How to Make One Addend the Next Tens Number: A Complete Guide to Faster Mental Math
Mental math is an invaluable skill that saves time and builds confidence in mathematics. This technique transforms complex additions into simple calculations that anyone can perform mentally. One of the most powerful strategies for adding numbers quickly is learning how to make one addend the next tens number. Whether you are a student, a parent helping with homework, or simply someone who wants to calculate faster, this method will revolutionize the way you approach addition.
Understanding the Tens Number Strategy
The strategy of making one addend the next tens number involves adjusting one of the numbers in an addition problem to reach a convenient round number—specifically a multiple of ten. That said, since our number system is base-10, working with multiples of ten is naturally easier for the human brain. Once you adjust one number, you simply compensate for that change to maintain the correct sum Simple as that..
This method works because addition and subtraction are inverse operations. When you add to one number to make it a tens number, you must subtract the same amount from the final answer to keep the equation balanced. The beauty of this strategy lies in its flexibility: you can adjust either addend, whichever makes the calculation easier.
Take this: consider the problem 47 + 28. Since you added 3 to get from 47 to 50, you subtract 3 from 78 to get the final answer of 75. Instead of adding these numbers directly, you can transform 47 into 50 by adding 3. Now the problem becomes 50 + 28, which equals 78. The process takes seconds once you practice it.
Step-by-Step Process
Understanding the theoretical concept is only the beginning. Let us walk through the exact steps so you can apply this strategy immediately.
Step 1: Identify Your Addends
Look at the addition problem and identify the two numbers you are adding together. As an example, in 36 + 19, your addends are 36 and 19.
Step 2: Choose Which Addend to Adjust
Examine both numbers and decide which one is easier to transform into a tens number. On top of that, both work, but 36 requires only 4 more to become 40, while 19 requires only 1 more to become 20. In real terms, in 36 + 19, 36 is already close to 40, while 19 is close to 20. Ask yourself: which number is closer to a multiple of ten? Choose the one that requires the smallest adjustment.
Step 3: Add to Reach the Next Tens Number
Take your chosen addend and add just enough to make it a complete tens number. Consider this: if using 36, you add 4 to reach 40. If using 19, you add 1 to reach 20 Took long enough..
Step 4: Complete the Addition with the New Tens Number
Now add the adjusted tens number to the other original addend. Using 36 + 19 with adjustment to 40: 40 + 19 = 59. With adjustment to 20: 36 + 20 = 56.
Step 5: Compensate for Your Adjustment
This is the crucial final step. Since you added a certain amount to create the tens number, you must subtract that same amount from your result. If you added 4 to reach 40, subtract 4 from your answer. If you added 1 to reach 20, subtract 1. Following our example: 59 - 4 = 55, or 56 - 1 = 55. Both give you the correct answer.
Practical Examples
Let us explore several examples to solidify your understanding of this powerful strategy.
Example 1: 58 + 24
In this problem, 58 is only 2 away from 60, making it the obvious choice to adjust. And add 2 to transform 58 into 60. Now calculate 60 + 24 = 84. Finally, subtract the 2 you added: 84 - 2 = 82. The answer is 82.
Example 2: 67 + 45
Here, 67 is 3 away from 70, while 45 is 5 away from 50. Choose 67 and add 3 to reach 70. Calculate 70 + 45 = 115. Subtract the 3 you added: 115 - 3 = 112. The answer is 112 It's one of those things that adds up. Turns out it matters..
Example 3: 29 + 37
This interesting case has 29 just 1 away from 30, while 37 is 3 away from 40. The smaller adjustment wins: add 1 to 29 to make 30. Now calculate 30 + 37 = 67. Subtract the 1: 67 - 1 = 66. The answer is 66.
Example 4: 84 + 58
Number 84 needs 6 to become 90. Subtract 2: 144 - 2 = 142. Now, add 2 to 58 to make 60. The better choice is adjusting 58 because it requires less compensation. So calculate 84 + 60 = 144. Number 58 needs 2 to become 60. The answer is 142 Small thing, real impact. That alone is useful..
Notice how in each example, choosing the addend requiring the smallest adjustment minimizes the compensation step and reduces the chance of error.
Why This Strategy Works
The mathematical foundation behind making one addend the next tens number lies in the commutative property of addition and the relationship between addition and subtraction. When you modify one addend by a certain amount, you are essentially creating an equivalent equation that is easier to solve It's one of those things that adds up..
This strategy also leverages the brain's natural affinity for round numbers. Our minds process multiples of ten much faster than arbitrary numbers because we encounter them constantly in everyday life—currency, measurements, and time all frequently use multiples of ten. By restructuring problems to include these familiar numbers, calculation becomes almost intuitive Not complicated — just consistent..
Short version: it depends. Long version — keep reading.
Beyond that, this method builds number sense. On top of that, as you practice adjusting addends to tens numbers, you develop a deeper understanding of how numbers relate to each other and how our base-10 system works. This understanding transfers to other mathematical operations and concepts.
Applications Beyond Basic Addition
Once you master making one addend the next tens number, you can extend this thinking to more complex situations. In real terms, the same principle applies when working with larger numbers—adjusting to the next hundred or even thousand. It also appears in subtraction problems, where you might adjust to make subtracting from a round number easier No workaround needed..
This strategy serves as a foundation for more advanced mental math techniques. Those who become proficient at making addends into tens numbers often find it easier to learn other strategies like splitting numbers into place values or using doubles and near doubles.
Common Mistakes to Avoid
Even though this strategy is straightforward, beginners often make similar mistakes. But the most frequent error is forgetting to compensate. After creating the tens number and completing the addition, it is tempting to announce the result without subtracting the adjustment amount. Double-checking your work prevents this error.
Another mistake involves choosing the wrong addend to adjust. While any adjustment will yield the correct answer if you compensate properly, selecting the addend requiring the larger adjustment creates unnecessary work. Always look for the smallest adjustment first.
Finally, some learners struggle when both addends are equidistant from tens numbers. In these cases, either choice works equally well. Trust your instincts and proceed with whichever feels more comfortable Most people skip this — try not to..
Practice Problems
Test your understanding with these additional problems:
- 43 + 29 = ? (Answer: 72)
- 56 + 37 = ? (Answer: 93)
- 78 + 19 = ? (Answer: 97)
- 65 + 48 = ? (Answer: 113)
- 91 + 34 = ? (Answer: 125)
Work through each problem using the five-step process outlined above. With practice, you will find yourself adjusting numbers automatically without consciously thinking through each step Simple, but easy to overlook..
Conclusion
Making one addend the next tens number is more than just a tricks—it is a legitimate mathematical strategy that builds computational fluency and number sense. In real terms, by transforming challenging additions into simpler problems involving round numbers, you reduce cognitive load and increase calculation speed. The key steps are choosing the addend closest to a tens number, adding just enough to reach that tens number, completing the addition, and finally compensating by subtracting what you added Nothing fancy..
And yeah — that's actually more nuanced than it sounds.
This strategy empowers anyone to perform mental calculations with confidence. Worth adding: whether you are adding prices while shopping, calculating change, or solving math problems, this technique will serve you well. But practice consistently, and soon you will find yourself naturally reaching for tens numbers whenever you add. The journey to mental math mastery begins with a single step—and in this case, that step is simply adding enough to reach the next ten.
