Odd and even numbers are much like the alphabet. We learn them early, and after that, we rarely think twice about them.
But did you know they can also be useful as a mental math tool? One that helps us predict answers before we finish solving, spot mistakes instantly, and cut through multiple-choice questions faster than a calculator.
If you didn't know these numbers could do all that, keep reading. The Mathnasium team is sharing four simple tricks that put odd and even numbers to work in ways most students never expect.
An odd or even number's behavior in addition and multiplication is completely predictable, every time, with no exceptions. That predictability is exactly what makes every trick in this guide work.
Before we get to the first trick, let's refresh the two rules everything else builds on:
Even + even = even; odd + odd = even; even + odd = odd
Any product with at least one even factor is even; odd × odd is always odd
Try it with any pair of numbers, and the pattern holds.
Take 4 and 7: 4 is even and 7 is odd, so 4 + 7 = 11 (odd) and 4 × 7 = 28 (even). That's exactly what the rules predict.
Because these rules never break, we can put them to work immediately, starting with a trick that lets us predict an answer before we even finish solving it.
📕 You May Also Like: What Makes a Number Odd or Even? A Simple Guide
We can predict an answer's parity before we finish the calculation, and that gives us a built-in error check with no calculator required.
Before we start solving any addition problem, we can ask ourselves a simple question. Does this answer have to be odd, or does it have to be even?
Let's try it with 47 + 36.
47 is odd and 36 is even.
Odd + even = odd, so the answer has to be odd, no matter what.
When we solve it, 47 + 36 = 83, an odd number that fits the rule exactly.
But say we'd rushed and landed on 82 instead. 82 is even, and that breaks the rule immediately. We'd know something went wrong before we ever touched a calculator to check our work.
This kind of check won't catch every mistake, but it's fast enough to run every time. If our answer comes out with the wrong parity, that's our cue to slow down and see where things went sideways.
We can run the same check on multiplication. Let's try 23 × 14.
23 is odd and 14 is even.
Any product with an even factor is even, so the product has to be even.
The solution is 23 × 14 = 322, an even number that fits the rule exactly, just as predicted.
Either way, we already know what the answer should look like before we've finished a single calculation.
Even numbers can be split in half instantly, and that's exactly what makes the halve-and-double trick work. Instead of multiplying two large or awkward numbers directly, we can halve one and double the other. The product stays identical, but the numbers get much easier to work with.
Let's try it with 16 × 25.
16 × 25 → halve 16 to 8, double 25 to 50 → 8 × 50 = 400
8 × 50 → halve 8 to 4, double 50 to 100 → 4 × 100 = 400
4 × 100 is easy to solve in our heads, and it gives us 400.
We stopped there simply because 4 × 100 is the easiest pair to multiply. If we wanted to keep going, 16 could still be halved twice more, first to 2, then to 1, and the answer would still land on 400.
So how far can we push this trick? Let's try 12 × 15 to find out.
12 × 15 → halve 12 to 6, double 15 to 30 → 6 × 30 = 180
6 × 30 → halve 6 to 3, double 30 to 60 → 3 × 60 = 180
3 × 60 also gives us 180, matching the original problem.
Here's where the trick meets its limit.
3 is odd, so halving it again would give us 1.5 instead of a whole number. We can keep halving as long as the number we're halving stays even. The moment it turns odd, the clean, whole-number version of the trick stops working.
📕 You May Also Like: What Are Double Facts in Math? A Complete Overview
A number's parity tells us right away whether it splits evenly between two people, without doing any division at all. We can trust this because an even number, by definition, divides by 2 with nothing left over, exactly what splitting between two people means.
We split money, share snacks, and deal out cards with siblings and friends all the time, and this trick works in every one of those moments.
Let's take $50 split between two friends.
$50 is even, so it splits into $25 and $25, with nothing left over.
$47 is odd, so it doesn't split evenly. Someone ends up with an extra dollar, or the split needs coins to work out.
The same logic works with anything we can count, not just money.
18 cookies is even, so two kids get 9 each, with none left over.
15 cookies is odd, so two kids get 7 each, and one cookie is left over.
This trick works specifically for splitting into two equal groups. If we're dividing something three or four ways instead, we need a different rule, since odd and even alone can't tell us the answer.
