1. jim_thompson5910

are you able to convert 2 1/2 to an improper fraction?

2. KaloeMalia

yes

3. KaloeMalia

I did that

4. jim_thompson5910

what is 2 1/2 equal to

5. KaloeMalia

5/2

6. jim_thompson5910

good

7. jim_thompson5910

so you really have 5/2 times 8/9

8. KaloeMalia

yes.

9. jim_thompson5910

multiply straight across (the numerators pair up and multiply; so do the denominators)

10. jim_thompson5910

after multiplying, reduce as much as possible

11. KaloeMalia

40/18? then reduce right?

12. jim_thompson5910

correct

13. KaloeMalia

20/9

14. jim_thompson5910

very good

15. jim_thompson5910

optionally you can convert that result to a mixed number

16. KaloeMalia

but when i tried to turn back into a mixed number but it is a never ending 2.2222222222

17. jim_thompson5910

break that decimal into 2 parts the whole part which is 2 (left of the decimal) the fractional part which is 0.2222 repeating (right of the decimal)

18. jim_thompson5910

the decimal part 0.2222 gets multiplied with the denominator of 9 to get roughly 0.22222*9 = 1.99998 which is effectively 2 (there's a bit of rounding error) so 2.222222... = 2 2/9

19. jim_thompson5910

if you had something like 3.2222222..., then 3.2222222... = 3 2/9 or if you had 7.2222222..., then 7.2222222... = 7 2/9 and so on

20. jim_thompson5910

or you can think of it like this $\Large \frac{20}{9} = \color{red}{2} \text{ remainder } \color{blue}{2}$ $\Large \frac{20}{9} = \color{red}{2} \frac{\color{blue}{2}}{9}$

21. KaloeMalia

so 2 2/9 is my final answer?

22. jim_thompson5910

yes if they want the answer as a mixed number

23. KaloeMalia

okay! Thank you so much!

24. jim_thompson5910

25. mathstudent55

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26. mathstudent55

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