Basic Math Examples

$\frac{5 y + 40}{- 20} \div \frac{3 y + 24}{20}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 y + 40}{- 20} \cdot \frac{20}{3 y + 24}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $20$ .

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Step 2.1.1

Factor $20$ out of $- 20$ .

$\frac{5 y + 40}{20 (- 1)} \cdot \frac{20}{3 y + 24}$

Step 2.1.2

Cancel the common factor.

$\frac{5 y + 40}{20 \cdot - 1} \cdot \frac{20}{3 y + 24}$

Step 2.1.3

Rewrite the expression.

$\frac{5 y + 40}{- 1} \cdot \frac{1}{3 y + 24}$

Step 2.2

Multiply $\frac{5 y + 40}{- 1}$ by $\frac{1}{3 y + 24}$ .

$\frac{5 y + 40}{- (3 y + 24)}$

Step 2.3

Factor $5$ out of $5 y + 40$ .

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Step 2.3.1

Factor $5$ out of $5 y$ .

$\frac{5 (y) + 40}{- (3 y + 24)}$

Step 2.3.2

Factor $5$ out of $40$ .

$\frac{5 y + 5 \cdot 8}{- (3 y + 24)}$

Step 2.3.3

Factor $5$ out of $5 y + 5 \cdot 8$ .

$\frac{5 (y + 8)}{- (3 y + 24)}$

Step 3

Simplify the denominator.

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Step 3.1

Factor $3$ out of $3 y + 24$ .

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Step 3.1.1

Factor $3$ out of $3 y$ .

$\frac{5 (y + 8)}{- (3 (y) + 24)}$

Step 3.1.2

Factor $3$ out of $24$ .

$\frac{5 (y + 8)}{- (3 y + 3 \cdot 8)}$

Step 3.1.3

Factor $3$ out of $3 y + 3 \cdot 8$ .

$\frac{5 (y + 8)}{- (3 (y + 8))}$

$\frac{5 (y + 8)}{- 1 \cdot 3 (y + 8)}$

Step 3.2

Multiply $- 1$ by $3$ .

$\frac{5 (y + 8)}{- 3 (y + 8)}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $y + 8$ .

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Step 4.1.1

Cancel the common factor.

$\frac{5 (y + 8)}{- 3 (y + 8)}$

Step 4.1.2

Rewrite the expression.

$\frac{5}{- 3}$

Step 4.2

Move the negative in front of the fraction.

$- \frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{3}$

Decimal Form:

$- 1.\overline{6}$

Mixed Number Form:

$- 1 \frac{2}{3}$