Show How To Make A 10 To Solve 13-7

How to make a 10 to solve 13‑7

When you encounter a subtraction problem such as 13‑7, the quickest mental shortcut many students discover is to make a 10. This technique rewrites the numbers so that one of them becomes a multiple of ten, turning a potentially tricky subtraction into a simple “take‑away” operation. In this article you will learn exactly how to make a 10 to solve 13‑7, why the method works, and how to apply it confidently in everyday calculations.

Understanding the Concept of Making a Ten

The phrase make a ten originates from early‑grade arithmetic curricula, where children are taught to decompose numbers into parts that sum to ten. The idea is simple: whenever a subtraction involves a number close to a multiple of ten, you can adjust the minuend (the number you are subtracting from) so that the subtraction becomes easier. For 13‑7, the target ten is 10 itself. By regrouping the 13 into 10 + 3, you create a clear visual of “take away 7 from 10, then add back the leftover 3.

Why does this work?
Mathematically, subtraction is the inverse of addition. If you can express 13 as 10 + 3, then

13 − 7 = (10 + 3) − 7 = 10 − 7 + 3

Because 10 − 7 is a basic fact that most learners memorize (the answer is 3), the whole expression reduces to 3 + 3 = 6. The make a ten strategy therefore transforms a subtraction that might feel unfamiliar into a combination of two easy operations.

Step‑by‑Step Guide to Make a 10 to Solve 13‑7

Below is a clear, numbered sequence that you can follow each time you need to make a 10 for subtraction problems.

1. Identify the minuend and subtrahend - In 13‑7, the minuend is 13 and the subtrahend is 7.

2. Determine how far the minuend is from the nearest ten

   • 13 is 3 away from 10 (13 = 10 + 3).

3. Rewrite the minuend as a sum that includes ten

   • Express 13 as 10 + 3.

4. Apply the subtraction to the ten part first - Compute 10 − 7 = 3.

5. Add back the leftover part

   • Add the remaining 3 to the result from step 4: 3 + 3 = 6.

6. State the final answer

   • Which means, 13 − 7 = 6.

Visual representation

   13          →   10 + 3
 -  7                - 7
 -----               ----
   6                 (10‑7) + 3 = 3 + 3 = 6```  

By consistently following these steps, you internalize the habit of **making a ten** whenever a subtraction involves numbers near a multiple of ten.  

### Why This Strategy Works – Scientific Explanation  

From a cognitive‑load perspective, the human brain processes single‑digit subtraction faster than multi‑digit or “cross‑ten” calculations.  Research in educational psychology shows that *chunking*—breaking a problem into smaller, familiar units—reduces mental effort and speeds up problem solving.  When you **make a ten**, you are essentially chunking the original subtraction into two micro‑operations:  

- **Chunk 1:** Subtract from a round number (10).  
- **Chunk 2:** Add the remainder.  

This aligns with the *working memory* capacity limits; by offloading the “hard” part (13‑7) into a “easy” part (10‑7) plus a simple addition, you stay within the brain’s optimal processing window.  

Beyond that, the *commutative property* of addition guarantees that the order of operations does not affect the final result.  Because 10 − 7 + 3 is mathematically identical to 3 + (10 − 7), you can rearrange the steps to suit your mental preference, further easing the computation.  

### Frequently Asked Questions  

**Q1: Can I use the *make a ten* method for any subtraction?**  
*A:* It works best when the minuend is close to a multiple of ten (e.g., 12, 15, 23).  If the minuend is far from any ten, you may need to adjust by creating a different “friendly” number, such as 20 or 30, using the same principle.  

**Q2: What if the subtrahend is larger than the part I’m subtracting from?**  *A:* In that case, you would need to *borrow* from the next higher place value (e.g., turning 13 into 10 + 3 and borrowing 1 from the tens column).  The *make a ten* technique still applies, but you must first ensure the part you are subtracting from is at least as large as the subtrahend.  **Q3: Does *making a ten* only apply to whole numbers?**  
*A:* Primarily it is taught for whole numbers, but the underlying concept of decomposing a number into a round component plus a remainder can be extended to decimal subtraction (e.g., 12.5 − 7.3 becomes (10 + 2.5) − 7.3).  

