A cabinet has shelves that are 12 1/2 in. apart. On one shelf, Katherine stacked a CD player that is 4 5/8 in/ high on top of an amplifier that is 6 3/4 in. high. How much space was left above the CD player?
I got 1 1/4; I added 6 3/4 and 4 5/8 and got 11 2/8. Then I subtracted it from 12 1/2.
I get the player's and amp's combined height is 11 3/8 inches.
To find out how much space is left above the CD player, you correctly added the heights of the CD player and the amplifier: 6 3/4 + 4 5/8 = 11 2/8 inches.
Next, you subtracted this total height from the distance between the shelves: 12 1/2 - 11 2/8 = 1 1/4 inches.
Therefore, there is 1 1/4 inches of space left above the CD player on the shelf. Good job with your calculations!
Your approach to solving the problem was correct. Let's go through the steps again to double-check the calculations:
1. Add the height of the CD player (4 5/8 in) and the height of the amplifier (6 3/4 in):
4 5/8 + 6 3/4 = 33/8 + 27/4 = 99/8 + 54/8 = 153/8 inches
2. Convert the resulting fraction to a mixed number:
153/8 inches = 19 1/8 inches
3. Subtract the combined height of the CD player and amplifier from the distance between the shelves (12 1/2 in):
12 1/2 - 19 1/8 = 25/2 - 19 1/8 = 25/2 - 153/8
Now, let's simplify the subtraction:
- Find a common denominator for 2 (the denominator of 25/2) and 8 (the denominator of 153/8):
The least common multiple of 2 and 8 is 8.
- Rewrite the fractions with the common denominator of 8:
25/2 = 100/8, and 153/8 remains the same.
- Perform the subtraction:
100/8 - 153/8 = -53/8
Therefore, the result is -53/8 inches.
It seems there is an error in your calculation at the step where you subtracted 11 2/8 from 12 1/2. The correct answer is -53/8 inches, indicating that there was not enough space above the CD player to fit it properly.