Integers online worksheet for 7 - Free Printable

Let's solve each question step by step, explaining the reasoning and properties involved.

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1. Fill the given blanks without actual additions.

We use the Commutative Property of Addition:
> $ a + b = b + a $

So, changing the order of addends does not change the sum.

(i) $ 25 + 35 = 60 $ then $ 35 + 25 = \boxed{60} $
→ Commutative property: same sum.

(ii) $ 105 + 307 = 412 $ then $ 307 + 105 = \boxed{412} $
→ Again, commutative property.

(iii) $ 605 + 350 = 955 $ then $ 350 + 605 = \boxed{955} $
→ Same logic.

(iv) $ (-105) + 70 = -35 $ then $ 70 + (-105) = \boxed{-35} $
→ Still commutative property applies to integers.

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2. Match the following

We match each statement with the correct property.

(i) $ 45 + (-25) = (-25) + 45 $ → This shows order changed, so it’s:

→ (E) Commutative property under addition

(ii) $ (-5) + 2025 = 2020 $ → This is just an addition result. But notice:
- $ -5 + 2025 = 2020 $
- It doesn't show identity or inverse directly, but let's see what's being asked.
Wait — this is just a computation. But no property is clearly shown here unless we interpret it as:
- Adding two numbers gives another number → Closure property?

But wait: Let's check options.

Actually, this is not matching any property directly. Wait — perhaps there's a typo? Let's recheck.

But looking at the list:
- (A) Additive Identity
- (B) Additive Inverse
- (C) Associative
- (D) Closure
- (E) Commutative
- (F) Multiplicative identity

Now, $ (-5) + 2025 = 2020 $ — this is just a calculation. But it shows that the sum of two integers is an integer → So this illustrates:

→ (D) Closure property under addition

Yes! Because integers are closed under addition.

So:
(ii) → (D)

(iii) $ (6+7) + (-4) = 6 + (7 + (-4)) $
→ This shows grouping changed: $(a+b)+c = a+(b+c)$

→ (C) Associative property under addition

(iv) $ 3, -3 $ are called as to each other
→ They are opposites; when added give zero.

→ (B) Additive Inverse

(v) Zero (0) → The additive identity because $ a + 0 = a $

→ (A) Additive Identity

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Matching Summary:

| Statement | Answer |
|--------|--------|
| (i) $ 45 + (-25) = (-25) + 45 $ | (E) Commutative property |
| (ii) $ (-5) + 2025 = 2020 $ | (D) Closure property |
| (iii) $ (6+7) + (-4) = 6 + (7 + (-4)) $ | (C) Associative property |
| (iv) $ 3, -3 $ are called as to each other | (B) Additive Inverse |
| (v) Zero (0) | (A) Additive Identity |

Note: (F) Multiplicative identity is not used here.

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3. Find the following using properties of addition

We use commutative and associative properties to regroup and simplify.

(i) $ 25 + 45 + 65 $

Group: $ (25 + 65) + 45 = 90 + 45 = 135 $

Or: $ 25 + (45 + 65) = 25 + 110 = 135 $

→ Answer: 135

(ii) $ (-50) + 60 + (-70) $

Regroup: $ [(-50) + (-70)] + 60 = (-120) + 60 = -60 $

Or: $ (-50) + [60 + (-70)] = (-50) + (-10) = -60 $

→ Answer: -60

(iii) $ 607 + (-705) + (-402) $

Group: $ 607 + [(-705) + (-402)] = 607 + (-1107) = -500 $

Or: $ [607 + (-705)] + (-402) = (-98) + (-402) = -500 $

→ Answer: -500

(iv) $ (-400) + 35 + (-25) $

Group: $ [(-400) + (-25)] + 35 = (-425) + 35 = -390 $

Or: $ (-400) + [35 + (-25)] = (-400) + 10 = -390 $

→ Answer: -390

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4. Find the sum of 2020 and additive identity.

Additive identity is 0.

So: $ 2020 + 0 = \boxed{2020} $

Now, what property does $ 25 + (-10) + 25 $ represent?

Let’s rewrite: $ 25 + (-10) + 25 = (25 + 25) + (-10) = 50 + (-10) = 40 $

But more importantly, notice: 25 appears twice, and we're adding a negative.

But the expression is: $ 25 + (-10) + 25 $

We can rearrange: $ 25 + 25 + (-10) = 50 - 10 = 40 $

This uses commutative and associative properties.

But is there a specific property?

Actually, this is just a combination of commutative and associative properties used to reorder and group.

But the key idea: It doesn’t follow a single named property, but rather we use commutative and associative properties to compute.

Alternatively, if we think about the structure:

$ 25 + (-10) + 25 $ → It's not symmetric like additive inverse.

But notice: $ 25 + (-10) + 25 = 25 + 25 + (-10) $ → we are reordering terms.

So the property used is:

→ Commutative and Associative Properties of Addition

Reason: We can rearrange and regroup the terms freely when adding integers.

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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 the same result: 15000

→ What do you observe?

→ The grouping changes, but the sum remains the same.

→ This illustrates the Associative Property of Addition:

> $ (a + b) + c = a + (b + c) $

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

The problem says “the following sums” but doesn't list them. However, based on context, likely referring to previous examples where grouping changed but sum remained same.

So again, this is the Associative Property of Addition.

If no sums are listed, perhaps it's a repeat of Q5.

Assuming same idea:

→ Observation: Changing the grouping of numbers in addition does not affect the sum.

→ Property: Associative property under addition.

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7. Find:

(i) $ 309 + 0 = \boxed{309} $
(ii) $ (-39) + 0 = \boxed{-39} $
(iii) $ 0 + (-39) = \boxed{-39} $
(iv) $ 5 + 0 = \boxed{5} $

→ All these show that adding zero to any integer gives the same integer.

→ Property used: Additive Identity Property

> $ a + 0 = a $ and $ 0 + a = a $

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8. Find the following:

(i) $ 6 + 1 = \boxed{7} $
(ii) $ 1 + 6 = \boxed{7} $
(iii) $ (-35) + 1 = \boxed{-34} $

→ What do you observe?

When we add 1 to any integer, we get the next consecutive integer.

- For positive: $ 6 + 1 = 7 $ → next number
- For negative: $ -35 + 1 = -34 $ → less negative, closer to zero

→ Adding 1 to any integer gives its successor.

So, observation: Adding 1 to any integer gives the next integer in the number line.

This is the concept of successor.

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✔ Final Answers Summary:

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#### 1. Fill the blanks:
(i) 60
(ii) 412
(iii) 955
(iv) -35

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#### 2. Match:
(i) → (E) Commutative
(ii) → (D) Closure
(iii) → (C) Associative
(iv) → (B) Additive Inverse
(v) → (A) Additive Identity

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#### 3. Find using properties:
(i) 135
(ii) -60
(iii) -500
(iv) -390

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#### 4.
Sum of 2020 and additive identity: $ 2020 + 0 = 2020 $

Expression $ 25 + (-10) + 25 $ uses Commutative and Associative Properties to rearrange and group.

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#### 5.
(i) 15000
(ii) 15000
(iii) 15000

→ Observation: Sum is same regardless of grouping.
→ Property: Associative Property of Addition

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#### 6.
→ Observation: Grouping doesn’t affect sum.
→ Property: Associative Property of Addition

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#### 7.
(i) 309
(ii) -39
(iii) -39
(iv) 5

→ Property: Additive Identity

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#### 8.
(i) 7
(ii) 7
(iii) -34

→ Observation: Adding 1 to any integer gives the next integer (its successor).

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