The image you've shared is an educational resource explaining how to
add and subtract integers, using visual models with counters (positive and negative). Let's break down the two examples shown and explain the reasoning behind each.
---
🔹 Example 1: Adding Integers
Problem:
$$
-5 + 3 = ?
$$
#### Step-by-step Explanation:
We are adding a negative number (-5) and a positive number (+3).
1.
Visual Representation:
- Use
red counters for negative numbers (–).
- Use
green counters for positive numbers (+).
- Start with
5 red counters (representing –5).
- Add
3 green counters (representing +3).
2.
Form Zero Pairs:
A
zero pair is one positive and one negative counter, which cancel out to zero:
$$
(+1) + (-1) = 0
$$
- From the 5 red and 3 green counters, we can form
3 zero pairs (one red and one green each), which cancel out.
- That leaves us with
2 red counters (since 5 – 3 = 2).
3.
Result:
The remaining counters are
2 negative counters, so:
$$
-5 + 3 = -2
$$
✔ Answer: –2
---
🔹 Example 2: Subtracting Integers
Problem:
$$
2 - (+5) = ?
$$
This means:
Subtract +5 from 2.
But we start with only
2 positive counters, and we want to subtract
5 positive counters — we don’t have enough!
So, we use the
zero pair method to make subtraction possible.
#### Step-by-step Explanation:
1.
Start with 2 positive counters (green):
Representing +2.
2.
We need to remove 5 positive counters, but we only have 2.
So, we
add zero pairs (equal numbers of positive and negative counters) without changing the value.
- Add
3 zero pairs (each is +1 and –1), so total added:
$$
+3 \text{ and } -3
$$
Now our total is still $+2$ because:
$$
2 + 3 - 3 = 2
$$
3.
Now remove 5 positive counters:
We now have:
- Original 2 positives
- Plus 3 new positives → Total of 5 positives
- And 3 negatives
Remove 5 positive counters → all of them are gone.
4.
What’s left?
Only the
3 negative counters remain.
5.
Result:
$$
2 - (+5) = -3
$$
✔ Answer: –3
---
✔ Summary of Rules (from the example):
| Operation | Rule |
|---------|------|
|
Adding Integers | Combine like signs; if signs differ, subtract smaller absolute value from larger and keep sign of larger. |
|
Subtracting Integers | Change subtraction to addition of the opposite: $a - b = a + (-b)$ |
So:
- $-5 + 3 = -2$
- $2 - (+5) = 2 + (-5) = -3$
These examples show how
visual models help understand integer operations, especially when dealing with negative numbers.
Let me know if you'd like practice problems or further explanation! 😊
Parent Tip: Review the logic above to help your child master the concept of adding integers worksheet with answers.
