Question

And divide rational numbers QuickChek

Answer 1

To divide rational numbers, you follow a specific process. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero.

### Steps to Divide Rational Numbers

1. **Write the Division as a Fraction**: Dividing by a number is the same as multiplying by its reciprocal. For example, dividing \( a/b \) by \( c/d \) is the same as multiplying \( a/b \) by \( d/c \).

\[
\frac{a}{b} ÷ \frac{c}{d} = \frac{a}{b} × \frac{d}{c}
\]

2. **Multiply the Fractions**: After converting to multiplication, multiply the numerators together and the denominators together.

\[
\frac{a × d}{b × c}
\]

3. **Simplify**: If possible, simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and denominator.

### Example

Let’s say we want to divide \( \frac{3}{4} \) by \( \frac{2}{5} \).

1. **Write it as Multiplication**:
\[
\frac{3}{4} ÷ \frac{2}{5} = \frac{3}{4} × \frac{5}{2}
\]

2. **Multiply the Fractions**:
\[
= \frac{3 × 5}{4 × 2} = \frac{15}{8}
\]

3. **Simplify**: In this case, \( \frac{15}{8} \) is already in simplest form.

So, \( \frac{3}{4} ÷ \frac{2}{5} = \frac{15}{8} \).

### Additional Tips

- Always remember that dividing a number by zero is undefined.
- When simplifying, you can factor both the numerator and the denominator to find common factors more easily.

If you have any specific questions or examples you want to go over, feel free to ask!