Pre-Algebra Examples

$5 \div 7 y - 9 \div 14$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{5}{7 y} - 9 \div 14$

Step 1.2

Rewrite the division as a fraction.

$\frac{5}{7 y} - \frac{9}{14}$

Step 2

To write $\frac{5}{7 y}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{7 y} \cdot \frac{2}{2} - \frac{9}{14}$

Step 3

To write $- \frac{9}{14}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{5}{7 y} \cdot \frac{2}{2} - \frac{9}{14} \cdot \frac{y}{y}$

Step 4

Write each expression with a common denominator of $14 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{7 y}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 2}{7 y \cdot 2} - \frac{9}{14} \cdot \frac{y}{y}$

Step 4.2

Multiply $2$ by $7$ .

$\frac{5 \cdot 2}{14 y} - \frac{9}{14} \cdot \frac{y}{y}$

Step 4.3

Multiply $\frac{9}{14}$ by $\frac{y}{y}$ .

$\frac{5 \cdot 2}{14 y} - \frac{9 y}{14 y}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 - 9 y}{14 y}$

Step 6

Multiply $5$ by $2$ .

$\frac{10 - 9 y}{14 y}$