Estimating the product of two numbers using compatible numbers involves rounding the original numbers to values that are easy to work with mentally, while still maintaining the overall sense of the problem. In this case, we are given the numbers 2.4 and -0.18, and their compatible counterparts are 2.5 and -0.2, respectively.
Let's estimate the product (2.4)(-0.18) using these compatible numbers:
Estimate=Compatible Number for 2.4×Compatible Number for -0.18
Estimate=Compatible Number for 2.4×Compatible Number for -0.18
Estimate=2.5×(−0.2)Estimate=2.5×(−0.2)
Now, we can perform the multiplication:
Estimate=−0.5Estimate=−0.5
The estimated product of 2.4 and -0.18, using compatible numbers 2.5 and -0.2, is approximately -0.5.
Now, let's delve into the rationale behind choosing compatible numbers and how this estimation process works
Choosing Compatible Numbers:
Compatible numbers are chosen based on their ease of multiplication or other mathematical operations.
In this case, 2.5 and -0.2 are chosen because they are close to 2.4 and -0.18, respectively, and the multiplication of these rounded numbers is simpler.
Rounding to Compatible Numbers:
The process involves rounding each original number to a more manageable, often whole or decimal number.
2.4 is rounded to 2.5, and -0.18 is rounded to -0.2.
Performing the Estimation:
The rounded numbers are then multiplied together to provide an estimate of the actual product.
The product of 2.5 and -0.2 is calculated to be -0.5.
Interpreting the Result:
The estimated product, -0.5, gives a quick and reasonable approximation of the actual product, maintaining the general magnitude and sign.
Estimation using compatible numbers is a valuable skill, especially when a quick approximation is needed without the precision of exact arithmetic. It is particularly useful in mental math and in situations where a rough answer is sufficient for the context of the problem.