Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Convert $3 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

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

Step 2.2

Add $3$ and $\frac{1}{3}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $3$ .

$\frac{9 + 1}{3} - 2 \frac{1}{4} + 1 \frac{5}{6}$

Step 2.2.4.2

Add $9$ and $1$ .

$\frac{10}{3} - 2 \frac{1}{4} + 1 \frac{5}{6}$

Step 3

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{10}{3} - (2 + \frac{1}{4}) + 1 \frac{5}{6}$

Step 3.2

Add $2$ and $\frac{1}{4}$ .

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Step 3.2.1

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

$\frac{10}{3} - (2 \cdot \frac{4}{4} + \frac{1}{4}) + 1 \frac{5}{6}$

Step 3.2.2

Combine $2$ and $\frac{4}{4}$ .

$\frac{10}{3} - (\frac{2 \cdot 4}{4} + \frac{1}{4}) + 1 \frac{5}{6}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{10}{3} - \frac{2 \cdot 4 + 1}{4} + 1 \frac{5}{6}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $4$ .

$\frac{10}{3} - \frac{8 + 1}{4} + 1 \frac{5}{6}$

Step 3.2.4.2

Add $8$ and $1$ .

$\frac{10}{3} - \frac{9}{4} + 1 \frac{5}{6}$

Step 4

Convert $1 \frac{5}{6}$ to an improper fraction.

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Step 4.1

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

$\frac{10}{3} - \frac{9}{4} + 1 + \frac{5}{6}$

Step 4.2

Add $1$ and $\frac{5}{6}$ .

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Step 4.2.1

Write $1$ as a fraction with a common denominator.

$\frac{10}{3} - \frac{9}{4} + \frac{6}{6} + \frac{5}{6}$

Step 4.2.2

Combine the numerators over the common denominator.

$\frac{10}{3} - \frac{9}{4} + \frac{6 + 5}{6}$

Step 4.2.3

Add $6$ and $5$ .

$\frac{10}{3} - \frac{9}{4} + \frac{11}{6}$

Step 5

Find the common denominator.

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Step 5.1

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

$\frac{10}{3} \cdot \frac{4}{4} - \frac{9}{4} + \frac{11}{6}$

Step 5.2

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

$\frac{10 \cdot 4}{3 \cdot 4} - \frac{9}{4} + \frac{11}{6}$

Step 5.3

Multiply $\frac{9}{4}$ by $\frac{3}{3}$ .

$\frac{10 \cdot 4}{3 \cdot 4} - (\frac{9}{4} \cdot \frac{3}{3}) + \frac{11}{6}$

Step 5.4

Multiply $\frac{9}{4}$ by $\frac{3}{3}$ .

$\frac{10 \cdot 4}{3 \cdot 4} - \frac{9 \cdot 3}{4 \cdot 3} + \frac{11}{6}$

Step 5.5

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

$\frac{10 \cdot 4}{3 \cdot 4} - \frac{9 \cdot 3}{4 \cdot 3} + \frac{11}{6} \cdot \frac{2}{2}$

Step 5.6

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

$\frac{10 \cdot 4}{3 \cdot 4} - \frac{9 \cdot 3}{4 \cdot 3} + \frac{11 \cdot 2}{6 \cdot 2}$

Step 5.7

Multiply $3$ by $4$ .

$\frac{10 \cdot 4}{12} - \frac{9 \cdot 3}{4 \cdot 3} + \frac{11 \cdot 2}{6 \cdot 2}$

Step 5.8

Reorder the factors of $4 \cdot 3$ .

$\frac{10 \cdot 4}{12} - \frac{9 \cdot 3}{3 \cdot 4} + \frac{11 \cdot 2}{6 \cdot 2}$

Step 5.9

Multiply $3$ by $4$ .

$\frac{10 \cdot 4}{12} - \frac{9 \cdot 3}{12} + \frac{11 \cdot 2}{6 \cdot 2}$

Step 5.10

Reorder the factors of $6 \cdot 2$ .

$\frac{10 \cdot 4}{12} - \frac{9 \cdot 3}{12} + \frac{11 \cdot 2}{2 \cdot 6}$

Step 5.11

Multiply $2$ by $6$ .

$\frac{10 \cdot 4}{12} - \frac{9 \cdot 3}{12} + \frac{11 \cdot 2}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{10 \cdot 4 - 9 \cdot 3 + 11 \cdot 2}{12}$

Step 7

Simplify each term.

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Step 7.1

Multiply $10$ by $4$ .

$\frac{40 - 9 \cdot 3 + 11 \cdot 2}{12}$

Step 7.2

Multiply $- 9$ by $3$ .

$\frac{40 - 27 + 11 \cdot 2}{12}$

Step 7.3

Multiply $11$ by $2$ .

$\frac{40 - 27 + 22}{12}$

Step 8

Simplify by adding and subtracting.

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Step 8.1

Subtract $27$ from $40$ .

$\frac{13 + 22}{12}$

Step 8.2

Add $13$ and $22$ .

$\frac{35}{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{12}$

Decimal Form:

$2.91\overline{6}$

Mixed Number Form:

$2 \frac{11}{12}$