Question

5
for each statement, decide whether the number that should go in the blank is greater than 1 or less than 1, and then find that number.
draw a tape diagram to represent the question: what fraction of 2\frac{1}{2} is \frac{4}{5}?
then find the answer.

Explanation:

Step 1: Convert mixed number to improper fraction

First, convert \(2\frac{1}{2}\) to an improper fraction. \(2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}\). We want to find what fraction \(x\) satisfies \(x\times\frac{5}{2}=\frac{4}{5}\). So we need to solve for \(x\) by dividing \(\frac{4}{5}\) by \(\frac{5}{2}\).

Step 2: Divide the fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So \(x=\frac{4}{5}\div\frac{5}{2}=\frac{4}{5}\times\frac{2}{5}=\frac{8}{25}\). Now, check if \(\frac{8}{25}\) is less than 1 (since \(\frac{8}{25}<1\) as the numerator is less than the denominator).

Answer:

The fraction is \(\frac{8}{25}\) (and it is less than 1).