Final answer:
After converting Janet's leftover cakes and the donated cakes to improper fractions, we found the common denominator and subtracted the two. Janet had 5(1)/(6) birthday cakes remaining after the donation. So, 31/6 becomes 5(1)/(6), meaning Janet had 5(1)/(6) birthday cakes remaining.
Step-by-step explanation:
The student asked how many birthday cakes remained after Janet donated some to the children's hospital. To find this, we subtract the number of cakes donated from the total number of cakes. Janet had 10(5)/(6) leftover birthday cakes and she donated 5(2)/(3) birthday cakes.
To perform the subtraction, we first convert the mixed numbers to improper fractions:
- 10(5)/(6) = (10 × 6 + 5)/6 = 65/6
- 5(2)/(3) = (5 × 3 + 2)/3 = 17/3
Then we find a common denominator, which is 6, and convert the second fraction:
- 17/3 = (17 × 2)/(3 × 2) = 34/6
Now we subtract the two fractions:
- 65/6 - 34/6 = (65 - 34)/6 = 31/6
To convert the improper fraction back to a mixed number, we divide 31 by 6:
- 31 ÷ 6 = 5 with a remainder of 1
So, 31/6 becomes 5(1)/(6), meaning Janet had 5(1)/(6) birthday cakes remaining.