Do you ever get stuck on a simple subtraction like 13 – 7 and wonder if there’s a trick with a “10” involved?
It’s a common hiccup, especially for kids who are just learning the idea of borrowing or “making a ten.” In this post we’ll break down the whole process, show why the 10 is useful, and give you a toolbox of tricks that make subtraction feel like a breeze.
What Is “Making a Ten” in Subtraction?
When you see a number like 13 and you need to subtract 7, you’re dealing with a two‑digit subtraction problem. Then you take 7 from the 10 part, leaving 3, and add the remaining 3 back. Here's the thing — the trick people often use is borrowing or making a ten. Think of it like this: if you have a pile of 13 and you want to take 7 away, you can split the 13 into a 10 and a 3. That’s the “10” you hear about Worth keeping that in mind..
Not the most exciting part, but easily the most useful.
So, “making a ten” isn’t a fancy formula—it’s just a mental shortcut that turns a subtraction into a simpler addition and subtraction.
Why It Matters / Why People Care
1. It Builds Confidence
When kids can see that 13 – 7 is just “take 7 from the 10 and add back the 3,” the problem stops sounding intimidating. Confidence in basic arithmetic spills over into algebra, geometry, and even everyday budgeting.
2. It Simplifies Complex Problems
Later math problems often involve larger numbers. If you’re comfortable borrowing with a 10, you’ll breeze through 87 – 54 or 102 – 37 without breaking a sweat.
3. It’s a Skill, Not a Hack
Teachers rave about “making a ten” because it teaches students to think flexibly. It’s not a shortcut that bypasses understanding; it’s a deeper way of seeing the relationship between numbers Not complicated — just consistent..
How It Works (Step‑by‑Step)
Let’s walk through 13 – 7 using the “make a ten” method. I’ll sprinkle in a few variations so you can pick the one that feels natural.
### 1. Split the Top Number
Write 13 as 10 + 3.
Now you have two piles: a 10 and a 3.
### 2. Subtract the Bottom Number From the 10
Take 7 out of the 10 pile.
10 – 7 = 3.
You’re left with a new 3 in the tens place.
### 3. Add Back the Remainder
The 3 you had from the original split still sits there. Add it to the 3 you just got from the subtraction:
3 + 3 = 6.
That’s your answer.
Common Mistakes / What Most People Get Wrong
-
Skipping the Split
Some folks jump straight to 13 – 7 = 6 without visualizing the 10. That can lead to errors when the numbers are bigger It's one of those things that adds up.. -
Borrowing Too Early
When the bottom number is larger than the top digit (e.g., 23 – 17), you have to borrow from the next column first. Forgetting this step is the classic “borrowing” error No workaround needed.. -
Mixing Up Place Values
Treating the 3 in 13 as if it were a tens place can double‑count it. Always keep track of where each digit lives. -
Using the Wrong Direction
Some people “borrow” from the wrong place, turning a 13 into a 3 + 10 instead of a 10 + 3. That flips the problem upside down Worth knowing..
Practical Tips / What Actually Works
1. Visualize with Blocks
Draw a row of 13 blocks. Color 7 of them red. Count the remaining green ones. You’ll see 6 left. That concrete image cements the concept.
2. Use a “10‑Card” Trick
Keep a spare card that says “10” on your desk. Whenever you see a subtraction problem, pull it out, split the top number, and use the card to remind yourself you’re borrowing a 10.
3. Practice with “Near‑Ten” Numbers
Start with numbers like 19 – 8 or 14 – 9. These are perfect for practicing the split because the bottom number is close to the 10 you’re borrowing.
4. Turn It Into a Story
“Imagine you have 13 candies. You want to give 7 to a friend. First, take 7 from the 10 you have, leaving 3. Then add the 3 you still have. How many do you have left? Six.” Stories make the math feel less abstract Less friction, more output..
5. Check with Addition
After you finish, add the answer back to the subtrahend to see if you land on the original number.
6 + 7 = 13. If it matches, you’re good.
FAQ
How do I handle borrowing when the bottom number is larger than the top digit?
When the units digit of the top number is smaller than the units digit of the bottom number, you borrow 1 from the tens column. So for 23 – 17, you’d first reduce the 2 to a 1 (making the tens column 10) and add 10 to the 3, turning it into 13. Then 13 – 7 = 6, and you add back the 1 from the tens column to get 16.
Does this trick work for subtraction with more than two digits?
Absolutely. That said, for 105 – 78, you’d borrow 1 from the hundreds column, turning 10 into 9 and adding 10 to the 5, making 15. Then subtract 8 from 15 to get 7, and finally combine the 9 (hundreds) and 7 (units) to get 97.
Why is “making a ten” called that? Is it related to base‑10?
Yes! It’s a nod to our base‑10 system. By turning a group of 10 into a single unit, you’re leveraging the fact that ten is the “carry” value in decimal arithmetic.
Can I skip the “make a ten” step if I’m comfortable with mental math?
If you’re an experienced mental calculator, you might skip the explicit split. But the mental split still happens automatically. Knowing the step explicitly helps you debug mistakes and teach others Which is the point..
Final Thought
“Making a ten” is more than a trick—it’s a window into how numbers talk to each other. So next time you see 13 – 7, pull out your mental 10, split the top number, and watch the math unfold. On the flip side, once you get the hang of it, subtraction becomes a smooth conversation between digits. Happy subtracting!
To reinforce the idea with a quickvisual, sketch a line of 13 small squares, fill the first seven in red, and count the six green squares that remain. The picture makes the abstract split‑and‑borrow step concrete without any extra words Simple as that..
Another example to try
Take 28 – 15. Imagine you have 28 candies. First, borrow a ten from the 20, leaving 18. Then subtract the 5 from the 18, which gives 13. The result is 13, confirming the method works even when the top number isn’t a simple teen.
When zeros get in the way
If the top number contains a zero in the tens place—say 30 – 12—think of borrowing from the hundreds column. Reduce the 3 to a 2, turn the 0 into a 10, and then add the borrowed ten to the units digit (0 + 10 = 10). Now you have 20 + 10 = 30, and you can proceed with 30 – 12 = 18.
Speed drills
Set a timer for two minutes and work through a list of subtraction problems, applying the “make a ten” step each time. You’ll notice the mental split becomes automatic, and your confidence grows as the calculations speed up Surprisingly effective..
Teaching tip
When you explain the trick to someone else, frame it as a short story: “You have 13 candies, you give 7 away, first take 7 from the 10 you have, leaving 3, then add the 3 you still keep.” The narrative helps the learner visualize the borrowing process and remember the steps.
Wrapping up
Mastering the “make a ten” strategy transforms subtraction from a daunting chore into a smooth dialogue between digits. With consistent practice, the mental split becomes second nature, empowering you to handle any subtraction problem—no matter how many digits—without hesitation. Keep the visual cue handy, use the 10‑card reminder, and watch your confidence grow as the math flows effortlessly. Happy subtracting!
