Rational numbers: find a rational number 31/10 and 16/5

[dell]

my teacher gave us work that we never went over.
help pleaseeeeeee.

find a rational number 31/10 and 16/5

 

[mmm4444bot]

Re: Rational numbers

find a rational number 31/10 and 16/5

Of course, I'm just guessing, but I'm changing your teacher's problem.

Find a rational number between 31/10 and 16/5.

(If you are in a calculus class, then you should be able to easily convert 16/5 to 32/10.)

One number between 31/10 and 32/10 is the number that appears midway between them on the number line. There are different ways to determine this number.

Or, you could skip all that, and just say 31/10 + 1/100.

Cheers,

~ Mark

 

[Denis]

Or (to expand on Mark's idea) change your fractions to 310/100 and 320/100;
then you can easily impress your teacher with 9 "nice" solutions: 311/100, 312/100, ... , 319/100 :idea:

 

[soroban]

Hello, dell!

my teacher gave us work that we never went over.
. . He/she probably expected to do some Thinking . . . the rat!

$\displaystyle \text{Find a rational number between }\frac{31}{10}\text{ and }\frac{16}{5}$

There are dozens of ways to find an answer . . . Here's one using baby-talk.


$\displaystyle \text{Let's see ... we want a number between }\,3 + \frac{1}{10}\,\text{ and }\,3 + \frac{1}{5}$

\(\displaystyle \text{Se we want a fraction between }\frac{1}{10}\text{ and }\frac{1}{5} \quad\hdots\quad\text{ between }\frac{1}{10}\text{ and }\frac{2}{10}\)


$\displaystyle \text{What number is between }{\bf one}\text{-tenth and }{\bf two}\text{-tenths?}$
. . $\displaystyle \text{How about }{\bf one\text{-}and\text{-}a\text{-}half}\text{ tenths?}$

\(\displaystyle \text{So, we have: }\;\frac{1\frac{1}{2}}{10} \:=\:\frac{\frac{3}{2}}{10} + \frac{3}{20}\quad\hdots\:\text{ There!}\)


$\displaystyle \text{Therefore, one possible answer is: }\;3 + \frac{3}{20} \;=\;\boxed{\frac{63}{20}}$

 

[MathHelpPlease]

To make everything "easy", you could convert everything to decimals.
For example, 31/10 would be 3 1/10 or 3.1
And, 16/5 would be 3 1/5 or 3.2
What's between 3.1 and 3.2? Well, how about 3.15?
So, that would be 3 and 15/100 which simplifies to 3 and 3/20