Algebra Examples

$- 5 \frac{1}{2} + 6 \frac{3}{4} + (- 4 \frac{1}{4})$

Step 1

Remove parentheses.

$- 5 \frac{1}{2} + 6 \frac{3}{4} - 4 \frac{1}{4}$

Step 2

Convert $5 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$- (5 + \frac{1}{2}) + 6 \frac{3}{4} - 4 \frac{1}{4}$

Step 2.2

Add $5$ and $\frac{1}{2}$ .

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Step 2.2.1

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

$- (5 \cdot \frac{2}{2} + \frac{1}{2}) + 6 \frac{3}{4} - 4 \frac{1}{4}$

Step 2.2.2

Combine $5$ and $\frac{2}{2}$ .

$- (\frac{5 \cdot 2}{2} + \frac{1}{2}) + 6 \frac{3}{4} - 4 \frac{1}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{5 \cdot 2 + 1}{2} + 6 \frac{3}{4} - 4 \frac{1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $2$ .

$- \frac{10 + 1}{2} + 6 \frac{3}{4} - 4 \frac{1}{4}$

Step 2.2.4.2

Add $10$ and $1$ .

$- \frac{11}{2} + 6 \frac{3}{4} - 4 \frac{1}{4}$

Step 3

Convert $6 \frac{3}{4}$ to an improper fraction.

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Step 3.1

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

$- \frac{11}{2} + 6 + \frac{3}{4} - 4 \frac{1}{4}$

Step 3.2

Add $6$ and $\frac{3}{4}$ .

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Step 3.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{11}{2} + 6 \cdot \frac{4}{4} + \frac{3}{4} - 4 \frac{1}{4}$

Step 3.2.2

Combine $6$ and $\frac{4}{4}$ .

$- \frac{11}{2} + \frac{6 \cdot 4}{4} + \frac{3}{4} - 4 \frac{1}{4}$

Step 3.2.3

Combine the numerators over the common denominator.

$- \frac{11}{2} + \frac{6 \cdot 4 + 3}{4} - 4 \frac{1}{4}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $6$ by $4$ .

$- \frac{11}{2} + \frac{24 + 3}{4} - 4 \frac{1}{4}$

Step 3.2.4.2

Add $24$ and $3$ .

$- \frac{11}{2} + \frac{27}{4} - 4 \frac{1}{4}$

Step 4

Convert $4 \frac{1}{4}$ to an improper fraction.

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Step 4.1

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

$- \frac{11}{2} + \frac{27}{4} - (4 + \frac{1}{4})$

Step 4.2

Add $4$ and $\frac{1}{4}$ .

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Step 4.2.1

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

$- \frac{11}{2} + \frac{27}{4} - (4 \cdot \frac{4}{4} + \frac{1}{4})$

Step 4.2.2

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

$- \frac{11}{2} + \frac{27}{4} - (\frac{4 \cdot 4}{4} + \frac{1}{4})$

Step 4.2.3

Combine the numerators over the common denominator.

$- \frac{11}{2} + \frac{27}{4} - \frac{4 \cdot 4 + 1}{4}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $4$ by $4$ .

$- \frac{11}{2} + \frac{27}{4} - \frac{16 + 1}{4}$

Step 4.2.4.2

Add $16$ and $1$ .

$- \frac{11}{2} + \frac{27}{4} - \frac{17}{4}$

Step 5

Combine fractions.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{- 11}{2} + \frac{27 - 17}{4}$

Step 5.2

Subtract $17$ from $27$ .

$\frac{- 11}{2} + \frac{10}{4}$

Step 6

Simplify each term.

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Step 6.1

Move the negative in front of the fraction.

$- \frac{11}{2} + \frac{10}{4}$

Step 6.2

Cancel the common factor of $10$ and $4$ .

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Step 6.2.1

Factor $2$ out of $10$ .

$- \frac{11}{2} + \frac{2 (5)}{4}$

Step 6.2.2

Cancel the common factors.

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Step 6.2.2.1

Factor $2$ out of $4$ .

$- \frac{11}{2} + \frac{2 \cdot 5}{2 \cdot 2}$

Step 6.2.2.2

Cancel the common factor.

$- \frac{11}{2} + \frac{2 \cdot 5}{2 \cdot 2}$

Step 6.2.2.3

Rewrite the expression.

$- \frac{11}{2} + \frac{5}{2}$

Step 7

Combine fractions.

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Step 7.1

Combine the numerators over the common denominator.

$\frac{- 11 + 5}{2}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Add $- 11$ and $5$ .

$\frac{- 6}{2}$

Step 7.2.2

Divide $- 6$ by $2$ .

$- 3$