Final answer:
After adding 3 zero pairs to 6 positive counters and taking away 3 negative counters, you are left with 6 positive counters, which equals 9. This is similar to the arithmetic expression 6 - (-3), which is 6 + 3 = 9 after changing the sign during subtraction.
Step-by-step explanation:
To solve the problem of starting with 6 positive counters and taking away 3 negative counters, we first need to understand the concept of zero pairs. A zero pair consists of one positive counter and one negative counter, which when combined, cancel each other out and equal zero. When the question asks to take away 3 negative counters, we add three zero pairs to the original 6 positive counters, then remove the 3 negative counters. The result is the subtraction of a positive and negative number. As per the rules of addition and subtraction with integers:
- When two positive numbers add, the answer has a positive sign (e.g., 3+2 = 5).
- When two negative numbers add, the answer has a negative sign (e.g., -4 + (-2) = -6).
- When two numbers with opposite signs add, subtract the smaller number from the larger number, and the answer has the sign of the larger number (e.g., -5 +3 = -2).
- In subtraction, change the sign of the subtracted number and then follow the addition rules (e.g., subtract 3 from 5).
In this case, after adding three zero pairs to 6 positive counters and removing 3 negative counters, we are left with 6 positive counters, or simply, 6. This is identical to the arithmetic expression 6 - (-3), which becomes 6 + 3 after changing the sign of -3 to its opposite during subtraction, giving a total of 9.