Question

roy collected 4 bins of glass bottles to recycle. ling collected 4 1/2 times as many bins as roy. how many bins of bottles did ling collect? write your answer as a fraction or as a whole or mixed number. bins

Explanation:

Step1: Convert mixed number to improper fraction

Ling collected \(4\frac{1}{2}\) times as many bins as Roy. First, convert \(4\frac{1}{2}\) to an improper fraction. \(4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2}\).

Step2: Multiply by Roy's bins

Roy collected 4 bins. So, Ling's bins are \(\frac{9}{2}\times4\). Calculate this: \(\frac{9}{2}\times4 = 9\times2=18\). Wait, no, wait. Wait, \(4\frac{1}{2}\) is \(\frac{9}{2}\), and \(4\) is \(\frac{4}{1}\). So \(\frac{9}{2}\times\frac{4}{1}=\frac{9\times4}{2\times1}=\frac{36}{2} = 18\)? Wait, no, that can't be. Wait, no, Roy collected 4 bins, Ling collected \(4\frac{1}{2}\) times that. Wait, \(4\frac{1}{2}\) times 4. Wait, \(4\frac{1}{2}\) is 4.5, so 4.5 4 = 18? Wait, but let's check again. Wait, \(4\frac{1}{2}\) is \(\frac{9}{2}\), so \(\frac{9}{2}\times4=\frac{9\times4}{2}= \frac{36}{2}=18\). Wait, but maybe I made a mistake. Wait, no, the problem says Ling collected \(4\frac{1}{2}\) times as many as Roy. Roy has 4, so \(4\frac{1}{2}\times4\). Let's do it as mixed number: \(4\frac{1}{2}\times4=(4 + \frac{1}{2})\times4 = 4\times4+\frac{1}{2}\times4=16 + 2 = 18\). Oh, right, that's correct. Wait, but let me check again. Wait, \(4\frac{1}{2}\) is 4.5, 4.54=18. Yes, that's right.

Answer:

18