Even and Odd Numbers Quiz, Explanations and Step-by-Step Review
Use the question set below to practice even and odd numbers (also called parity). If you want a refresher, click Start lesson to open a step-by-step guide with definitions, patterns, and rules for operations.
Answer the question set and review your mistakes at the end.
How this even and odd numbers practice works
1. Take the practice set: answer the even/odd questions below.
2. Open the lesson (optional): learn how to identify parity fast and apply parity rules for addition and multiplication.
3. Retry: return to the question set and apply what you reviewed right away.
What you will learn in the even and odd numbers lesson
Meaning & vocabulary
What even numbers and odd numbers mean
Parity (even/odd) and multiple of 2
Why 0 is even (it is divisible by 2)
Identify even or odd quickly
Last digit rule for whole numbers (0, 2, 4, 6, 8 vs. 1, 3, 5, 7, 9)
Pairing rule: can you make equal pairs with no leftovers?
Next even/odd number and alternating patterns
Parity rules for operations
Even + even is even, odd + odd is even
Even + odd is odd (and subtraction follows the same parity pattern)
Even × anything is even; odd × odd is odd
Problem solving & practice skills
Decide if a sum or product is even/odd without fully calculating
Work with expressions like \(7 + 4\times 5\) by doing multiplication first
Count odds/evens in a list and pick the smallest even/odd
Purpose: Build a clear understanding of even and odd numbers and learn reliable parity rules you can use in any problem.
Success criteria
Define even and odd using pairing and divisibility by 2.
Identify if a whole number is even or odd using the last digit rule.
Find the next even or next odd number after a given number.
Use parity rules to decide whether a sum or product is even/odd.
Evaluate the parity of expressions by doing multiplication first.
Count and select even/odd numbers in lists and small ranges.
Key vocabulary
Even number: a whole number divisible by 2 (can be paired with no leftovers).
Odd number: a whole number not divisible by 2 (one leftover when pairing).
Parity: whether a number is even or odd.
Multiple of 2: any number of the form \(2k\) where \(k\) is a whole number.
Quick pre-check
Pre-check 1: Which number is even?
Hint: An even number ends in 0, 2, 4, 6, or 8.
Pre-check 2: What is the next even number after \(17\)?
Hint: Even numbers increase by 2: \(\dots,16,18,20,\dots\).
What Even & Odd Mean
Even and odd: pairing and divisibility by 2
Learning goal: Explain what even and odd numbers mean and identify parity using simple tests.
Key idea
A whole number is even if you can split it into two equal groups with no leftovers. This is the same as saying the number is divisible by 2. A whole number is odd if one object is left over when you try to make pairs.
Fast check (last digit rule)
For whole numbers, look at the last digit: Even numbers end in \(0,2,4,6,8\). Odd numbers end in \(1,3,5,7,9\).
Worked example
Example: Decide if \(14\) and \(15\) are even or odd
\(14\) ends in \(4\), so \(14\) is even. \(15\) ends in \(5\), so \(15\) is odd.
Try it
Try it 1: Is \(42\) even or odd?
Hint: \(42\) ends in \(2\).
Try it 2: Which of these is odd?
Hint: Odd numbers end in \(1,3,5,7,9\).
Summary
Even means divisible by 2 (pairs with no leftovers).
Odd means not divisible by 2 (one leftover when pairing).
The last digit rule is a fast way to check parity for whole numbers.
Next Even / Next Odd
Next even and next odd numbers
Learning goal: Find the next even or odd number and explain why parity alternates.
Key idea
Whole numbers go even, odd, even, odd in a repeating pattern. Adding \(1\) switches parity: even + 1 = odd and odd + 1 = even. Adding \(2\) keeps the same parity.
Algebra connection
An even number can be written as \(2k\). An odd number can be written as \(2k+1\). So if \(n\) is odd, \(n+1\) is even.
Worked example
Example: Next odd number after \(5\)
Odd numbers go up by \(2\): \(\dots,3,5,7,9,\dots\). The next odd number after \(5\) is \(7\).
Try it
Try it 1: What is the next odd number after \(13\)?
Hint: Add 2 to an odd number to get the next odd number.
Try it 2: What is the next even number after \(8\)?
Hint: Even numbers increase by 2: \(\dots,6,8,10,12,\dots\).
Summary
Parity alternates when you add \(1\).
The next even (or odd) number is found by adding \(2\).
If \(n\) is odd, then \(n+1\) is even.
Add & Subtract Parity
Even and odd rules for addition and subtraction
Learning goal: Decide whether sums and differences are even or odd using parity rules.
Key rules (addition)
Even + even = even
Odd + odd = even
Even + odd = odd (and odd + even = odd)
Key rules (subtraction)
Even − even = even
Odd − odd = even
Even − odd = odd and odd − even = odd
Worked examples
Example 1: Is \(7 + 9\) even or odd?
\(7\) is odd and \(9\) is odd. Odd + odd = even, so \(7 + 9\) is even (in fact, \(7+9=16\)).
Example 2: Is \(100 + 101 + 102\) even or odd?
