Pre-Algebra Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $42$ .

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Step 1.1

Multiply $\frac{3 + \frac{1}{6}}{5 - \frac{3}{7}}$ by $\frac{42}{42}$ .

$\frac{42}{42} \cdot \frac{3 + \frac{1}{6}}{5 - \frac{3}{7}}$

Step 1.2

Combine.

$\frac{42 (3 + \frac{1}{6})}{42 (5 - \frac{3}{7})}$

Step 2

Apply the distributive property.

$\frac{42 \cdot 3 + 42 (\frac{1}{6})}{42 \cdot 5 + 42 (- \frac{3}{7})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $6$ .

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Step 3.1.1

Factor $6$ out of $42$ .

$\frac{42 \cdot 3 + 6 (7) \frac{1}{6}}{42 \cdot 5 + 42 (- \frac{3}{7})}$

Step 3.1.2

Cancel the common factor.

$\frac{42 \cdot 3 + 6 \cdot 7 \frac{1}{6}}{42 \cdot 5 + 42 (- \frac{3}{7})}$

Step 3.1.3

Rewrite the expression.

$\frac{42 \cdot 3 + 7}{42 \cdot 5 + 42 (- \frac{3}{7})}$

Step 3.2

Cancel the common factor of $7$ .

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Step 3.2.1

Move the leading negative in $- \frac{3}{7}$ into the numerator.

$\frac{42 \cdot 3 + 7}{42 \cdot 5 + 42 (\frac{- 3}{7})}$

Step 3.2.2

Factor $7$ out of $42$ .

$\frac{42 \cdot 3 + 7}{42 \cdot 5 + 7 (6) \frac{- 3}{7}}$

Step 3.2.3

Cancel the common factor.

$\frac{42 \cdot 3 + 7}{42 \cdot 5 + 7 \cdot 6 \frac{- 3}{7}}$

Step 3.2.4

Rewrite the expression.

$\frac{42 \cdot 3 + 7}{42 \cdot 5 + 6 \cdot - 3}$

Step 3.3

Multiply $6$ by $- 3$ .

$\frac{42 \cdot 3 + 7}{42 \cdot 5 - 18}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $42$ by $3$ .

$\frac{126 + 7}{42 \cdot 5 - 18}$

Step 4.2

Add $126$ and $7$ .

$\frac{133}{42 \cdot 5 - 18}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $42$ by $5$ .

$\frac{133}{210 - 18}$

Step 5.2

Subtract $18$ from $210$ .

$\frac{133}{192}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{133}{192}$

Decimal Form:

$0.692708\overline{3}$