**Q4: How can I practice this skill efficiently?**  *A:* Create a set of subtraction problems where the minuend ends in 1‑9 and the subtrahend is a single digit.  Solve each by first rewriting the minuend as a sum that includes ten, then follow the five‑step process outlined above.  Repetition builds automaticity.  

### Common Mistakes and How to Avoid Them  

- **Skipping the decomposition step** – Some learners

Mastering subtraction near a multiple of ten can significantly boost accuracy and confidence. By understanding the structure of these problems, you harness the brain’s natural preference for patterns and simplifications. The key lies in recognizing when to adjust the minuend to form a “ten” and then leveraging addition to reach the answer.  

It’s also important to keep in mind that while the *make a ten* method streamlines calculations, it’s not a one‑size‑fits‑all solution. This leads to when dealing with larger numbers or more complex operations, revisiting standard algorithms ensures you remain flexible. This adaptability is crucial in real‑world scenarios, where problems may vary in format.  

Remember, practice reinforces neural pathways, making the process feel intuitive over time. As you become more comfortable, you’ll find these strategies second nature, turning potentially tricky subtractions into smooth, confident tasks.  

At the end of the day, the *make a ten* technique is a powerful tool grounded in cognitive science, and with consistent application, it becomes second nature. In practice, embrace the process, refine your approach, and always trust your mental shortcuts. Conclusion: By strategically breaking down subtractions around multiples of ten, you empower yourself to tackle challenges with clarity and precision.

**Extending the idea to larger numbers**

When the numbers you’re working with exceed two digits, the same principle can be applied in layers. Now, suppose you need to compute \( 84 - 27 \). First, notice that 27 is close to 30, a tidy multiple of ten. So rather than trying to subtract 27 directly, you can think of the problem as \( 84 - (30 - 3) \). By borrowing a ten from 84, you rewrite it as \( 70 + 14 \). Now subtract 30, arriving at \( 70 + 14 - 30 = 50 + 14 = 64 \), and finally add back the borrowed 3, giving \( 64 + 3 = 67 \). The steps echo the earlier “make a ten” routine, but they are repeated at a higher magnitude, reinforcing the pattern of decomposing, borrowing, and recombining.

**Using complements for quick mental checks**

Another handy shortcut is to use the *ten’s complement* of the subtrahend. Plus, when you subtract \( b \) from a number ending in 9, you can add the complement instead: \( 9 - b = (10 - b) - 1 \). , 100) and then subtracting 16, yielding the same result. That's why extending this, \( 84 - 27 \) can be approached by adding the complement of 27 (which is 73) to the next higher ten (i. e.For any single‑digit number \( b \), its complement to ten is \( 10 - b \). This method is especially useful when the minuend ends in 9 or when you’re dealing with a series of subtractions that share a common subtrahend.

**Practical exercises to cement the skill**

1. **Mixed‑digit drills** – Write down a column of problems such as \( 53 - 8 \), \( 71 - 9 \), \( 86 - 12 \), and solve each by first adjusting the minuend to the nearest ten, then performing the subtraction, and finally adding back any borrowed units.  
2. **Two‑step borrowing** – Tackle expressions like \( 250 - 197 \). Here you first round 197 up to 200, subtract to get 50, and then add back the 3 you over‑subtracted.  3. **Real‑world scenarios** – Estimate change while shopping: if an item costs \$47 and you pay with a \$50 bill, think of 50 as the “ten” you’re aiming for, subtract 47 to find the change (\$3).  

Regularly alternating between these exercises trains your brain to spot the nearest round number automatically, turning what once felt like a manual algorithm into an instinctive mental shortcut.

**A final perspective**

The power of this approach lies not merely in the mechanical steps but in the way it reshapes how you view numbers—as flexible building blocks rather than rigid symbols. ” you cultivate a habit of abstraction that serves you across arithmetic, algebra, and even everyday problem‑solving. Because of that, by consistently asking yourself, “What round number can I use to simplify this? Embracing this mindset transforms routine calculations into opportunities for mental agility, empowering you to figure out numerical challenges with confidence and speed.  

**Conclusion**  
When you internalize the habit of reshaping subtraction problems around convenient multiples of ten, you reach a streamlined, reliable pathway to accurate results, turning complexity into clarity with each mental adjustment.