Jonas is given a test question asking him to show that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?

Every time you add two odd numbers, the sum is an even number.

Look at these different examples: 5 + 3 = 8, 15 + 7 = 22, 21 + 13 = 34. So the sum of two odd numbers must be even.

Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.

Let (2a + 1) be one odd number, and let (2b + 1) be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2 (a + b + 1). Because 2 (a + b + 1) is a multiple of 2, it is an even number.

Question

Mathematics

Elena Bernard

30 September, 14:10

Jonas is given a test question asking him to show that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?

Every time you add two odd numbers, the sum is an even number.

Look at these different examples: 5 + 3 = 8, 15 + 7 = 22, 21 + 13 = 34. So the sum of two odd numbers must be even.

Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.

Let (2a + 1) be one odd number, and let (2b + 1) be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2 (a + b + 1). Because 2 (a + b + 1) is a multiple of 2, it is an even number.

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Answers (1)

Know the Answer?

Tucker Robbins · Answer 1

Let (2a + 1) be one odd number, and let (2b + 1) be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2 (a + b + 1). Because 2 (a + b + 1) is a multiple of 2, it is an even number.

Step-by-step explanation

When you multiply any number by two, it becomes even. Also, if you divide any number by two without a remainder, it is even. For this case

Let (2a + 1) be one odd number, and let (2b + 1) be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2 (a + b + 1). Because 2 (a + b + 1) is a multiple of 2, it is an even number.

Substituting any odd number in a and b gives you an even number