Final answer:
The compatible numbers equation that would help Sheila check the reasonableness of the expression -8 + 19 - 8 is Option 1: 10 + 20 - 10. This simplification makes the mental calculation straightforward and gives a reasonable check of the original expression.
Step-by-step explanation:
Sheila wants to test the reasonableness of her answer to the expression -8 + 19 - 8 by using compatible numbers. Compatible numbers are simplified numbers that are close to the actual numbers and make it easier to perform mental arithmetic. To check the reasonableness of the expression, we should look for an equation with numbers that are close to and compatible with -8, 19, and -8, which makes the mental calculation straightforward.
Here are the factors to consider while choosing the compatible numbers:
- When two positive numbers add, the answer has a +ve sign, e.g., 3+2 = 5.
- When two negative numbers add, the answer will also be negative, e.g., -4 + (-2) = -6.
- When two numbers with opposite signs add, subtract the smaller number from the larger one, and the answer carries the sign of the larger number, for example, -5 + 3 = -2.
- In subtraction, change the sign of the subtracted number and then follow the addition rules, for example, 5 - (+3) = 5 - 3 = 2.
Given these rules, the compatible numbers should reflect the combined effect of addition and subtraction while keeping the operation easy to perform mentally. Therefore, the correct compatible numbers equation that could help Sheila check the reasonableness is:
Option 1: 10 + 20 - 10
This option effectively simplifies -8 to -10, 19 to 20, and the other -8 to -10, which will give an outcome with a +ve sign, and it is easy to calculate mentally: 10 + 20 - 10 = 20, which appears reasonable when compared to the original expression -8 + 19