Have you ever sat there staring at a math problem, feeling that tiny flicker of frustration because the numbers just aren't clicking? It happens to the best of us. You look at something like 13 minus 7, and suddenly, your brain decides to take a nap.
Maybe you’re helping a kid with their homework. Maybe you’re brushing up on your own mental math skills because you want to be faster, sharper, and more confident. Either way, you’ve hit a wall.
Here’s the thing — math isn't about memorizing endless strings of digits. It’s about seeing the patterns. Once you see the pattern, the "hard" part disappears.
What Is Making a 10
When we talk about "making a 10," we’re talking about one of the most powerful shortcuts in arithmetic. It’s a mental strategy used to simplify subtraction and addition by using the number 10 as a bridge Easy to understand, harder to ignore..
Think about it. Still, we use a base-10 number system for everything. Our fingers, our currency, our entire way of counting is built around the number 10. Because of that, 10 is the "anchor" of our math system. It’s the easiest number to work with.
The Bridge Concept
If you are trying to subtract 7 from 13, you're essentially trying to figure out the gap between those two numbers. Instead of counting backward one by one (12, 11, 10, 9...), which is slow and prone to mistakes, you break the problem into two smaller, easier steps. You use 10 as a stepping stone to get from the larger number to the smaller one No workaround needed..
Why We Use It
We use this because human brains aren't naturally great at calculating large, awkward jumps. We are, however, incredibly good at recognizing "friends of ten." If you know that 7 needs 3 more to become 10, you've already solved half the problem without even trying.
Why It Matters
You might be thinking, "Why bother? Consider this: " Sure, you can. I can just use my fingers or a calculator.But there’s a massive difference between calculating and understanding Easy to understand, harder to ignore..
When you understand the "make a 10" strategy, you stop seeing math as a series of chores and start seeing it as a series of connections. This is the foundation of number sense Easy to understand, harder to ignore. That alone is useful..
Speed and Accuracy
In a classroom setting, kids who master this strategy move away from "counting on fingers" much faster. They stop relying on physical movements and start doing the math in their heads. This speed is crucial as math gets harder. You can't solve complex algebra if you're still struggling to subtract single digits.
Building Confidence
Math anxiety is real. A lot of it comes from the fear of losing track of a sequence. If you lose your place while counting down from 13, you have to start all over. But if you use the "make a 10" method, you have a fixed point to return to. It provides a safety net. It turns a messy process into a structured one Easy to understand, harder to ignore..
How to Solve 13 - 7 Using the 10 Strategy
Alright, let's get into the actual mechanics. Plus, how do you actually take 13, subtract 7, and use 10 to get the answer? I'll break it down into a simple, repeatable process.
Step 1: Decompose the Larger Number
The first thing you need to do is look at 13 and break it apart. We want to see how many "tens" are inside it.
In the number 13, you have one group of 10 and three leftovers (the ones). On the flip side, we call this decomposing. Instead of seeing 13 as one big chunk, see it as 10 + 3 That's the whole idea..
Step 2: Subtract to Reach the Anchor
Now, look at the number you are subtracting: 7.
Our goal is to use that 10 we just identified to get as close to our target as possible. But wait—we aren't subtracting 7 from 10 yet. We are subtracting 7 from the whole 13.
Here is the trick: We want to see how much we need to take away from 13 to get down to 10.
Actually, let's look at it another way. Let's see how much 7 "needs" to become 10. 7 + 3 = 10.
Step 3: The Two-Step Subtraction
This is where the magic happens. We are going to subtract the 7 in two smaller bites Easy to understand, harder to ignore..
- First, take away enough from 13 to get to 10. To get from 13 down to 10, you subtract 3.
- Now, look at what's left of your 7. You started with 7, and you just used 3 of it. How much of the 7 is left? 4.
- Finally, subtract that remaining 4 from the 10 you reached earlier.
10 - 4 = 6.
So, 13 - 7 = 6 Small thing, real impact..
Let's Visualize It
If you're explaining this to someone else, try this: Imagine you have 13 marbles. You want to give away 7. First, you set aside 3 marbles to get your pile down to a nice, even 10. You still owe 4 more marbles (because 7 minus the 3 you already gave away is 4). Take those 4 marbles out of your pile of 10. You are left with 6 Small thing, real impact..
It sounds a bit longer than just "doing the math," but once you get the rhythm, it's lightning-fast The details matter here..
Common Mistakes / What Most People Get Wrong
Even though the concept is simple, people trip over it all the time. Most people don't fail because they don't understand the math; they fail because they lose track of the "leftovers."
Forgetting the Remainder
The biggest mistake is subtracting the "bridge" number but forgetting to subtract the rest of the subtrahend And that's really what it comes down to..
In our example (13 - 7), someone might see that 3 gets them to 10, and then they just stop. They say "10." But they forgot that they only subtracted 3, and they were supposed to subtract 7. You have to account for the entire number you are subtracting That's the whole idea..
Mixing Up Addition and Subtraction
This sounds silly, but it happens. When people are trying to "make a 10," they sometimes accidentally add the numbers instead of subtracting the difference That's the part that actually makes a difference..