📕 You May Also Like: 5 Strategies to Help Your Child Make Sense of Division
We can tell whether an answer has to be odd or even before we finish solving, letting us cross out wrong answer choices right away. On a quiz or a standardized test, that can save real time when every second counts.
Let's try 14 × 9. On the test, we can choose from 126, 133, 140, and 151.
14 is even and 9 is odd, so the product has to be even, since any product with an even factor is even.
133 and 151 are both odd, so we can cross them out right away, before finishing any arithmetic.
That leaves 126 and 140. When we solve it, 14 × 9 = 126, matching one of the two remaining choices.
This kind of check works on any multiple-choice math problem, not just this one. We don't get the final answer for free, but we narrow the field before we've written a single step of work. That's a small habit that pays off any time a test hands us answer choices to work with.
These tricks make the most sense once we try them ourselves. Work through each one below, then check your thinking against the answers later in this guide.
Predict the parity:
Without solving it, is 24 + 19 going to be odd or even?
Without solving it, is 6 × 15 going to be odd or even?
Halve and double:
Use halving and doubling to solve 14 × 25.
Use halving and doubling to solve 18 × 15. Where does the halving have to stop?
Check for a fair split:
Can 42 trading cards split evenly between two friends?
Can $35 split evenly between two kids without needing coins?
Eliminate wrong answers:
For 16 × 5, we have four answer choices: 78, 80, 85, and 91. Which ones can we eliminate before solving?
For 9 × 12, we have four answer choices: 104, 108, 111, and 117. Which ones can we eliminate before solving?
Mathnasium's specially trained instructors help students spot patterns like these, turning quick number tricks into lasting number sense.
Mathnasium is a math-only learning center dedicated to helping K–12 students of all skill levels excel in math.
Whether children are learning to spot patterns in odd and even numbers, building mental math fluency, or tackling more advanced problem-solving, we can support them.
Our proprietary teaching approach, the Mathnasium Method™, is designed around each student's needs and learning style to help them learn and master math. Our approach includes:
Assessment and Personalized Learning Plans: Each student begins their Mathnasium journey with a diagnostic assessment that identifies current skills, strengths, and gaps. From those findings, we build a personalized learning plan tailored to their goals, whether they're building foundational number sense or preparing for more advanced problem-solving.
Teaching for Understanding: Our specially trained instructors use natural language and a mix of verbal, visual, mental, tactile, and written techniques so each concept lands before we move forward.
Problem-Solving and Critical Thinking: We give students time to work through problems independently. That productive struggle helps them learn to trust their own reasoning. When we do step in, we explain both the how and the why behind each answer, so students build problem-solving and critical thinking skills they can use in math and beyond.
An Engaging and Fun Learning Environment: Sessions include games, earned rewards, and consistent celebration of progress. Students build confidence alongside fluency, and many develop a more positive relationship with math over time.
The impact extends beyond the classroom:
94% of parents report an improvement in their child's math skills and understanding
93% of parents report their child's improved attitude toward math after attending Mathnasium
90% of students saw an improvement in their school grades
With over 1,100 learning centers across North America, there's likely one near you.
For families in and around Chester, VA, Mathnasium of Chester brings that same approach to the local community.
📅 Schedule a Free Assessment at Mathnasium of Chester
Not near Chester?
📍 Find a Mathnasium Learning Center Near You
How did you do? Let's find out together.
24 is even and 19 is odd, so the answer has to be odd. 24 + 19 = 43, an odd number, exactly as predicted.
6 is even, so the product has to be even, since any product with an even factor is even. 6 × 15 = 90, an even number.
Halving 14 to 7 and doubling 25 to 50 gives us 7 × 50 = 350, matching 14 × 25 exactly.
Halving 18 to 9 and doubling 15 to 30 gives us 9 × 30 = 270, matching 18 × 15. Since 9 is odd, the halving stops there.
42 is even, so it splits evenly into 21 and 21.
35 is odd, so it doesn't split evenly between two kids without coins.
16 is even, so the product has to be even, ruling out 85 and 91 right away. 16 × 5 = 80, matching one of the remaining choices.
12 is even, so the product has to be even, ruling out 111 and 117 right away. 9 × 12 = 108, matching one of the remaining choices.
(804) 706-4321
