Question

Amanda was given three numbers: 8,5, and 1. She needs to use two ofthese numbers to make a fraction.Can she make a fraction that isgreater than four-fifths?

Answer 1

We will have the following:

Amanda will be able to construct the following fractions:

`\mleft\lbrace(1)/(8),(1)/(5),(8)/(5),(5)/(8),(8)/(1),(5)/(1)\mright\rbrace`

From these, the fractions that are greater than 4/5 are:

`\mleft\lbrace(8)/(5),(8)/(1),(5)/(1)\mright\rbrace`

So, yes; Amanda will be able to make a fraction that is greater than 4/5.

***Explanation***

We are trying to find a fraction with a value greater than 4/5, that is:

`(4)/(5)=0.8`

So, a fraction that has a value greater than 0.8.

From the values given, when we solve for the selected fractions we will obtain:

`\begin{cases}(8)/(5)=1.6 \\ \\ (8)/(1)=8 \\ \\ (5)/(1)=5\end{cases}`

All these values are greater than 0.8 and thus the fractions which represent them are greater than 4/5.