if a and b are both odd integers, which equation is always true?
1 a/b= b/a
2 a-b= b-a
3 a+2b= b+2a
4 a+b= b+a
help me plz..............
Why on earth would 1 + 3 be different from 3 + 1 ????
To determine which equation is always true when a and b are both odd integers, let's analyze each option:
1. a/b = b/a
To verify this equation, we can substitute odd integers for a and b. Let's choose a = 3 and b = 5.
3 / 5 = 5 / 3
0.6 = 1.6667
Since 0.6 is not equal to 1.6667, this equation is not always true for all odd integers. Therefore, option 1 is not the correct answer.
2. a - b = b - a
Let's substitute odd integers for a and b again, using a = 3 and b = 5:
3 - 5 = 5 - 3
-2 = 2
Since -2 is not equal to 2, this equation is also not always true for all odd integers. Option 2 is incorrect.
3. a + 2b = b + 2a
Once again, let's substitute odd integers for a and b, using a = 3 and b = 5:
3 + 2(5) = 5 + 2(3)
13 = 11
Since 13 is not equal to 11, this equation is not always true for all odd integers. Option 3 is incorrect.
4. a + b = b + a
This equation is the commutative property of addition, stating that the order of adding two numbers does not affect the result. It holds true for all numbers, including odd integers. Therefore, option 4 is always true for all odd integers.
Hence, the correct answer is option 4: a + b = b + a.