Question

which number fits between 1/4 and 1/3? hint: change to decimals first!

Explanation:

Step 1: Convert fractions to decimals

First, convert \(\frac{1}{4}\) and \(\frac{1}{3}\) to decimals.
\(\frac{1}{4} = 0.25\) and \(\frac{1}{3} \approx 0.333\cdots\)

Step 2: Find a number between them

We need to find a number \(x\) such that \(0.25 < x < 0.333\cdots\). For example, \(0.26\) (or \(\frac{13}{50}\), since \(13\div50 = 0.26\)) is between \(0.25\) and \(0.333\cdots\). There are infinitely many numbers between them, but a simple one is \(0.26\) (or \(\frac{7}{25}=0.28\), \(\frac{11}{40} = 0.275\) etc.). If we take the average of \(\frac{1}{4}\) and \(\frac{1}{3}\): \(\frac{\frac{1}{4}+\frac{1}{3}}{2}=\frac{\frac{3 + 4}{12}}{2}=\frac{\frac{7}{12}}{2}=\frac{7}{24}\approx0.2917\), which is also between them.

Answer:

A number between \(\frac{1}{4}\) (0.25) and \(\frac{1}{3}\) (≈0.333) is, for example, \(0.26\) (or \(\frac{7}{24}\approx0.2917\), \(\frac{13}{50} = 0.26\), etc.).