When dividing fractions, the first step is to invert the divisor.
Here's a detailed, step-by-step explanation:
1. Invert the Divisor: Flip the second fraction (the divisor). This means you swap the numerator (top number) and the denominator (bottom number) of the second fraction. For instance, if you are dividing by [tex]\( \frac{a}{b} \)[/tex], you invert it to [tex]\( \frac{b}{a} \)[/tex].
2. Change Division to Multiplication: After inverting the second fraction, you change the division operation to a multiplication operation.
3. Multiply the Fractions: Multiply the numerators of the two fractions together to get the new numerator. Similarly, multiply the denominators of the two fractions together to get the new denominator.
4. Simplify the Result: If possible, simplify the resulting fraction by dividing the numerator and the denominator by their greatest common divisor (GCD).
For example, let's divide [tex]\( \frac{3}{4} \)[/tex] by [tex]\( \frac{2}{5} \)[/tex]:
- Step 1: Invert the divisor: [tex]\( \frac{2}{5} \)[/tex] becomes [tex]\( \frac{5}{2} \)[/tex].
- Step 2: Change the division to multiplication: [tex]\( \frac{3}{4} \div \frac{2}{5} \)[/tex] turns into [tex]\( \frac{3}{4} \times \frac{5}{2} \)[/tex].
- Step 3: Multiply the fractions: [tex]\( \frac{3 \times 5}{4 \times 2} = \frac{15}{8} \)[/tex].
- Step 4: Simplify if possible (in this case, [tex]\( \frac{15}{8} \)[/tex] is already in simplest form).
Thus, the first step when dividing fractions is to invert the divisor.
