## Estimation

Estimation is an inexact result that does not require calculations but logical thinking.
Round the numbers given in the exercise and think logically.

### What is estimation?

Estimation is, indeed, a guess based on data that tells us what the approximate answer is.
Estimation does not require an exact calculation, therefore, the key to success is knowing how to round.
All you need to know is how to round numbers correctly and act in a logical manner. Quite simple, isn't it?

### Let's remember: How do we round off?

We will always try to round by approximating to tens, hundreds, or thousands.

#### Round to the nearest ten

Let's look at the digit in the ones place, if it is equal to or less than 4 we will round down.
If it is equal to or greater than 5 we will round up.

#### Round to the nearest hundred

Let's look at the tens digit, if it is 4 or less we will round down.
If it is 5 or more we will round up.

## Estimation

Estimation exercises are simple and friendly when you approach them with logic.
In this article, we will teach you what estimation is and how you should act when facing addition or subtraction exercises.

### What is estimation?

Estimation is, indeed, a guess based on data that tells us what the approximate answer is.
Estimation does not require an exact calculation, therefore, the key to success is knowing how to round.
All you need to know is how to round numbers correctly and act in a logical manner. Quite simple, isn't it?

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### Let's remember: How do we round?

We will always try to round by approximating to tens, hundreds, or thousands.

#### Round to the nearest ten

Let's look at the digit in the ones place, if it is equal to or less than $4$ we will round down.
If it is equal to or greater than $5$ we will round up.

#### Round to the nearest hundred

Let's look at the tens digit, if it is equal to or less than $4$ we will round down.
If it is equal to or greater than $5$ we will round up.

### How do you round a decimal number?

We round a decimal number to an integer.
We will look at the digit that appears after the decimal point. If it is equal to or less than $4$ we round down, if it is equal to or greater than $5$ we round up.

Now, after having reviewed how to round numbers, it will be easier for us to move on to estimation exercises.
Since they do not require an exact calculation, we should round them correctly and check the result.

## Exercises with Solutions

### Exercise 1

Without doing calculations, determine which of the following exercises will have a result greater than $12$?

1. $6.4+6.01=$
2. $0.8+5=$
3. $4.68+3.9=$
4. $15.04-1.98=$

Solution:
1 and 4.

Explanation
To answer, we will need to round the numbers.
We will round $6.4$ to $6$ and $6.01$ to $6$.
Together they add up to $12$. Right away, the same numbers are greater than $6$, which tells us that the real answer is more than $12$.
Even at a glance, we can determine that the result will be greater than $12$ because we know that
$6+6=12$ and in the exercise, there are $2$ numbers that are greater than $6$.

Let's continue with answer 4 –>
We will round $15.04$ to $15$. We will round $1.98$ to $2$
$15-2=13$
Therefore, in exercise 4 the answer will also be greater than $12$.

If we had rounded the numbers in the answers from 2 and 3, we would have received results less than $12$
and, therefore, they were disqualified.

### Exercise 2

Another estimation exercise:
If we subtract a number greater than $400$ from $2000$, the result we could obtain is:

1. $1600$
2. $1650$
3. $1550$
4. $1700$

Solution:

3. $1550$

Explanation:
To answer, we must use logic.
If we subtract the number $400$ from $2000$, we would get $1600$, and therefore, if we subtracted a number larger than $400$, the result would be less than $1600$.
Thus, only answer $3$ is correct.

### Exercise 3

Mark without calculating $<,>,=$
$34+12$ _____$32+11$

Solution: We see that the expression on the right side contains larger numbers, therefore, the sum will also be larger.

### Exercise 4

Oscar has $100$$in his wallet. He wants to buy the following items at the mall: A T-shirt for $38$$, an egg sandwich for $26$$, a chocolate milk for $12$$, and a phone case for $13$\$.
Without calculating, determine if Oscar will be able to buy everything he wants.

Solution:
We will round the numbers correctly and add them to see what approximate result we get.
If it is less than $100$, Oscar can probably buy everything, if it is more than $100$ it seems that he cannot.
$38$ we round to $40$, $26$ we round to $30$, $12$ we round to $10$, and $13$ we round to $10$.
$40+30+10+10=90$
We got $90$, therefore, Oscar will be able to buy everything he wanted with $100$.

### Exercise 5

Complete the following exercise without calculating:
$106+□= 107+96$

Solution:
$97$.
We need to achieve an equality. $106$ is $1$ less than $107$, therefore, we must add $1$ to the second term. That is $96+1=97$.

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