The Correct Answer and Explanation is:
The correct answer is 50.
To find a reasonable estimate for the equation 2,132 ÷ 41, the goal is to simplify the numbers into ones that are easier to calculate mentally. This process involves rounding the original numbers to values that are close but more convenient to work with.
First, let’s look at the divisor, 41. It is very close to the round number 40. Rounding 41 down to 40 is a logical first step that will make the division much easier.
Next, we need to adjust the dividend, 2,132, to a number that is easily divisible by our new divisor, 40. This is known as finding compatible numbers. A good strategy is to look at the first part of the dividend, 21, and the first digit of our rounded divisor, 4. Since 4 goes into 20 five times, rounding 2,132 to 2,000 is an excellent choice. The number 2,000 is not only close to 2,132 but also a simple multiple of 40.
Now we can perform the estimated calculation with these new, simpler numbers: 2,000 ÷ 40. To solve this, we can simplify the problem by canceling out one zero from both the dividend and the divisor. This leaves us with the much more manageable equation of 200 ÷ 4. Dividing 200 by 4 gives us 50.
Therefore, 50 is a very reasonable estimate. When we compare this result to the given options (40, 50, 400, 500), it matches one of them exactly. The other options are not as close. For instance, an estimate of 400 would mean 400 × 40 = 16,000, which is far too high. For confirmation, the exact answer to 2,132 ÷ 41 is 52, which makes 50 the closest and most reasonable estimate provided.
