Final answer:
The new lamp is 1 3/8 feet taller than the old lamp. This was calculated by converting the mixed numerals to improper fractions, finding a common denominator, and then subtracting the heights.
Step-by-step explanation:
To determine how much taller the new lamp is compared to the old one, we will subtract the height of the old lamp from the height of the new lamp. We need to convert the mixed numerals into improper fractions before doing the subtraction.
The old lamp's height is 2 1/4 ft which can be converted to an improper fraction like this: 2 x 4 + 1 = 9/4 ft.
The new lamp's height is 3 5/8 ft,
which converts to: 3 x 8 + 5 = 29/8 ft.
To perform the subtraction, we need a common denominator, which is 8 in this case.
We convert 9/4 to an equivalent fraction with a denominator of 8, multiplying both numerator and denominator by 2, becoming 18/8.
Now we subtract: 29/8 - 18/8 = 11/8 ft. Converting this back to a mixed numeral gives us 1 3/8 ft, which means the new lamp is 1 3/8 feet taller than the old lamp.