The diameter of Alana's basketball is 8 1/3 inches and the diameter of her hoop is 17 1/2 inches. How much greater is the diameter of Alana's hoop than the diameter of her basketball?
Write your answer as a fraction or as a whole or mixed number.
inches
The difference in diameter between the hoop and the basketball is 17 1/2 inches - 8 1/3 inches. To subtract these mixed numbers, first convert them to improper fractions:
17 1/2 inches = (17*2 + 1)/2 = 35/2 inches
8 1/3 inches = (8*3 + 1)/3 = 25/3 inches
So, the difference in diameter is 35/2 inches - 25/3 inches.
To subtract fractions, we need to have a common denominator. Since 2 and 3 have a common multiple of 6, let's express each fraction with a denominator of 6:
35/2 = (35/2) * (3/3) = 105/6
25/3 = (25/3) * (2/2) = 50/6
Now we can subtract the fractions:
105/6 - 50/6 = (105 - 50)/6 = 55/6
Therefore, the diameter of the hoop is 55/6 inches greater than the diameter of the basketball.