\(100\) is even, \(101\) is odd, \(102\) is even. Even + odd = odd, then odd + even = odd. So \(100 + 101 + 102\) is odd (the sum is \(303\)).
Try it
Try it 1: Is \(5 + 4\) even or odd?
Hint: Odd + even = odd.
Try it 2: Is \(4 + 5 + 6\) even or odd?
Hint: \(4\) is even, \(5\) is odd, \(6\) is even. Track parity step-by-step.
Summary
Two odds added together make an even number.
Adding one odd and one even makes an odd number.
Subtraction follows the same parity patterns as addition.
Multiply Parity
Even and odd rules for multiplication
Learning goal: Decide whether a product is even or odd using simple parity rules.
Key rules
Even × anything = even (because there is at least one factor of 2).
Odd × odd = odd (no factor of 2 appears).
0 is even because \(0 = 2\times 0\) (it is divisible by 2).
Worked examples
Example 1: Is \(3 \times 5\) even or odd?
\(3\) is odd and \(5\) is odd. Odd × odd = odd, so \(3 \times 5\) is odd (in fact, \(3\times 5=15\)).
Example 2: Is \(6 \times 9\) even or odd?
\(6\) is even, so the product \(6 \times 9\) is even (even × anything = even).
Try it
Try it 1: Is the product of two odd numbers even or odd?
Hint: Odd numbers have no factor of 2, and odd × odd stays odd.
Try it 2: Is \(12 \times 7\) even or odd?
Hint: If one factor is even, the product is even.
Summary
Even × anything is even.
Odd × odd is odd.
Use the rules to decide parity quickly without computing the full product.
Expressions
Even or odd in expressions: multiply first
Learning goal: Decide whether an expression is even or odd by using order of operations and parity rules.
Key idea
When an expression contains \(+\) or \(−\) and \( \times \), do multiplication first (then add or subtract). You can often decide parity without doing every step of arithmetic.
Worked example
Example: Is \(7 + 4\times 5\) even or odd?
Step 1: Multiply first: \(4\times 5\) is even (even × anything = even). Step 2: Add: \(7\) is odd, and odd + even = odd. So \(7 + 4\times 5\) is odd (it equals \(27\)).
Try it
Try it 1: Is \(15 - 6\times 2\) even or odd?
Hint: \(6\times 2\) is even. Odd − even stays odd.
Try it 2: Is \(100 + 101 + 102\) even or odd?
Hint: Track parity: even + odd = odd, then odd + even = odd.
Worked solution
\(100\) is even, \(101\) is odd, \(102\) is even. Even + odd = odd, and odd + even = odd. So the total is odd (the sum is \(303\)).
Summary
Do multiplication first in mixed expressions.
Use parity rules to decide even/odd without heavy computation.
Track parity step-by-step for longer expressions.
Lists & Counting
Find and count even and odd numbers
Learning goal: Choose the smallest even/odd number in a list and count how many evens/odds appear.
Key idea
To answer list questions, first mark each number as even or odd (use the last digit rule). Then you can count the evens/odds or compare the numbers to find the smallest.
Worked examples
Example 1: How many odd numbers are in \([1,2,3,4,5]\)?
The odd numbers are \(1,3,5\). Answer: There are \(3\) odd numbers.
Example 2: Which is the smallest even number in \([5, 8, 11, 14]\)?
The even numbers are \(8\) and \(14\). Answer: The smallest even number is \(8\).
Try it
Try it 1: How many odd numbers are in \([14, 15, 16, 17]\)?
Hint: The odd numbers are \(15\) and \(17\).
Try it 2: How many even numbers are in \([2, 3, 4, 5, 6]\)?
Hint: The even numbers are \(2,4,6\).
More quick checks
Smallest odd in \([131,132,133,134]\) is \(131\).
Next odd after \(8\) is \(9\).
Next even after \(17\) is \(18\).
Summary
Use the last digit rule to label each number even/odd.
Count the labeled numbers to answer “how many” questions.
Compare only the matching parity numbers to find the smallest even/odd.
Applications & Patterns
Why even and odd numbers matter
Learning goal: Connect parity to patterns, pairing situations, and quick reasoning in math.
Where you use parity
Making pairs: Can everyone have a partner with no one left out?
Mental math: Decide if an answer should be even or odd as a quick error check.
Algebra: Use \(2k\) and \(2k+1\) to describe all even and odd numbers.
Computing: Many systems use “even/odd” (parity) checks to detect simple errors.
Worked example: pairing
Example: A class has \(14\) students. Can the teacher make pairs with no one left out?
\(14\) is even, so it can be split into two equal groups or paired with no leftovers. Answer: Yes — \(14\) students can make \(7\) pairs.
Try it
Try it 1: A team has \(15\) players. If you try to make pairs, will there be a leftover?
Hint: Odd means one leftover when pairing.
Final recap
Even numbers are divisible by 2; odd numbers are not.
Parity alternates as you count: even, odd, even, odd.
Use parity rules to decide whether sums and products are even/odd.
Do multiplication first in mixed expressions, then apply parity.
Parity is useful for patterns, pairing, and quick error checks.
Next step: Close this lesson and try your quiz again. If you miss a question, reopen the book and review the page that matches the skill.
