Which shows the correct way to use the rule “multiply by the reciprocal” for the expression below?

Question

5 divided by StartFraction 2 Over 9 EndFraction
StartFraction 5 Over 1 EndFraction times StartFraction 9 Over 2 EndFraction = StartFraction 45 Over 2 EndFraction
StartFraction 5 Over 1 EndFraction times StartFraction 2 Over 9 EndFraction = StartFraction 10 Over 9 EndFraction
StartFraction 1 Over 5 EndFraction times StartFraction 9 Over 2 EndFraction = StartFraction 9 Over 10 EndFraction
StartFraction 1 Over 5 EndFraction times StartFraction 2 Over 9 EndFraction = StartFraction 2 Over 45 EndFraction

Answer 1

To apply the rule "multiply by the reciprocal" correctly, we first need to express the division of 5 by a fraction \( \frac{2}{9} \) in multiplication by its reciprocal.

The expression \( 5 \div \frac{2}{9} \) can be rewritten as \( 5 \times \frac{9}{2} \).

Now let's analyze the options:

1. Option 1: \( \frac{5}{1} \times \frac{9}{2} = \frac{45}{2} \)

   • This is correct: \( 5 \times \frac{9}{2} = \frac{45}{2} \).

2. Option 2: \( \frac{5}{1} \times \frac{2}{9} = \frac{10}{9} \)

   • This is incorrect for our original problem.

3. Option 3: \( \frac{1}{5} \times \frac{9}{2} = \frac{9}{10} \)

   • This is incorrect for our original problem.

4. Option 4: \( \frac{1}{5} \times \frac{2}{9} = \frac{2}{45} \)

   • This is incorrect for our original problem.

Thus, the correct way to use the rule “multiply by the reciprocal” for the given expression is Option 1: \[ \frac{5}{1} \times \frac{9}{2} = \frac{45}{2} \]