Even and Odd Numbers

Show your work for each problem.

1.
Which number is even?
1. a)14
2. b)17
3. c)31
4. d)23
Answer: 14
14 ends in 4, which is an even digit. The others (17, 23, 31) end in odd digits (7, 3, 1).
2.
Which number is odd?
1. a)100
2. b)26
3. c)45
4. d)88
Answer: 45
45 ends in 5, which is an odd digit. The others (26, 88, 100) end in even digits (6, 8, 0).
3.
Is 56 even? Check it by dividing: what is $56 \div 2$ ?
Answer: 28
$56 \div 2 = 28$ , because $28 \times 2 = 56$ . There is no remainder, so 56 is even. The last digit, 6, tells you the same thing.
4.
83 is odd. What is the next odd number after 83?
Answer: 85
Odd and even numbers alternate: 83 (odd), 84 (even), 85 (odd). The next odd number is always 2 more: $83 + 2 = 85$ .
5.
Determine if 124 is even or odd by looking at the last digit.
Answer: 124: even
1. What is the last digit of 124? 4
2. Is 4 in the list of even digits (0, 2, 4, 6, 8)? yes
3. Is 124 even or odd? even
6.
Is 0 (zero) even or odd?
1. a)Even
2. b)Odd
3. c)Neither
4. d)Both
Answer: Even
0 is even! $0 \div 2 = 0$ with no remainder. Also, 0 ends in 0, which is an even digit.
7.
What is the remainder when $6 + 5$ is divided by 2? (Remainder 0 means even, remainder 1 means odd.)
Answer: 1
$6 + 5 = 11$ , and $11 = 2 \times 5 + 1$ , so the remainder is 1 and 11 is odd. Remember: Even + Odd = Odd.
8.
You have 18 stickers to share equally between 2 friends. Can it be done fairly?
Answer: Yes, 9 stickers each
1. What is the last digit of 18? 8
2. Is 18 even or odd? even
3. Can 18 be divided by 2 with no remainder? yes
4. How many stickers does each friend get? 9
9.
What is the result of adding two odd numbers?
1. a)Cannot be determined
2. b)Sometimes even, sometimes odd
3. c)Always odd
4. d)Always even
Answer: Always even
Odd + Odd = Even! Examples: $3 + 5 = 8$ , $7 + 9 = 16$ , $1 + 3 = 4$ . All results are even.
10.
Determine if $7 + 9$ is even or odd without calculating the exact sum.
Answer: $7 + 9$ : even
1. Is 7 even or odd? odd
2. Is 9 even or odd? odd
3. What is Odd + Odd? even
4. So is $7 + 9$ even or odd? even
11.
How many of these numbers are even: 347, 512, 230, 89, 64?
Answer: 3
Last digits: 347 ends in 7 (odd), 512 in 2 (even), 230 in 0 (even), 89 in 9 (odd), 64 in 4 (even). So 3 numbers are even: 512, 230 and 64.
12.
A class has 25 students. Can they form pairs with no one left over?
Answer: No, 1 student is left over
1. What is the last digit of 25? 5
2. Is 25 even or odd? odd
3. Can an odd number be divided evenly by 2? no
4. Will someone be left without a partner? yes
13.
If you multiply an even number by an odd number, the result is:
1. a)Always even
2. b)Sometimes even, sometimes odd
3. c)Always odd
4. d)Even or odd, like the bigger number
Answer: Always even
Even $\times$ Odd = Even! Examples: $4 \times 3 = 12$ , $6 \times 5 = 30$ , $2 \times 7 = 14$ . All even!
14.
Is $4 + 8 + 3$ even or odd? Solve step by step.
Answer: $4 + 8 + 3$ : odd
1. Is 4 even or odd? even
2. Is 8 even or odd? even
3. What is Even + Even? even
4. Is 3 even or odd? odd
5. What is Even + Odd? odd
15.
What is the remainder when $3 \times 5$ is divided by 2? (Remainder 0 means even, remainder 1 means odd.)
Answer: 1
$3 \times 5 = 15$ , and $15 = 2 \times 7 + 1$ , so the remainder is 1. Both 3 and 5 are odd, and Odd $\times$ Odd = Odd.
16.
Is $-12$ even or odd?
Answer: $-12$ : even
1. What is the last digit of -12 (ignore the sign)? 2
2. Is 2 an even or odd digit? even
3. Does the negative sign change if a number is even or odd? no
4. Is $-12$ even or odd? even
17.
You want to arrange 31 chairs in rows of 2. How many complete rows can you make, and how many chairs are left over?
Answer: 15 rows, 1 chair left over
1. Is 31 even or odd? odd
2. What is $31 \div 2$ (whole number part)? 15
3. How many chairs are left over? 1
4. Check: what is $15 \times 2 + 1$ ? 31