Pre-Algebra Examples

$- 7 \frac{2}{3} + (- 5 \frac{1}{2}) + 8 \frac{3}{4}$

Step 1

Remove parentheses.

$- 7 \frac{2}{3} - 5 \frac{1}{2} + 8 \frac{3}{4}$

Step 2

Convert $7 \frac{2}{3}$ to an improper fraction.

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Step 2.1

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

$- (7 + \frac{2}{3}) - 5 \frac{1}{2} + 8 \frac{3}{4}$

Step 2.2

Add $7$ and $\frac{2}{3}$ .

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Step 2.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- (7 \cdot \frac{3}{3} + \frac{2}{3}) - 5 \frac{1}{2} + 8 \frac{3}{4}$

Step 2.2.2

Combine $7$ and $\frac{3}{3}$ .

$- (\frac{7 \cdot 3}{3} + \frac{2}{3}) - 5 \frac{1}{2} + 8 \frac{3}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{7 \cdot 3 + 2}{3} - 5 \frac{1}{2} + 8 \frac{3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $7$ by $3$ .

$- \frac{21 + 2}{3} - 5 \frac{1}{2} + 8 \frac{3}{4}$

Step 2.2.4.2

Add $21$ and $2$ .

$- \frac{23}{3} - 5 \frac{1}{2} + 8 \frac{3}{4}$

Step 3

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

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Step 3.1

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

$- \frac{23}{3} - (5 + \frac{1}{2}) + 8 \frac{3}{4}$

Step 3.2

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

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Step 3.2.1

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

$- \frac{23}{3} - (5 \cdot \frac{2}{2} + \frac{1}{2}) + 8 \frac{3}{4}$

Step 3.2.2

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

$- \frac{23}{3} - (\frac{5 \cdot 2}{2} + \frac{1}{2}) + 8 \frac{3}{4}$

Step 3.2.3

Combine the numerators over the common denominator.

$- \frac{23}{3} - \frac{5 \cdot 2 + 1}{2} + 8 \frac{3}{4}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $5$ by $2$ .

$- \frac{23}{3} - \frac{10 + 1}{2} + 8 \frac{3}{4}$

Step 3.2.4.2

Add $10$ and $1$ .

$- \frac{23}{3} - \frac{11}{2} + 8 \frac{3}{4}$

Step 4

Convert $8 \frac{3}{4}$ to an improper fraction.

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Step 4.1

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

$- \frac{23}{3} - \frac{11}{2} + 8 + \frac{3}{4}$

Step 4.2

Add $8$ and $\frac{3}{4}$ .

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Step 4.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{23}{3} - \frac{11}{2} + 8 \cdot \frac{4}{4} + \frac{3}{4}$

Step 4.2.2

Combine $8$ and $\frac{4}{4}$ .

$- \frac{23}{3} - \frac{11}{2} + \frac{8 \cdot 4}{4} + \frac{3}{4}$

Step 4.2.3

Combine the numerators over the common denominator.

$- \frac{23}{3} - \frac{11}{2} + \frac{8 \cdot 4 + 3}{4}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $8$ by $4$ .

$- \frac{23}{3} - \frac{11}{2} + \frac{32 + 3}{4}$

Step 4.2.4.2

Add $32$ and $3$ .

$- \frac{23}{3} - \frac{11}{2} + \frac{35}{4}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{23}{3}$ by $\frac{4}{4}$ .

$- (\frac{23}{3} \cdot \frac{4}{4}) - \frac{11}{2} + \frac{35}{4}$

Step 5.2

Multiply $\frac{23}{3}$ by $\frac{4}{4}$ .

$- \frac{23 \cdot 4}{3 \cdot 4} - \frac{11}{2} + \frac{35}{4}$

Step 5.3

Multiply $\frac{11}{2}$ by $\frac{6}{6}$ .

$- \frac{23 \cdot 4}{3 \cdot 4} - (\frac{11}{2} \cdot \frac{6}{6}) + \frac{35}{4}$

Step 5.4

Multiply $\frac{11}{2}$ by $\frac{6}{6}$ .

$- \frac{23 \cdot 4}{3 \cdot 4} - \frac{11 \cdot 6}{2 \cdot 6} + \frac{35}{4}$

Step 5.5

Multiply $\frac{35}{4}$ by $\frac{3}{3}$ .

$- \frac{23 \cdot 4}{3 \cdot 4} - \frac{11 \cdot 6}{2 \cdot 6} + \frac{35}{4} \cdot \frac{3}{3}$

Step 5.6

Multiply $\frac{35}{4}$ by $\frac{3}{3}$ .

$- \frac{23 \cdot 4}{3 \cdot 4} - \frac{11 \cdot 6}{2 \cdot 6} + \frac{35 \cdot 3}{4 \cdot 3}$

Step 5.7

Multiply $3$ by $4$ .

$- \frac{23 \cdot 4}{12} - \frac{11 \cdot 6}{2 \cdot 6} + \frac{35 \cdot 3}{4 \cdot 3}$

Step 5.8

Multiply $2$ by $6$ .

$- \frac{23 \cdot 4}{12} - \frac{11 \cdot 6}{12} + \frac{35 \cdot 3}{4 \cdot 3}$

Step 5.9

Reorder the factors of $4 \cdot 3$ .

$- \frac{23 \cdot 4}{12} - \frac{11 \cdot 6}{12} + \frac{35 \cdot 3}{3 \cdot 4}$

Step 5.10

Multiply $3$ by $4$ .

$- \frac{23 \cdot 4}{12} - \frac{11 \cdot 6}{12} + \frac{35 \cdot 3}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 23 \cdot 4 - 11 \cdot 6 + 35 \cdot 3}{12}$

Step 7

Simplify each term.

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Step 7.1

Multiply $- 23$ by $4$ .

$\frac{- 92 - 11 \cdot 6 + 35 \cdot 3}{12}$

Step 7.2

Multiply $- 11$ by $6$ .

$\frac{- 92 - 66 + 35 \cdot 3}{12}$

Step 7.3

Multiply $35$ by $3$ .

$\frac{- 92 - 66 + 105}{12}$

Step 8

Simplify the expression.

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Step 8.1

Subtract $66$ from $- 92$ .

$\frac{- 158 + 105}{12}$

Step 8.2

Add $- 158$ and $105$ .

$\frac{- 53}{12}$

Step 8.3

Move the negative in front of the fraction.

$- \frac{53}{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{53}{12}$

Decimal Form:

$- 4.41\overline{6}$

Mixed Number Form:

$- 4 \frac{5}{12}$