Question

level 157
here are models of two fractions.
which statement about the fractions is true?
select an answer
a (\frac{2}{3}) is closer to 1 than (\frac{3}{4}), because (\frac{1}{3}) is greater than (\frac{1}{4}).
b (\frac{3}{4}) is closer to 1 than (\frac{2}{3}), because (\frac{1}{4}) is less than (\frac{1}{3}).
c (\frac{3}{4}) is closer to 1 than (\frac{2}{3}), because (\frac{1}{4}) is greater than (\frac{1}{5}).
d (\frac{2}{3}) is closer to 1 than (\frac{3}{4}), because (\frac{1}{3}) is less than (\frac{1}{4}).

Explanation:

Step1: Analyze the fractions

The first fraction model (for \(\frac{2}{3}\)) has 1 white part out of 3, so the remaining (distance to 1) is \(\frac{1}{3}\). The second fraction model (for \(\frac{3}{4}\)) has 1 white part out of 4, so the remaining (distance to 1) is \(\frac{1}{4}\).

Step2: Compare the distances to 1

To see which fraction is closer to 1, we compare \(\frac{1}{3}\) and \(\frac{1}{4}\). Since \(\frac{1}{4}<\frac{1}{3}\) (a smaller remaining part means closer to 1), \(\frac{3}{4}\) is closer to 1 than \(\frac{2}{3}\) because \(\frac{1}{4}\) (remaining for \(\frac{3}{4}\)) is less than \(\frac{1}{3}\) (remaining for \(\frac{2}{3}\)).

Answer:

B. \(\frac{3}{4}\) is closer to 1 than \(\frac{2}{3}\), because \(\frac{1}{4}\) is less than \(\frac{1}{3}\).