Without calculating, which of these pairs must produce an odd sum?
A24 + 16 — both are even
B13 + 9 — both are odd
C35 + 14 — one odd, one even
D42 + 28 — both are even
Odd + Even = Odd. 35 is odd and 14 is even, so their sum is odd (35 + 14 = 49). Option A: Even + Even = Even. Option B: Odd + Odd = Even — the two leftover units pair up, making an even result. Option D: Even + Even = Even. The parity rules let you predict the result without adding.
Question 2 Multiple Choice
A student claims: 'Adding two odd numbers always gives an odd answer.' Which example directly disproves this?
A3 + 5 = 8 — both are odd, but the sum is even
B2 + 6 = 8 — both are even, and the sum is even
C7 + 2 = 9 — one odd, one even
D4 + 4 = 8 — both are even
3 + 5 = 8: both 3 and 5 are odd, yet the sum is 8, which is even. This directly contradicts the claim. Odd + odd = even, always. The other examples don't involve two odd numbers being added, so they can't disprove a claim specifically about odd + odd.
Question 3 True / False
The sum of two odd numbers is always even.
TTrue
FFalse
Answer: True
True — and this surprises many students. Each odd number has one extra unpaired unit. When you combine two odd numbers, those two leftover units pair up with each other, leaving nothing unpaired in the total. For example: 3 + 5 = 8, 7 + 9 = 16, 11 + 13 = 24. This holds without exception.
Question 4 True / False
You is expected to calculate the actual sum to determine whether 47 + 38 is odd or even.
TTrue
FFalse
Answer: False
False. Parity rules let you predict without calculating. 47 is odd and 38 is even; odd + even = odd. So 47 + 38 must be odd — and indeed, 47 + 38 = 85, which is odd. Using known structure to predict outcomes without full calculation is exactly what these rules are for.
Question 5 Short Answer
Why does odd + odd always equal even? Use the idea of 'pairs' in your explanation.
Think about your answer, then reveal below.
Model answer: Every even number is made entirely of pairs with nothing left over. Every odd number is an even number plus one extra lone unit. When you add two odd numbers, you combine two sets of pairs plus two lone units. Those two lone units pair up with each other, so the final total has no leftovers — which means it is even.
The 'one extra' in each odd number is the key. Two extras combine into one pair, restoring the all-pairs structure that defines an even number. Visualizing this with dots — ●● ●● ● + ●● ●● ● = ●● ●● ●● ●● — makes the logic concrete and memorable.