If you're working with 13 - 7, and you realize 7 needs 3 to become 10, you might accidentally think the answer is 13 + 3 or 10 + 7. You have to keep your direction clear: are we moving toward 10, or are we moving away from it?
Overcomplicating the Decomposition
Some people try to break 13 into 6 and 7. While that works, it's not "making a 10." The whole point of this strategy is to use the base-10 structure of the number. If you don't use 10 as your pivot point, you're just doing standard subtraction, and you've missed the whole benefit of the shortcut Practical, not theoretical..
Practical Tips / What Actually Works
If you want to master this—whether you're a student or an adult trying to sharpen your brain—here is what actually works in practice.
Learn Your "Friends of Ten"
This is the absolute foundation. You shouldn't have to think about what plus what equals 10. It should be instant Surprisingly effective..
- 1 + 9
- 2 + 8
- 3 + 7
- 4 + 6
- 5 + 5
If you know these by heart, the "make a 10" strategy becomes a reflex rather than a calculation.
Use Visual Aids (Even if You're an Adult)
If you're struggling, use a number line or even just draw
Practical Tips / What Actually Works
1. Turn the “bridge” into a mental shortcut
The moment you spot that a number is just a few steps away from the next multiple of ten, picture that distance as a bridge you cross Most people skip this — try not to..
- Example: 13 → 10 is a bridge of 3 because you need to add 3 to reach 10.
- Example: 27 → 30 is a bridge of 3 because you need to add 3 to reach 30.
When you’re subtracting, you’re actually walking backward across that bridge. The size of the bridge tells you how many units you must first “undo” before you can finish the subtraction.
2. Break the subtraction into two micro‑steps
- Cross the bridge – add (or think of adding) the amount needed to hit the nearest ten.
- Finish the journey – subtract the remainder of the original subtrahend after you’ve crossed.
Using the earlier illustration (13 – 7):
- Bridge size = 3 (13 → 10).
- Remainder to subtract = 7 – 3 = 4.
- After crossing, you have 10 – 4 = 6.
The whole process collapses to “subtract the bridge, then subtract what’s left.”
3. Practice with numbers that already sit on a ten
When the minuend is already a multiple of ten, the bridge is zero, so the method reduces to ordinary subtraction.
- 50 – 18: Bridge = 0 (50 is already a ten).
- Subtract the remainder directly: 50 – 18 = 32.
Seeing the bridge as “0” reinforces that the technique works for any starting point; it simply becomes invisible when you’re already on a ten.
4. Extend the idea to larger numbers
The same principle scales up when you’re working with hundreds or thousands That alone is useful..
- 382 – 47:
- Identify the next convenient ten‑multiple: 382 → 390 (bridge = 8).
- Adjust the subtrahend: 47 – 8 = 39.
- Subtract the adjusted amount from the rounded number: 390 – 39 = 351.
You can think of it as “round up, compensate, then subtract.” The mental load stays light because you only ever deal with small bridge values The details matter here. But it adds up..
5. Use the “make‑a‑ten” habit for everyday calculations
- Mental math drills: Spend a minute each day visualizing pairs that sum to ten. Flashcards, quick quizzes, or even smartphone apps can cement the pattern.
- Real‑world scenarios: When checking a grocery bill, rounding the total to the nearest ten and then adjusting the change trains the habit without feeling like practice.
- Teach the bridge: Explaining the concept to a peer forces you to articulate the steps, which deepens your own understanding.
6. Anticipate common slip‑ups and how to catch them
- Skipping the second subtraction: After crossing the bridge, always ask, “What’s left to subtract?” If the answer feels too small, double‑check that you haven’t forgotten the remainder.
- Confusing addition with subtraction: The bridge is a forward move toward a ten, but the overall operation is backward (you’re taking away). Keep the direction arrow in mind: → for building the ten, ← for the final subtraction.
- Choosing the wrong bridge: If a number is closer to a lower ten (e.g., 27 is nearer to 20 than 30), you can still use the bridge, but you’ll be subtracting a negative amount. It’s often simpler to pick the nearest higher ten to keep the bridge positive.
Conclusion
The “make‑a‑ten” subtraction shortcut is more than a neat trick; it’s a mental scaffold that turns a potentially cumbersome calculation into a series of tiny, predictable steps. By internalizing the size of the bridge, consistently breaking the problem into two micro‑operations, and rehearsing with numbers that already sit on a ten, you gain speed, confidence, and fewer opportunities for error. Whether you’re a student polishing basic arithmetic, a professional who needs quick estimates, or simply someone who enjoys sharpening cognitive muscles, master
ing this technique will pay dividends in everyday numeracy. The beauty of the "make-a-ten" method lies not in its complexity, but in its consistency—it works the same way whether you're subtracting 7 from 13 or 47 from 382. With regular practice and mindful application, what once felt like mental arithmetic becomes intuitive pattern recognition, freeing up cognitive space for deeper problem-solving and mathematical fluency.
Short version: it depends. Long version — keep reading.
