Final answer:
Jessie needs an additional 19/24 gallons of paint to complete painting her room. We arrived at this answer by converting mixed numbers to improper fractions, finding a common denominator, and then subtracting the fractions.
Step-by-step explanation:
Jessie needs a total of 1 5/8 gallons of paint, but she currently has only 5/6 of a gallon. To find out how much more paint she needs, we must subtract the amount she has from the amount required.
Firstly, convert the mixed number to an improper fraction: 1 5/8 = (1×8 + 5)/8 = (8/8 + 5/8) = 13/8.
Now, subtract the fraction representing the paint she has from the total required:
- Total paint needed: 13/8 gallons
- Paint Jessie has: 5/6 gallons
To subtract these, find a common denominator. The least common multiple of 8 and 6 is 24. Convert both fractions to have this common denominator:
- 13/8 = (13×3)/(8×3) = 39/24
- 5/6 = (5×4)/(6×4) = 20/24
Now subtract the second fraction from the first:
39/24 - 20/24 = 19/24 gallons
Jessie still needs 19/24 gallons of paint to have enough to paint her room.