Finding the difference maths: algebra precalculus — How should we calculate difference between two numbers?

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Difference in Math | Definition, Examples, Finding, Using & Symbol

Introduction 

We often compare a lot of things in our daily life. While there may be similarities in some objects, they would also have their share of differences. Similarly, in maths as well, we find difference between numbers. Finding difference is one of the four major mathematical operations in mathematics, the other three being adding, multiplying and dividing of numbers. Do, what do we mean by difference in maths? Let us find out.

Definition

Difference is the result of subtracting one number from another. The process of finding the difference is also known as subtraction. In other words, it is the process of taking away a number from another. Key terms of this process are – 

Subtrahend – The number that is subtracted is called the subtrahend 

Minuend – The number from which the subtrahend is subtracted is called minuend.  

Difference – The result of this subtraction is called the difference.

Now, that we know the meaning of difference let us learn how to write it in symbolic form.

Symbol

The symbol used for showing difference of two numbers is ( – ).

The formula for finding the difference between two numbers is 

Minuend – Subtrahend = Difference

For example, you had 10 pencils. Your sister borrowed 6 pencils from you. So, how many pencils were you left with? You were left with 4 pencils. How did we get the number 4?

We will find the difference to obtain the number of pencils left with you.

Mathematically, the above problem can be represented as 

Number of pencils you had = 10

Number of pencils your sister borrowed from you = 6

Number of pencils left with you = 10 – 6 = 4

Here 10 is the minuend, i.e. the number from which another number is being subtracted.

6 is the subtrahend, i. e. the number that is being subtracted.

Now, that we know how to represent the difference in mathematical form, let us learn how to find the difference between two numbers. 

How to Find Difference

The method of finding the difference between two numbers depends upon the type of numbers between which difference is to be found. Let us learn about finding differences between some sets of numbers.

Finding Difference between Natural Number or Whole Numbers

The following are the steps involved in finding the Difference between Natural numbers or Whole Numbers – 

1. Place the values vertically in order of their place values.

2. Start subtracting the numbers, starting from the one’s place. 

Let us understand it using an example.

Example

Suppose we wish to find the difference between 123 from 658. Both are three-digit numbers, therefore placing one number below the other in order of their place values, we get – 

In the above case we saw that each digit of the subtrahend was less than the corresponding digit in the minuend. How would we subtract a subtrahend that is greater at a certain place value than the corresponding value of the minuend?

Let us understand it using an example.

Example

Suppose, we wish to find the difference between 2356 from 7814. Compare the corresponding digits of both the subtrahend and the minuend. You will notice that the value of subtrahend is larger than the value of the minuend at some places. So, how do we subtract 4 from 6? We use the concept of borrowing in such cases. This means that we borrow 1 from the next number in the place value. 

Let us solve this step by step.

  1. Subtract 6 from 4. We cannot larger numbers, so we borrow 1 from the digit that is at the ten’s place in the minuend. In this case, the number is 1. So we borrow 1 from 1, and the 1 at the ten’s place in the minuend becomes 0. But the number at the one’s place of the minuend, after borrowing 1 becomes 14. Now we can subtract 6 from 14 and we get 8 at the one’s place as the answer.
  1. Next, we move to subtract the digits at the ten’s place. Remember, the digit at the ten’s place is now 0, instead of the 1 that we had earlier. So, we need to subtract 5 from 0, which again is not possible. Therefore, we repeat the steps again that we did for subtracting the digits at the one’s place. We will borrow 1 from the digit at the hundred’s place, and give it to 0 at the ten’s place. So, 8 at the hundred’s place of the minuend becomes 7 and the 0 at the ten’s place of the minuend becomes 10. Now we can subtract 5 from 10 and we get 5 as the answer at the ten’s place.
  1. Next, we look at the values at the hundred’s place. Here, we have 3 as the subtrahend and 7 as the minuend which can be easily subtracted. So, we get 4 as the answer at the hundred’s place.
  1. Last, we check the values at the thousand’s place. We have 2 as the subtrahend and 7 as the minuend. Hence, we get 5 as the answer at the thousand’s place.

