Mental Math for Addition

Mental Math with Number Complements
Mental math with number complements is a strategy that uses pairs of numbers that add up to a power of 10, like 10, 100, or 1,000. It’s especially useful for making addition and subtraction easier by converting them into problems that are simpler to solve. The core idea is that it’s often easier to work with “friendly” round numbers.

Key Concepts
Complements: Two numbers that add up to a round number (e.g., 10, 100, 1000). For example, the complement of 7 is 3 (because 7+3=10). The complement of 25 is 75 (because 25+75=100).

The “make 10” strategy: This is the most basic form of using complements and is a foundation for more complex calculations. The goal is to break apart one of the addends and use a part of it to “make a 10” with the other addend. This works because it is much easier to add numbers to 10 than to other numbers. The strategy is built on the concept of number complements, which are pairs of numbers that add up to 10.

How it Works
Let’s use the example of 8+5 to illustrate the steps:

1. Identify the first addend. In this case, it’s 8.
   
2. Find the complement to 10. To get from 8 to 10, you need to add 2. So, the complement of 8 is 2.
   
3. Break apart the second addend. The second addend is 5. We need to break 5 into two parts, one of which is the complement we just found (2). The other part will be 5−2=3. So, 5 is broken into 2 and 3.
   
4. Make the 10. Now, you can combine the 8 with the 2 to make 10.
   8+2=10.
   
5. Add the remaining part. Add the remaining part of the second number (3) to the 10.
   10+3=13.
   So, 8+5=13.

This strategy helps students develop a strong number sense and is an important stepping stone toward more advanced mental math techniques.

Using Complements for Addition
This strategy works best when one of the numbers is close to a round number. The goal is to adjust the numbers to make the problem simpler.
Example: 47+8

1. The complement of 7 (the ones digit of 47) is 3. We need 3 to get to the next friendly number, 50.
   
2. Take 3 from the 8. This leaves us with 8−3=5.
   
3. Add the 3 to 47, which gives us 50.
   
4. Now, the problem is a simple addition: 50+5=55.

Videos

The following videos show some math tricks that will help you to do mental addition quickly and efficiently.

Mental Math Secrets - The Secret to Mental Addition
We learn the most important secret of mental addition that can be applied to addition problems of any length.
Complement of Numbers

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Mental Math - Single Column Addition
Here we learn how to add columns of single digit numbers together rapidly and mentally. We focus on finding complements of numbers to speed up the process.

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Mental Math Secrets - Two Column Addition
Can you add 27+19+34+62 mentally?
In this episode, we learn how to mentally add two digit numbers rapidly using left-to-right addition.

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Addition - Mental Math
More practice for column addition

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Free Addition Games
One More, One Less	1-Digit Addition	1-Digit Addition (Timed)
Add Doubles	Number Bonds	Add 3 or more single digits
2-Digit + 1-Digit (no regrouping)	2-Digit + 1-Digit (with regrouping)	Add Multiples of 10
2-Digit + 2-Digit (no regrouping)	2-Digit + 2-Digit (with regrouping)	3-Digit Addition

 

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