Elizabeth was helping her sister make their mother a necklace. They had 3 6/8 cups of beads. When they finished, they had 1 2/4 cups left. How many cups of beads did Elizabeth and her sister use?%C2%A0 Write your answer in simplest form.
To find the amount of beads that Elizabeth and her sister used, we need to subtract the amount left from the amount they started with.
We can rewrite 3 6/8 as an improper fraction by multiplying the whole number by the denominator and adding the numerator:
= (3 * 8) + 6/8 = 24/8 + 6/8 = 30/8
So, they started with 30/8 cups of beads.
To find the amount used, we subtract the amount left from the amount they started with:
30/8 - 1 2/4 = 30/8 - 6/4
We need to make the denominators the same, so we rewrite 30/8 as 30/8 * 2/2 = 60/16.
60/16 - 6/4 = 60/16 - 24/16 = 36/16.
We can simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:
= (36/4) / (16/4) = 9/4.
Therefore, Elizabeth and her sister used 9/4 cups of beads or 2 1/4 cups of beads.