Neutral Element (Identiy Element)

What is a Neutral Element?

In mathematics, a neutral element is an element that does not alter the rest of the numbers when we perform an operation with it.

Neutral Element - Addition

With addition, $0$ is considered a neutral element because it does not modify the number to which it is added.

$0+3=3$

Neutral Element - Multiplication

In multiplication, $1$ is considered a neutral element because it does not affect the result.

$4\times1=4$

Neutral Element - Subtraction and Division

The neutral element in subtraction is $0$ , while in division it is $1$ .

Detailed explanation

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Test yourself on special cases (0 and 1, inverse, fraction line)!

$8\times(5\times1)=$

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Addition and Subtraction Exercises with a Neutral Number

$18-0=18$
$22+0=22$
$1000000-0=1000000$
$0+12-0=12$

Multiplication Exercises with a Neutral Number

$13\times 1=13$
$220\times 1=220$
$\frac{1}{2}\times 1=\frac{1}{2}$
$X\times 1=X$
$2000000\times 1=2000000$

Note that in a multiplication operation, $-1$ is not considered a neutral number because it affects the the number it is multiplied with by changing its sign.

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Test your knowledge

Question 1

$7\times1+\frac{1}{2}=$

Question 2

$\frac{6}{3}\times1=$

Question 3

Solve the following exercise:

$12+3\cdot0=$

Review Questions

What is a neutral element?

A neutral element is a number that does not alter the other numbers when an operation is applied to it.

Why is there no neutral element for addition?

The only neutral element for addition is $0$ and zero is not part of the set of natural numbers. Therefore, there is no neutral of addition in this set.

Do you know what the answer is?

Question 1

Solve the following exercise:

$$ 2+0:3= $$

Question 2

$\frac{25+25}{10}=$

Question 3

$$ 0:7+1= $$

How do you determine the neutral element for a product?

If there is a non-zero number a and we must find the value of $x$ when $ax=a$ , then by solving the equation we find that the neutral of the product is 1.

What is the neutral element for division?

The neutral element for division is $1$ .

Check your understanding

Question 1

$$ 12+1+0= $$

Question 2

$$ 0+0.2+0.6= $$

Question 3

$\frac{1}{2}+0+\frac{1}{2}=$

What does absorbing element mean?

The absorbing element of multiplication is 0 because any number multiplied by $0$ is $0$ .

What defines the additive neutral of real numbers?

The additive neutral of real numbers does not modify the value of any number that it is added to.

Example: $0$ is the additive neutral of real numbers since $a+0=a$ .

Do you think you will be able to solve it?

Question 1

$$ 9-0+0.5= $$

Question 2

$$ 19+1-0= $$

Question 3

$$ 2+0:3= $$

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Well, yes! This is because there will be some subjects that come to you easily, while others may take you longer to grasp.

Test your knowledge

Question 1

$12+3\times0=$

Question 2

$1\times\frac{1}{2}:2$

Question 3

$8\times(5\times1)=$

What can you do in this case?

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You can browse Tutorela for helpful explanations covering various mathematics topics.

Do you know what the answer is?

Question 1

$7\times1+\frac{1}{2}=$

Question 2

$\frac{6}{3}\times1=$

Question 3

Solve the following exercise:

$12+3\cdot0=$

Examples with solutions for Neutral Element (Identiy Element)

Exercise #1

$8\times(5\times1)=$

Video Solution

Step-by-Step Solution

According to the order of operations, we first solve the expression in parentheses:

$5\times1=5$

Now we multiply:

$8\times5=40$

Answer

Exercise #2

$7\times1+\frac{1}{2}=$

Video Solution

Step-by-Step Solution

According to the order of operations rules, we first insert the multiplication exercise into parentheses:

$(7\times1)+\frac{1}{2}=$

Let's solve the exercise inside the parentheses:

$7\times1=7$

And now we get the exercise:

$7+\frac{1}{2}=7\frac{1}{2}$

Answer

$7\frac{1}{2}$

Exercise #3

$\frac{6}{3}\times1=$

Video Solution

Step-by-Step Solution

According to the order of operations rules, we will solve the exercise from left to right, since there are only multiplication and division operations:

$\frac{6}{3}=2$

$2\times1=2$

Answer

$2$

Exercise #4

Solve the following exercise:

$12+3\cdot0=$

Step-by-Step Solution

According to the order of operations, we first multiply and then add:

$12+(3\cdot0)=$

$3\times0=0$

$12+0=12$

Answer

$12$

Exercise #5

Solve the following exercise:

$2+0:3=$

Step-by-Step Solution

According to the order of operations rules, we first divide and then add:

$2+(0:3)=$

$0:3=0$

$2+0=2$

Answer

$2$

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