Pre-Algebra Examples

$\frac{7}{5} - \frac{7}{12} + \frac{1}{6}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{7}{5}$ by $\frac{12}{12}$ .

$\frac{7}{5} \cdot \frac{12}{12} - \frac{7}{12} + \frac{1}{6}$

Step 1.2

Multiply $\frac{7}{5}$ by $\frac{12}{12}$ .

$\frac{7 \cdot 12}{5 \cdot 12} - \frac{7}{12} + \frac{1}{6}$

Step 1.3

Multiply $\frac{7}{12}$ by $\frac{5}{5}$ .

$\frac{7 \cdot 12}{5 \cdot 12} - (\frac{7}{12} \cdot \frac{5}{5}) + \frac{1}{6}$

Step 1.4

Multiply $\frac{7}{12}$ by $\frac{5}{5}$ .

$\frac{7 \cdot 12}{5 \cdot 12} - \frac{7 \cdot 5}{12 \cdot 5} + \frac{1}{6}$

Step 1.5

Multiply $\frac{1}{6}$ by $\frac{10}{10}$ .

$\frac{7 \cdot 12}{5 \cdot 12} - \frac{7 \cdot 5}{12 \cdot 5} + \frac{1}{6} \cdot \frac{10}{10}$

Step 1.6

Multiply $\frac{1}{6}$ by $\frac{10}{10}$ .

$\frac{7 \cdot 12}{5 \cdot 12} - \frac{7 \cdot 5}{12 \cdot 5} + \frac{10}{6 \cdot 10}$

Step 1.7

Multiply $5$ by $12$ .

$\frac{7 \cdot 12}{60} - \frac{7 \cdot 5}{12 \cdot 5} + \frac{10}{6 \cdot 10}$

Step 1.8

Reorder the factors of $12 \cdot 5$ .

$\frac{7 \cdot 12}{60} - \frac{7 \cdot 5}{5 \cdot 12} + \frac{10}{6 \cdot 10}$

Step 1.9

Multiply $5$ by $12$ .

$\frac{7 \cdot 12}{60} - \frac{7 \cdot 5}{60} + \frac{10}{6 \cdot 10}$

Step 1.10

Multiply $6$ by $10$ .

$\frac{7 \cdot 12}{60} - \frac{7 \cdot 5}{60} + \frac{10}{60}$

Step 2

Combine the numerators over the common denominator.

$\frac{7 \cdot 12 - 7 \cdot 5 + 10}{60}$

Step 3

Simplify each term.

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Step 3.1

Multiply $7$ by $12$ .

$\frac{84 - 7 \cdot 5 + 10}{60}$

Step 3.2

Multiply $- 7$ by $5$ .

$\frac{84 - 35 + 10}{60}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Subtract $35$ from $84$ .

$\frac{49 + 10}{60}$

Step 4.2

Add $49$ and $10$ .

$\frac{59}{60}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{60}$

Decimal Form:

$0.98\overline{3}$