Pre-Algebra Examples

$3 - \frac{6}{7} \div \frac{5}{3} + \frac{1}{2}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$3 - (\frac{6}{7} \cdot \frac{3}{5}) + \frac{1}{2}$

Step 1.2

Multiply $\frac{6}{7} \cdot \frac{3}{5}$ .

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Step 1.2.1

Multiply $\frac{6}{7}$ by $\frac{3}{5}$ .

$3 - \frac{6 \cdot 3}{7 \cdot 5} + \frac{1}{2}$

Step 1.2.2

Multiply $6$ by $3$ .

$3 - \frac{18}{7 \cdot 5} + \frac{1}{2}$

Step 1.2.3

Multiply $7$ by $5$ .

$3 - \frac{18}{35} + \frac{1}{2}$

Step 2

Find the common denominator.

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Step 2.1

Write $3$ as a fraction with denominator $1$ .

$\frac{3}{1} - \frac{18}{35} + \frac{1}{2}$

Step 2.2

Multiply $\frac{3}{1}$ by $\frac{70}{70}$ .

$\frac{3}{1} \cdot \frac{70}{70} - \frac{18}{35} + \frac{1}{2}$

Step 2.3

Multiply $\frac{3}{1}$ by $\frac{70}{70}$ .

$\frac{3 \cdot 70}{70} - \frac{18}{35} + \frac{1}{2}$

Step 2.4

Multiply $\frac{18}{35}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 70}{70} - (\frac{18}{35} \cdot \frac{2}{2}) + \frac{1}{2}$

Step 2.5

Multiply $\frac{18}{35}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 70}{70} - \frac{18 \cdot 2}{35 \cdot 2} + \frac{1}{2}$

Step 2.6

Multiply $\frac{1}{2}$ by $\frac{35}{35}$ .

$\frac{3 \cdot 70}{70} - \frac{18 \cdot 2}{35 \cdot 2} + \frac{1}{2} \cdot \frac{35}{35}$

Step 2.7

Multiply $\frac{1}{2}$ by $\frac{35}{35}$ .

$\frac{3 \cdot 70}{70} - \frac{18 \cdot 2}{35 \cdot 2} + \frac{35}{2 \cdot 35}$

Step 2.8

Reorder the factors of $35 \cdot 2$ .

$\frac{3 \cdot 70}{70} - \frac{18 \cdot 2}{2 \cdot 35} + \frac{35}{2 \cdot 35}$

Step 2.9

Multiply $2$ by $35$ .

$\frac{3 \cdot 70}{70} - \frac{18 \cdot 2}{70} + \frac{35}{2 \cdot 35}$

Step 2.10

Multiply $2$ by $35$ .

$\frac{3 \cdot 70}{70} - \frac{18 \cdot 2}{70} + \frac{35}{70}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 \cdot 70 - 18 \cdot 2 + 35}{70}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $70$ .

$\frac{210 - 18 \cdot 2 + 35}{70}$

Step 4.2

Multiply $- 18$ by $2$ .

$\frac{210 - 36 + 35}{70}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $36$ from $210$ .

$\frac{174 + 35}{70}$

Step 5.2

Add $174$ and $35$ .

$\frac{209}{70}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{209}{70}$

Decimal Form:

$2.98571428 \dots$

Mixed Number Form:

$2 \frac{69}{70}$