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Exercise 2.2

1. Which of the following mathematical statements are true?

a. [tex]208 + 1076 = 1076 + 208[/tex]

b. [tex]304 + 513 = 403 + 315[/tex]

c. [tex]40 - 72 = 72 - 40[/tex]

d. [tex]0 + 1001 = 1001 + 0[/tex]

e. [tex](10 - 6) - 4 = 10 - (6 - 4)[/tex]

f. [tex]15 - 0 = 0 - 15[/tex]

g. [tex]18 + (4 + 7) = (18 + 4) + 7[/tex]

Sagot :

GinnyAnsweridn
Let's analyze each of the mathematical statements step by step to determine which of them are true.

### Statement a:
[tex]\[ 208 + 1076 = 1076 + 208 \][/tex]

This statement is an example of the commutative property of addition, which states that the order of addition does not change the sum. Therefore, this statement is true.

### Statement b:
[tex]\[ 304 + 513 = 403 + 315 \][/tex]

Here, we will add both sides:
- Left side: [tex]\( 304 + 513 = 817 \)[/tex]
- Right side: [tex]\( 403 + 315 = 718 \)[/tex]

Since [tex]\( 817 \neq 718 \)[/tex], this statement is false.

### Statement c:
[tex]\[ 40 - 72 = 72 - 40 \][/tex]

Here, we will calculate both sides:
- Left side: [tex]\( 40 - 72 = -32 \)[/tex]
- Right side: [tex]\( 72 - 40 = 32 \)[/tex]

Since [tex]\( -32 \neq 32 \)[/tex], this statement is false.

### Statement d:
[tex]\[ 0 + 1001 = 1001 + 0 \][/tex]

This statement is another example of the commutative property of addition, stating that the order of addition does not matter. Therefore, this statement is true.

### Statement e:
[tex]\[ (10 - 6) - 4 = 10 - (6 - 4) \][/tex]

To evaluate this, we compute both sides step by step:
- Left side: [tex]\( (10 - 6) - 4 = 4 - 4 = 0 \)[/tex]
- Right side: [tex]\( 10 - (6 - 4) = 10 - 2 = 8 \)[/tex]

Since [tex]\( 0 \neq 8 \)[/tex], this statement is false.

### Statement f:
[tex]\[ 15 - 0 = 0 - 15 \][/tex]

Here, we will compute both sides:
- Left side: [tex]\( 15 - 0 = 15 \)[/tex]
- Right side: [tex]\( 0 - 15 = -15 \)[/tex]

Since [tex]\( 15 \neq -15 \)[/tex], this statement is false.

### Statement g:
[tex]\[ 18 + (4 + 7) = (18 + 4) + 7 \][/tex]

This statement is an example of the associative property of addition, which states that how numbers are grouped in addition does not change the sum. Therefore, this statement is true.

### Conclusion:

Based on the analysis, the true or false values of the statements are as follows:
a. [tex]\( 208 + 1076 = 1076 + 208 \)[/tex] — True
b. [tex]\( 304 + 513 = 403 + 315 \)[/tex] — False
c. [tex]\( 40 - 72 = 72 - 40 \)[/tex] — False
d. [tex]\( 0 + 1001 = 1001 + 0 \)[/tex] — True
e. [tex]\( (10 - 6) - 4 = 10 - (6 - 4) \)[/tex] — False
f. [tex]\( 15 - 0 = 0 - 15 \)[/tex] — False
g. [tex]\( 18 + (4 + 7) = (18 + 4) + 7 \)[/tex] — True
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