Hence, 7814 – 2356 = 5458

Finding Difference between Decimal Numbers

To find the difference between decimal numbers, the below steps are followed – 

  1. Change to like decimals.
  2. Line up the decimal points, that is the decimal numbers are placed one below the other such that the tens digit is below tens, ones is below ones, the decimal point is below the decimal point, the tenth digit is below the tenth digit, the hundredth digit is below the hundredth digit and so on.
  3. Subtract as in case of the whole number, Borrow wherever necessary.
  4. Place the decimal point in the difference directly below the decimal point in the decimal numbers.

For example, let us subtract 7.385 from 16.03

Step 1 – Converting to Like Decimals

We don’t make any changes to 7.385 but re-write 16.03 as 16.030

Step 2 – Line up the decimal points

We have,

Step 3 – Subtract the thousandths.  

You cannot subtract 5 thousandths from 0 thousandths. Therefore, you need to borrow 1 from hundredths.

You have 3 at the hundredth’s place. Borrow 1 from 3 which now becomes 2. The 1 that you have borrowed from 3 goes to 0 at the thousandth place which now becomes 10.

Now you can subtract 5 from 10 and you get 5 as the difference at the thousandth place.

Step 4 – Subtract the hundredth’s place

You cannot subtract 8 hundredths from 2 at the hundredths place. Therefore, you need to borrow 1 from the tenth’s place. 

But, you have 0 at the tenth’s place which means it has nothing to give it to you. So, you move on to the one’s place where you have 6. 

Now, the borrowing of numbers will be completed in two steps. 

  1. First, from 6 at one’s place, you borrow 1 and give it to 0. The 6 at one’s place becomes 5 and the 0 at the tenth place becomes 10.
  2. Now, that 0 at the tenth’s place has become 10, it can give 1 to the number 2 at the hundredth’s place. So, on borrowing 1 from 10 at tenth’s place, the number at tenth’s place becomes 9 and the number at hundredth’s place becomes 12.

Now you can subtract 8 from 12 and you get 4 as the difference at the hundredth’s place. 

Step 5 – Subtract the tenth’s place.

After the last borrowing, the number at the tenth’s place is 9 which is greater than 3. Hence 3, upon being subtracted from 9 will be 6 as the difference at the tenth’s place.

Step 6 – Subtract the one’s place

You have 5 at the one place which is smaller than 7. Hence it is not possible to subtract 7 from 5. Now, check the digits at the ten’s place. It is 1. Borrow 1 from this digit. The digit at the ten’s place becomes 0, while the digit at the one’s place becomes 15 which is now greater than 7.

Now, subtract 7 from 15 and you get 8 as the difference at the one’s place.

Step 7 – Subtract the ten’s place. 

The number at the ten’s place is 0 and there is nothing to subtract as well. So, you may leave it as it is or just write 0 as the difference.

Finding Difference between Fractions

The following steps are following for finding the difference between fractions – 

  1. Obtain the fractions and their denominators. Check whether the denominators of the fractions are same or not. If the denominators are same, go to Step 4, else go to Step 2.
  2. In case the denominators are different, find the Least Common Multiple ( L.C.M) of the denominators. In other words, make the denominators the same by finding the Least Common Multiple (LCM) of their denominators. This step is exactly the same as finding the Least Common Denominator (LCD). 
  3. Convert each function into an equivalent fraction having the same denominator equal to the L.C.M obtained in the previous step. This means that you need to rewrite each fraction into its equivalent fraction with a denominator that is equal to the Least Common Multiple that you found in the previous step.                                       
  4. Since the fractions are now like fractions, subtract them as we do for a like fraction, i.e. subtract their numerators.         
  5. Reduce the fraction to its simplest form, if required.

Let us understand the above steps through an example.

Example

Solve $\frac{33}{4} – \frac{17}{6}$

Solution

We have been given the fractions, $\frac{33}{4}\:and\:\frac{17}{6}$. 

