac{2 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $2$ .

$- \frac{3 q + 1}{10} = \frac{4 + 1}{2}$

Step 2.1.2.4.2

Add $4$ and $1$ .

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

Step 3

Multiply both sides of the equation by $- 10$ .

$- 10 (- \frac{3 q + 1}{10}) = - 10 (\frac{5}{2})$

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 $- 10 (- \frac{3 q + 1}{10})$ .

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Step 4.1.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{3 q + 1}{10}$ into the numerator.

$- 10 \frac{- (3 q + 1)}{10} = - 10 (\frac{5}{2})$

Step 4.1.1.1.2

Factor $10$ out of $- 10$ .

$10 (- 1) \frac{- (3 q + 1)}{10} = - 10 (\frac{5}{2})$

Step 4.1.1.1.3

Cancel the common factor.

$10 \cdot - 1 \frac{- (3 q + 1)}{10} = - 10 (\frac{5}{2})$

Step 4.1.1.1.4

Rewrite the expression.

$- - (3 q + 1) = - 10 (\frac{5}{2})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (3 q + 1) = - 10 (\frac{5}{2})$

Step 4.1.1.2.2

Multiply $3 q + 1$ by $1$ .

$3 q + 1 = - 10 (\frac{5}{2})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 10 (\frac{5}{2})$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $- 10$ .

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

Step 4.2.1.1.2

Cancel the common factor.

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

Step 4.2.1.1.3

Rewrite the expression.

$3 q + 1 = - 5 \cdot 5$

Step 4.2.1.2

Multiply $- 5$ by $5$ .

$3 q + 1 = - 25$

Step 5

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

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Step 5.1

Subtract $1$ from both sides of the equation.

$3 q = - 25 - 1$

Step 5.2

Subtract $1$ from $- 25$ .

$3 q = - 26$

Step 6

Divide each term in $3 q = - 26$ by $3$ and simplify.

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Step 6.1

Divide each term in $3 q = - 26$ by $3$ .

$\frac{3 q}{3} = \frac{- 26}{3}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $3$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{3 q}{3} = \frac{- 26}{3}$

Step 6.2.1.2

Divide $q$ by $1$ .

$q = \frac{- 26}{3}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$q = - \frac{26}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$q = - \frac{26}{3}$

Decimal Form:

$q = - 8.\overline{6}$

Mixed Number Form:

$q = - 8 \frac{2}{3}$