Integers online worksheet for 7 - Free Printable

Let’s go step by step through each question. I’ll solve them one at a time, carefully checking my work.

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1. Fill the blanks without actual additions.

This is about the commutative property of addition:
> Changing the order of numbers being added does NOT change the sum.

So:

(i) 25 + 35 = 60 → then 35 + 25 = 60
(ii) 105 + 307 = 412 → then 307 + 105 = 412
(iii) 605 + 350 = 955 → then 350 + 605 = 955
(iv) (-105) + 70 = -35 → then 70 + (-105) = -35

✔ All answers are just swapping the order — same result.

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2. Match the following

We need to match each equation or statement with the correct property.

Let’s look at each:

(i) 45 + (-25) = (-25) + 45
→ Order changed, sum same → Commutative property under addition → (E)

(ii) (-5) + 2025 = 2020
→ This is just an example of adding two integers and getting another integer → shows that integers are closed under addition → Closure property under addition → (D)

Wait — let’s double-check: Closure means when you add two integers, you get an integer. Yes, -5 and 2025 are integers, 2020 is also an integer → so yes, closure.

But note: sometimes people confuse this with identity or inverse. Let’s keep going.

(iii) (6+7) + (-4) = 6 + (7 + (-4))
→ Grouping changed, but sum same → Associative property under addition → (C)

(iv) 3, -3 are called as to each other
→ They add up to zero → they are additive inverses → (B)

(v) Zero (0)
→ When you add 0 to any number, it stays the same → Additive Identity → (A)

Note: (F) Multiplicative identity is for multiplication (like 1), not relevant here.

So matching:

(i) → E
(ii) → D
(iii) → C
(iv) → B
(v) → A

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3. Find using properties of addition

We can rearrange or group to make calculation easier.

(i) 25 + 45 + 65
Group 25 + 65 first? 25 + 65 = 90, then +45 = 135
Or 25 + 45 = 70, +65 = 135 → same.

Answer: 135

(ii) (-50) + 60 + (-70)
Group negatives: (-50) + (-70) = -120, then +60 = -60

(iii) 607 + (-705) + (-402)
First, 607 + (-705) = -98
Then -98 + (-402) = -500

Alternatively: group the negatives: (-705) + (-402) = -1107, then +607 = -500 → same.

(iv) (-400) + 35 + (-25)
Group 35 + (-25) = 10, then (-400) + 10 = -390

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4. Find the sum of 2020 and additive identity.

Additive identity is 0.

So 2020 + 0 = 2020

Now: “which property that 25 + (-10) + 25 represents? give reasons.”

Wait — the expression is 25 + (-10) + 25.

That’s just three numbers being added. It doesn’t show a specific property unless we rearrange or regroup.

Actually, maybe it’s trying to say: if we do 25 + 25 + (-10) = 50 -10 = 40 — which uses commutative property to reorder.

But strictly speaking, just writing 25 + (-10) + 25 doesn’t demonstrate a property unless we compare it to something else.

Perhaps it’s meant to be compared to 25 + 25 + (-10)? Then it would be commutative.

But as written, it’s just an expression. Maybe typo?

Wait — perhaps it’s asking what property is shown in the *way* we might compute it? Like grouping?

Actually, let me re-read: “which property that 25 + (-10) + 25 represents?”

It doesn’t clearly represent a single property. But if we consider that we can add in any order, it implies commutative property.

Reason: We can swap positions of 25 and (-10) or the two 25s, and sum remains same.

So answer: Commutative property, because changing order doesn’t change sum.

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5. Find:

(i) (4000 + 5000) + 6000 = 9000 + 6000 = 15000

(ii) 4000 + (5000 + 6000) = 4000 + 11000 = 15000

(iii) (4000 + 6000) + 5000 = 10000 + 5000 = 15000

All give same result → Associative property under addition — grouping doesn’t matter.

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6. What do you observe from the following sums? what is the property followed here?

Wait — no sums are given in question 6! Probably a copy-paste error. Looking back at original image — actually, in the user’s image, question 6 says:

“6. What do you observe from the following sums what is the property followed here ?”

But there are no sums listed. That must be a mistake. Perhaps it was meant to refer to question 5? Or maybe it’s missing.

Looking again — in the original problem set, after Q5, Q6 is blank? Actually, in the image provided, Q6 has no content — probably a formatting error.

Since nothing is given, I’ll skip or assume it refers to Q5.

But to be safe — since Q5 already asked for observation, and Q6 repeats similar wording, likely it’s redundant or misprinted.

I’ll leave it as: No sums provided — cannot determine.

But wait — looking back at the user’s text:

After Q5, it says:

> 6. What do you observe from the following sums what is the property followed here ?

And then immediately goes to Q7.

Probably, it’s a duplicate or error. Since no data, I’ll skip.

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7. Find:

(i) 309 + 0 = 309

(ii) (-39) + 0 = -39

(iii) 0 + (-39) = -39

(iv) 5 + 0 = 5

Property used: Additive Identity Property — adding zero doesn’t change the number.

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8. Find:

(i) 6 + 1 = 7

(ii) 1 + 6 = 7

(iii) (-35) + 1 = -34

What do you observe by adding '1' to any integer/number?

→ You get the next integer (successor).

For positive numbers: increases by 1.

For negative numbers: moves closer to zero (e.g., -35 +1 = -34).

So observation: Adding 1 gives the next whole number in sequence — the successor.

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Now, compiling all final answers clearly.

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Final Answer:

1.
(i) 60
(ii) 412
(iii) 955
(iv) -35

2.
(i) → E
(ii) → D
(iii) → C
(iv) → B
(v) → A

3.
(i) 135
(ii) -60
(iii) -500
(iv) -390

4.
Sum of 2020 and additive identity (0) = 2020
The expression 25 + (-10) + 25 demonstrates the Commutative Property because the order of addition can be changed without affecting the sum. For example, 25 + 25 + (-10) = 40, same as original.

5.
(i) 15000
(ii) 15000
(iii) 15000
Observation: The sum is the same regardless of how the numbers are grouped → Associative Property under Addition

6.
*(No sums provided in question — unable to answer)*

7.
(i) 309
(ii) -39
(iii) -39
(iv) 5
Property: Additive Identity Property

8.
(i) 7
(ii) 7
(iii) -34
Observation: Adding 1 to any integer gives its successor (the next integer in sequence).