### Mental Addition

# Mental Addition

Mental addition does not mean visualizing and performing the addition operation that you would do with paper and pencil. Instead,

**it requires you to display different, practical approaches from traditional addition methods**.## Adding by breaking the number down into its digits

Unlike traditional addition, we start adding not from the units place, but by adding the largest digits.

**Step:**20 + 40 = 60 (we added the tens, which are the largest place value)

**Step:**8 + 5 = 13 (we added the units to the units)

**Step:**60 + 13 = 73 (finally, we combined the total tens with the total units, so we added them all together)

# 2185 + 6534

Add the larger place values first.

# Partial addition (Counting On)

## 65+24

We can add 24 to 65, and we do the addition not all at once but in parts.

Step: 65 + 10 = 75

Step: 75 + 10 = 85

Step: 85 + 4 = 89

We have added a total of 24 to 65.

or ;

Step: 65 + 20 = 85

Step: 85+4=89

# Adding by Rounding

# 19+56

19 is almost 20, so let's consider it as 20. Let's add 20 and 56.

20+56 = 76

76-1 = 75

"By considering 19 as 20, I have increased the result by 1, so the real result is 1 less than the result I found. Let's subtract 1 from 76, making it 75."

# 97 + 86

**100+86=186**

97 is a number very close to 100, so let's round it to 100, or consider it as 100.

**186 - 3 = 183**

By considering 97 as 100, I have increased the result by 3, so the real result is 3 less than what I found. Let's subtract 3.

# Adding by Completing ( Adding with Carrying Over)

Since adding tens, hundreds, and thousands is much simpler, if you can complete the numbers, try to convert them into multiples of tens, hundreds, and thousands.

Let's take 2 from 57 and add it to 38.

Since we took 2 from 57, our number dropped to 55, and we added 2 to 38, so our number became 40.

## 55+40=95

Adding 55 and 40 is simpler than adding 57 and 38

# Adding the Easily Addable First

If there are more than two numbers to be added, you can prioritize adding the ones that are easily addable first.

# 17+28+33

Since 17 and 33 complete each other to multiples of 10, instead of adding 17 and 28, we can first add 17 and 33; 17 + 33 = 50. Then we can add 28 to 50; 50 + 28 = 78.

# Do you know?

Gauss is in elementary school, and his teacher asks the students to add all the numbers from 1 to 100. All the students except Gauss start adding the numbers one by one in a column. Gauss, on the other hand, looks for ways to add them more easily, and soon a brilliant idea comes to his mind. He develops the following method.

He adds the numbers to be summed once more, but in reverse order. The sum of each pair is 101.

How many 101s did we add?

We wrote the numbers from 1 to 100, so there were 100 instances of 101.

100 * 101 = 10,100 is the sum of 100 instances of 101.

Since we have written the numbers from 1 to 100 twice at this point, we need to divide by 2 to find the sum of the numbers from 1 to 100 once.

10,100 ÷ 2 = 5,050 is the sum of the numbers from 1 to 100.

## Dear Students,

Mental/practical operations are not taught to you just as a lesson to be left at that. From now on, you can easily use mental operations instead of traditional addition in your ongoing calculations. You may need to practice a bit for this. Over time, you will see that your operations are freed from clumsiness and that you are speeding up.

## Dear Colleague,

Your approach here is very important for students to get used to these operations and incorporate them into their lives after you show them mental operations in class. Displaying practical approaches in almost every operation will develop our children's intelligence and broaden their horizons.

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