Algebra Examples

$2 + \frac{7}{8} - \frac{5}{6}$

Step 1

Find the common denominator.

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Step 1.1

Write $2$ as a fraction with denominator $1$ .

$\frac{2}{1} + \frac{7}{8} - \frac{5}{6}$

Step 1.2

Multiply $\frac{2}{1}$ by $\frac{24}{24}$ .

$\frac{2}{1} \cdot \frac{24}{24} + \frac{7}{8} - \frac{5}{6}$

Step 1.3

Multiply $\frac{2}{1}$ by $\frac{24}{24}$ .

$\frac{2 \cdot 24}{24} + \frac{7}{8} - \frac{5}{6}$

Step 1.4

Multiply $\frac{7}{8}$ by $\frac{3}{3}$ .

$\frac{2 \cdot 24}{24} + \frac{7}{8} \cdot \frac{3}{3} - \frac{5}{6}$

Step 1.5

Multiply $\frac{7}{8}$ by $\frac{3}{3}$ .

$\frac{2 \cdot 24}{24} + \frac{7 \cdot 3}{8 \cdot 3} - \frac{5}{6}$

Step 1.6

Multiply $\frac{5}{6}$ by $\frac{4}{4}$ .

$\frac{2 \cdot 24}{24} + \frac{7 \cdot 3}{8 \cdot 3} - (\frac{5}{6} \cdot \frac{4}{4})$

Step 1.7

Multiply $\frac{5}{6}$ by $\frac{4}{4}$ .

$\frac{2 \cdot 24}{24} + \frac{7 \cdot 3}{8 \cdot 3} - \frac{5 \cdot 4}{6 \cdot 4}$

Step 1.8

Reorder the factors of $8 \cdot 3$ .

$\frac{2 \cdot 24}{24} + \frac{7 \cdot 3}{3 \cdot 8} - \frac{5 \cdot 4}{6 \cdot 4}$

Step 1.9

Multiply $3$ by $8$ .

$\frac{2 \cdot 24}{24} + \frac{7 \cdot 3}{24} - \frac{5 \cdot 4}{6 \cdot 4}$

Step 1.10

Reorder the factors of $6 \cdot 4$ .

$\frac{2 \cdot 24}{24} + \frac{7 \cdot 3}{24} - \frac{5 \cdot 4}{4 \cdot 6}$

Step 1.11

Multiply $4$ by $6$ .

$\frac{2 \cdot 24}{24} + \frac{7 \cdot 3}{24} - \frac{5 \cdot 4}{24}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 \cdot 24 + 7 \cdot 3 - 5 \cdot 4}{24}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $24$ .

$\frac{48 + 7 \cdot 3 - 5 \cdot 4}{24}$

Step 3.2

Multiply $7$ by $3$ .

$\frac{48 + 21 - 5 \cdot 4}{24}$

Step 3.3

Multiply $- 5$ by $4$ .

$\frac{48 + 21 - 20}{24}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Add $48$ and $21$ .

$\frac{69 - 20}{24}$

Step 4.2

Subtract $20$ from $69$ .

$\frac{49}{24}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{24}$

Decimal Form:

$2.041\overline{6}$

Mixed Number Form:

$2 \frac{1}{24}$