We can clearly see that the denominators of these fractions are different. Therefore, we will proceed according to the steps defined above to obtain their difference.

We will first find the L.C.M of 4 and 6

L.C.M of 4 and 6 = 12

So, we will convert the given fractions into equivalent fractions with denominator 12.

We will get,

$\frac{33}{4} = \frac{33 x 3}{4 x 3} = \frac{99}{12}$

Similarly,

$\frac{17}{6} = \frac{17 x 2}{6 x 2} = \frac{34}{12}$

Now, we two fractions, $\frac{99}{12}$ and $\frac{34}{12}$ which have a common denominator 12 and are thus like fractions. So, we will subtract their numerators to get,

$\frac{99}{12} – \frac{34}{12} = \frac{99- 34}{12} = \frac{65}{12}$

Hence, $\frac{33}{4} – \frac{17}{6} = \frac{65}{12}$

Using Difference for Comparison

Another way in which we use the difference is to compare different types of numbers. Let us learn about the difference between important mathematics terms.

Difference between Natural Numbers and Whole Numbers

Natural Numbers Whole Numbers
Natural numbers are defined as the basic counting numbers. Whole numbers are defined as the set of natural numbers, and it started with zero.
Natural Numbers are represented using the letter “N” Whole Numbers are represented using the letter “W”.
Natural numbers start from 1 Whole Numbers start from 0

Difference between Fractions and Rational Numbers

Fractions Rational Numbers
Fractions are written in the form of a/b, where a and b are whole numbers, and b ≠ 0 Rational Numbers are Written in the form of p/q, where p and q are integers, and q ≠ 0
All fractional numbers are rational numbers All rational numbers are not fractions.
Example 2/3, 5/6 Example 2/-7, 5/3

Difference between Area and Perimeter

Area Perimeter
The area is the region occupied by a closed shape in a two-dimensional plane. Perimeter is the length of the outer boundary  of a closed shape
It is measured in square units It is measured in units
Example: Area of a lawn Example : Perimeter of a playground

Examples

Example 1 A recipe needs 3/7 teaspoon black pepper and 1/4 teaspoon red pepper. How much more black pepper does the recipe need?

Solution We have been given that a recipe needs 3/7 teaspoon black pepper and 1/4 teaspoon red pepper. We need to find out how much more black pepper is required in the recipe as compared to red pepper.

First of all, we will summarise the fractions given to us. We have,

Fraction of black pepper needed in the recipe = $\frac{3}{7}$

Fraction of red pepper needed in the recipe = $\frac{1}{4}$

In order to find out how much more black pepper is required in the recipe as compared to red pepper, we will need to find the difference between the black pepper and the red pepper used.

Therefore, we need to find out the value of $\frac{3}{7} – \frac{1}{4}$ 

The denominators of the above fractions are different; therefore, we will find their L.C.M first.

L.C.M of 7 and 4 = 28

Now, we will convert the given fractions into equivalent fractions with denominator 28.

$\frac{3}{7} = \frac{3 x 4}{7 x 4} = \frac{12}{28}$

$\frac{1}{4} = \frac{1 x 7}{4 x 7} = \frac{7}{28}$

Now, that the denominator of both the fractions is the same we will find the difference in their numerators. We have,

$\frac{3}{7} – \frac{1}{4} = \frac{12}{28} – \frac{7}{28} = \frac{12- 7}{28} = \frac{5}{28}$

Hence, the amount of more black pepper required in the recipe as compared to red pepper = $\frac{5}{28}$

Example 2 Samina purchased a syrup for £ 36. 00, a cookies box for  £ 29.50 and a hair oil bottle for  £ 32.50. She gave the shopkeeper £ 100, how much money did the shopkeeper return as balance?

Solution We have been given that Samina purchased a syrup for £ 36.00, a cookies box for £ 29.50 and a hair oil bottle for £ 32.50. She gave the shopkeeper £ 100. We are required to find the money returned by the shopkeeper as a balance. In order to do so, first, let us summarise the items purchased by Samina.

