Pre-Algebra Examples

$\frac{5}{6} \div \frac{4}{5} - \frac{5}{8}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{6} \cdot \frac{5}{4} - \frac{5}{8}$

Step 1.2

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

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Step 1.2.1

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

$\frac{5 \cdot 5}{6 \cdot 4} - \frac{5}{8}$

Step 1.2.2

Multiply $5$ by $5$ .

$\frac{25}{6 \cdot 4} - \frac{5}{8}$

Step 1.2.3

Multiply $6$ by $4$ .

$\frac{25}{24} - \frac{5}{8}$

Step 2

To write $- \frac{5}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{25}{24} - \frac{5}{8} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{8}$ by $\frac{3}{3}$ .

$\frac{25}{24} - \frac{5 \cdot 3}{8 \cdot 3}$

Step 3.2

Multiply $8$ by $3$ .

$\frac{25}{24} - \frac{5 \cdot 3}{24}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 - 5 \cdot 3}{24}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 5$ by $3$ .

$\frac{25 - 15}{24}$

Step 5.2

Subtract $15$ from $25$ .

$\frac{10}{24}$

Step 6

Cancel the common factor of $10$ and $24$ .

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Step 6.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{24}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $24$ .

$\frac{2 \cdot 5}{2 \cdot 12}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 12}$

Step 6.2.3

Rewrite the expression.

$\frac{5}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{12}$

Decimal Form:

$0.41\overline{6}$