Final answer:
Josh's prediction that 2 ⅓ + 2 4/5 would be between 4 and 5 is incorrect. The actual sum of these two mixed numbers is 9 2/15, which is significantly greater than 5.
Step-by-step explanation:
Josh is solving the equation 2 ⅓ + 2 4/5 and predicts that his answer will be more than 4 but less than 5. To determine whether Josh's prediction is correct, we need to add the two mixed numbers together. First, convert each mixed number to an improper fraction:
- 2 ⅓ = ⅓ + 2 = (7/3) + (6/3) = 13/3
- 2 4/5 = 4/5 + 2 = (14/5) + (10/5) = 24/5
Next, find a common denominator for the two fractions, which would be 15, and add them together:
- (13/3) * (5/5) = 65/15
- (24/5) * (3/3) = 72/15
Add the fractions:
65/15 + 72/15 = 137/15
Convert the improper fraction back to a mixed number:
137/15 = 9 with a remainder of 2, therefore the mixed number is 9 2/15.
Since 9 2/15 is much greater than 4, Josh's prediction is incorrect.