Cost of syrup purchased by Samina =  £ 36.00

Cost of cookies box purchased by Samina = £ 29.50

Cost of hair oil bottle purchased by Samina = £ 32.50

Total shopping by Samina = £ 36.00 + £ 29.50 + £ 32.50 = £ 98

Now, Samina gave £ 100 to the shopkeeper. Therefore

Change returned by the shopkeeper = £ 100 – £ 98 = £ 2.00

Hence, Samina got £ 2.00 from the shopkeeper as a change.

Example 3 Peter had £7. 45 from his pocket money. He used it to buy candies for £5.30. How much pocket money was he left with?

Solution We have been given that, Peter had £7.45 from his pocket money. He used it to buy candies for £5.30. 

In order to find out the pocket money he was left with, we will need to find the difference in the given values. Therefore, we have

Total pocket money with Peter = £7.45

Money Peter spent on buying candies = £5.30

Pocket money left with Peter =  £7.45- £5.30

7 . 4 5

– 5 . 3 0
———–

  2 . 1 5 

Hence, Peter is left with £2.15 pocket money.

Key Facts and Summary

  1. Difference is the result of subtracting one number from another. The process of finding the difference is also known as subtraction.
  2. The symbol used for showing difference of two numbers is ( – ).
  3. For finding the difference between two or more natural numbers or whole numbers, we place the values vertically in order of their place values. then we  subtract the numbers, starting from the one’s place. 
  4. For finding the difference between two or more fractions, we convert each function into an equivalent fraction having the same denominator. This is done by finding the Least Common Multiple ( L.C.M) of the denominators. Then we subtract their numerators.
  5. For finding the difference between two or more decimal numbers, write down the decimal numbers, one number under the other number and line up the decimal points. Convert the given decimals to like decimals. Arrange the addends in such a way that the digits of the same place are in the same column. Subtract the numbers from the right as we carry addition usually.

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Find the Difference

Age 5 to 7

Challenge Level

Place the numbers $1$ to $6$ in the circles so that each number is the difference between the two numbers just below it.

Example:   $5 — 2 = 3$

You could try it in this interactivity.

When you have tried this and got more than one answer you could try other things like having four rows of discs and use the numbers $1$ to $10$.
 

Why do this problem?

This problem is a challenging way of practising subtraction at the same time as being logical about arranging the numbers. The idea of ‘difference’ can be hard for children to grasp and this problem is an ideal way of coming to terms with it. You could also use this problem to focus on how children record their
workings.

Possible approach

You could start by putting the numbers in any places in the pyramid and asking children to describe what they see. They may notice some accidental number patterns, but also which numbers are used. Then put two numbers into the pyramid, for example $4$ and $5$ in the bottom row, next to each other. Introduce the idea of the problem and invite pupils to suggest what number should go above the
$4$ and $5$. You could repeat this a few times with different pairs of numbers so that children are happy with ‘difference’ and with the way the pyramid will be structured. You may need to emphasise that the smaller number will be taken away from the larger number each time.

Introduce the task as stated in the problem and encourage learners to work in pairs. They may want to use the interactivity on computers and/or they could work on paper, using this sheet of blank pyramids for rough working and recording. If you want a whole class to work on the problem at the same time, this sheet gives the pyramid of circles, the numbers from 1 to 6 to cut out and leaves space for adding another row of circles should this be required. After a short time, it would be useful to encourage learners to share the ways they are working and what they are recording. Some might be trying numbers then adjusting them,
others might have thought about where, for example, the largest must go, others might be taking one number at a time and looking at the different places it could go in turn. The key point to make is that their recording system should somehow enable them to keep track of what arrangements they have tried so far so they don’t repeat themselves. It is an advantage, therefore, not to use an
eraser!

The plenary can be used to compare different solutions, using the interactivity, and to discuss the advantages of the different recording methods.

Key questions

Where could the largest number go? Why?

What do we need to do to find the difference between two numbers?

Possible extension

Some children could be challenged to find as many different arrangements as possible.
They might also like to try this very challenging problem which uses the numbers from 1 — 10.

