Final answer:
To determine the amount of flour left, we convert Rachel's original amount of flour to an improper fraction (45/16 pounds), calculate (2/3) of that amount, resulting in 15/8 pounds used for the recipe, and then subtract that from the original amount to get 15/16 pounds of flour remaining.
Step-by-step explanation:
To find out how many pounds of flour Rachel has left after using ¾ of the bag for a recipe, we will first need to determine what ¾ of 2⅛ (or 2.8125 in decimal form) pounds of flour is.
Firstly, let's convert the mixed number to an improper fraction:
- 2⅛ pounds = ⅛ + 2 = ⅛ pounds = 45/16 pounds
Now calculate ¾ of the flour:
- ¾ of 45/16 pounds = (2/3) × (45/16) = (2×45)/(3×16) = 90/48
- Reduce the fraction 90/48 to its simplest form, which is 15/8 or 1⅛ pounds
Since Rachel uses 1⅛ pounds for her recipe, we subtract this amount from the total:
- 2⅛ pounds - 1⅛ pounds = 45/16 pounds - 15/8 pounds
- To make the denominators the same, we can multiply the numerator and denominator of the second fraction by 2, giving us 15/8 to 30/16.
- Now we subtract: 45/16 - 30/16 = 15/16 pounds left
Rachel has 15/16 pounds of flour left in the bag.