An area model has 4 shaded parts and 1 unshaded part. The shaded parts are labeled StartFraction 4 Over 5 EndFraction

Question

4
5
÷ 1
10
= ?

To solve this problem, ask the question

The quotient is
.

Answer 1

To solve the problem using an area model with shaded and unshaded parts, we have the shaded parts representing \( \frac{4}{5} \) and we need to divide this by \( \frac{1}{10} \).

The question we want to ask is: "How many times does \( \frac{1}{10} \) fit into \( \frac{4}{5} \)?"

To find the answer, we can rewrite the division of fractions as multiplication by the reciprocal:

\[ \frac{4}{5} \div \frac{1}{10} = \frac{4}{5} \times \frac{10}{1} \]

Now, we can multiply:

\[ = \frac{4 \times 10}{5 \times 1} = \frac{40}{5} = 8 \]

So, the quotient is \( 8 \).