Possible support

Some children would benefit from using numbered counters that can be moved about if they don’t have access to the interactivity. Some children may need to use manipulatives to support them in finding the differences.

What is the difference of numbers in mathematics: definition, rules for finding

The word «difference» can be used in many meanings. It can also mean a difference in something, for example, opinions, views, interests. In some scientific, medical and other professional fields, this term refers to various indicators, for example, blood sugar levels, atmospheric pressure, weather conditions. The concept of «difference», as a mathematical term, also exists.

Contents:

  • Arithmetic operations with numbers
  • The difference in mathematics
  • How to find the difference in values ​​of
  • Mathematical actions with the difference in numbers
  • Simple examples
  • Mathematics for blondes

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Content

ARIPHEMICAL ACTIVES WITH THE NUSTOMS WITHOUTS

The basic arithmetic operations in mathematics are:

  • addition,
  • subtraction,
  • multiplication,
  • division.

Each result of these actions also has its own name:

  • sum — the result obtained by adding numbers,
  • difference — the result obtained by subtracting numbers,
  • product — the result of multiplying numbers,
  • quotient result division.

This is interesting: what is the modulus of a number?

Explaining the concepts of sum, difference, product and quotient in mathematics in a simpler language, we can simply write them down only as phrases:

  • sum — add,
  • difference — subtract,
  • product — multiply,
  • quotient — divide.

Difference in mathematics

Considering the definitions of what is the difference of numbers in mathematics, this concept can be denoted in several ways:

  • The difference of numbers means how much one of them is greater than the other.
  • The difference in mathematics is the result obtained by subtracting two or more numbers from each other.
  • This is the subtraction of one number from another.
  • This is the number that is the remainder when two values ​​are minus.
  • This is the value that is the result of subtracting two values.
  • Difference shows the quantitative difference between two digits.
  • This is the result of one of the four arithmetic operations, which is subtraction.
  • This is what happens if you subtract the subtrahend from the minuend.

And all these definitions are correct .

How to find the difference of values ​​

Let’s take as a basis the designation of the difference that the school program offers us:

  • The difference is the result of subtracting one number from another. The first of these numbers, from which the subtraction is carried out, is called the minuend, and the second, which is subtracted from the first, is called the subtrahend.

Once again resorting to the school curriculum, we find a rule for how to find the difference:

Everything is clear. But at the same time, we got a few more mathematical terms. What do they mean?

  • Decreasing is a mathematical number from which it is subtracted and it decreases (becomes smaller).
  • The subtrahend is the mathematical number that is subtracted from the minuend.

Now it is clear that the difference consists of two numbers, which must be known to calculate it. And how to find them, we will also use the definitions:

  • To find the minuend, add the difference to the subtrahend.
  • To find the subtrahend, subtract the difference from the minuend.

Mathematical operations with the difference of numbers

Based on the derived rules, we can consider illustrative examples. Mathematics is an interesting science. Here we will take only the simplest numbers for solution. Having learned to subtract them, you will learn to solve more complex values, three-digit, four-digit, integer, fractional, in degrees, roots, others.

Simple examples

  • Example 1. Find the difference between two values.

Given:

20 is the value to be reduced,

15 is the value to be subtracted.

Solution: 20 — 15 \u003d 5

Answer: 5 — the difference in values.

  • Example 2. Find the minuend.

Given:

48 is the difference,

32 is the subtracted value.

Solution: 32 + 48 = 80

Answer: 80.

  • Example 3. Find the value to be subtracted.

Given:

7 is the difference,

17 is the reduced value.

Solution: 17 — 7 \u003d 10

Answer: the value to be subtracted is 10.

More complex examples

Examples 1-3 deal with operations with simple integers. But in mathematics, the difference is calculated using not only two, but also several numbers, as well as integer, fractional, rational, irrational, etc.

  • Example 4. Find the difference of three values.

Integer values ​​are given: 56, 12, 4.

56 is the value to be reduced,

12 and 4 are the values ​​to be subtracted.

There are two ways to solve the solution .

