To show that multiplying by a reciprocal is the same as dividing by a number, we need an equation that illustrates this concept clearly.
The principle here is that when you divide by a fraction, it's equivalent to multiplying by its reciprocal. The reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \).
Now, let's evaluate the options you've provided in this context:
A) \( \frac{7}{\frac{2}{3}} = \frac{1}{7} \cdot \frac{3}{2} \)
- This is incorrect because it does not illustrate the reciprocal.
B) \( \frac{5}{\frac{1}{6}} = 5 \cdot \frac{6}{1} \)
- Correct: Dividing 5 by \( \frac{1}{6} \) is the same as multiplying by 6 (the reciprocal of \( \frac{1}{6} \)).
C) \( 8 \div \frac{2}{3} = \frac{1}{8} \cdot \frac{19}{8} \)
- Incorrect: Does not represent the reciprocal correctly.
D) \( \frac{6}{\frac{1}{6}} = 6 \cdot \frac{7}{6} \)
- Incorrect: This is also not demonstrating the reciprocal multiplication.
The correct choice that exemplifies the concept of dividing by a number being the same as multiplying by its reciprocal is option B: \( \frac{5}{\frac{1}{6}} = 5 \cdot \frac{6}{1} \).
1 answer