What is the quotient of 72 divided by 0.75?
The Correct Answer and Explanation is:
Answer:
The quotient of 72 divided by 0.75 is 96.
Explanation
To find the quotient of 72 divided by 0.75, we need to understand what division means in this context. Division tells us how many times the divisor (in this case, 0.75) fits into the dividend (72). In simpler terms, we are asking, “How many groups of 0.75 are there in 72?”
One effective way to perform this calculation is to eliminate the decimal from the divisor. This can be done by multiplying both the dividend and the divisor by the same number — in this case, 100 will turn 0.75 into 75. However, multiplying both by 100 might be more than needed. A simpler method is to multiply both numbers by 100 only if necessary. In our case, multiplying both numbers by 100 is not wrong, but a more efficient step is to multiply both by 100 to remove the decimal completely and then simplify the division.
Let’s do this step-by-step:
- Convert 0.75 to a fraction:
0.75 = 75/100
Simplify the fraction: 75/100 = 3/4 - Rewrite the division:
72 ÷ 0.75 = 72 ÷ (3/4) - Dividing by a fraction:
To divide by a fraction, multiply by its reciprocal.
So, 72 ÷ (3/4) = 72 × (4/3) - Multiply:
72 × (4/3) = (72 × 4) ÷ 3 = 288 ÷ 3 = 96
Therefore, the result is 96.
This result makes logical sense because 0.75 is less than 1, so we expect the quotient to be greater than 72. When dividing by a number less than 1, the answer increases, because more of those smaller parts fit into the whole. In this case, 96 groups of 0.75 are needed to make 72.
