The Correct Answer and Explanation is:
The correct answer is 30.
To find a reasonable estimate for the division problem 1,519 ÷ 49, we can use the technique of rounding to compatible numbers. This method involves changing the original numbers to simpler, nearby values that are easier to work with mentally. The goal is to make the calculation straightforward while keeping the result close to the actual answer.
First, let’s examine the divisor, which is 49. This number is very close to 50. Rounding 49 up to 50 is an excellent first step because 50 is a round number ending in a zero, which simplifies the process of division significantly.
Next, we turn our attention to the dividend, 1,519. We should round this number to a value that is easily divisible by our new divisor, 50. The number 1,500 is an ideal choice. It is very close in value to 1,519, and it is a multiple of 10 and 50, which makes it highly compatible with our rounded divisor.
By substituting these rounded numbers into the original problem, our complex calculation of 1,519 ÷ 49 transforms into a much simpler estimated problem: 1,500 ÷ 50.
To solve 1,500 ÷ 50, we can simplify it further. Since both the dividend (1,500) and the divisor (50) end in zero, we can divide both by 10. This is equivalent to canceling out a zero from each number, leaving us with the problem 150 ÷ 5. This calculation is much easier to perform. We know that 15 divided by 5 is 3. Following this pattern, 150 divided by 5 is 30.
Therefore, our estimated answer is 30. When we compare this result to the given options of 10, 30, 100, and 300, we see that 30 is a perfect match. The other options are not logical. For example, 10 * 50 = 500, which is far too small. 100 * 50 = 5,000, which is far too large. This confirms that 30 is the only reasonable estimate.