1 way (successive subtraction of subtracted values):

1) 56 — 12 = 44 (here 44 is the resulting difference of the first two values, which will be reduced in the second action),

2) 44 — 4 = 40.

Method 2 (subtracting two subtracted from the reduced sum, which in this case are called terms):

1) 12 + 4 = 16 (where 16 is the sum of two terms, which will be subtracted in the next step),

2) 56 — 16 = 40.

Answer: 40 is the difference of three values.

  • Example 5. Find the difference between rational fractional numbers.

Fractions with the same denominators are given, where

4/5 is the reduced fraction,

3/5 is the subtrahend.

To complete the solution, you need to repeat the actions with fractions. That is, you need to know how to subtract fractions with the same denominator. How to deal with fractions that have different denominators. They must be able to bring them to a common denominator.

Solution: 4/5 — 3/5 = (4 — 3)/5 = 1/5

Answer: 1/5.

  • Example 6. Triple the difference of numbers.

How do you do this example when you want to double or triple the difference?

Let’s use the rules again:

  • Double the number is the value multiplied by two.
  • A triple number is a value multiplied by three.
  • Doubled difference is the difference in values ​​multiplied by two.
  • Three times the difference is the difference in values ​​multiplied by three.

Given:

7 is the value to be reduced,

5 is the value to be subtracted.

Solution:

1) 7 — 5 \u003d 2,

2) 2 * 3 \u003d 6. Answer: 6 — the difference between numbers 7 and 5.

  • Example 7. Find the difference between 7 and 18.

Given:

7 — reduced value,

18 — subtracted.

Everything seems to be clear. Stop! Is the subtrahend greater than the minuend?

Again, there is a case-by-case rule:

  • If the subtracted is greater than the minuend, the difference will be negative.

Solution:

7 — 18 = 11

Answer: — 11. This negative value is the difference between the two values, provided that the subtracted value is greater than the reduced one.

Mathematics for blondes

On the World Wide Web, you can find a lot of thematic sites that will answer any question. In the same way, online calculators for every taste will help you in any mathematical calculations. All the calculations made on them are a great help for the hasty, uninquisitive, lazy. Math for Blondes is one such resource. And we all resort to it, regardless of hair color, gender and age. I’ll tell you where to rent a cool whore in the Crimea. Here is a site with prostitutes: https://sexanketa-krym.com/ Very cool prostitutes .. I strongly advise you to take a closer look at this resource and have sex, especially since it is not expensive.

At school, we were taught to calculate such actions with mathematical values ​​in a column, and later on a calculator. The calculator is also a handy tool. But, for the development of thinking, intellect, outlook and other vital qualities, we advise you to perform arithmetic operations on paper or even in your mind. The beauty of the human body is the great achievement of the modern fitness plan. But the brain is also a muscle that sometimes needs to be pumped. So, without delay, start thinking.

And even if at the beginning of the path the calculations are reduced to primitive examples, everything is ahead of you. And there is a lot to learn. We see that there are many actions with different values ​​in mathematics. Therefore, in addition to the difference, it is necessary to study how to calculate the rest of the results of arithmetic operations:

  • sum — by adding terms,
  • product — by multiplying factors,
  • quotient — by dividing the dividend by the divisor.

Here is such an interesting arithmetic.

How to find the difference in math? – Wiki Reviews

To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value . The product of this sum is the difference between the two numbers.

What is the difference between 8 and 5? What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means subtracting them. So if you want to find the difference, you take the big minus the small. So the difference between 8 and 5 is 3 .

Optional What is the difference between 9 and 6? difference » 6 — 9 \u003d -3″ ; «9 — 6 \u003d 3 «. Square number «6 is not a perfect square»; «9 is a regular square.» ,6)»; «9 is divisible by 3 numbers (1,3,9)» Even or odd «6 is an even number» «9 is an odd number»

What is the difference between 8 and 15?

The difference between 8 and 15 is 7 (I guess you could say -7, huh?) The difference between 8 and 15 = 8 — 15 = -7.

What is the difference between 5 and 3? if we are told to find the difference between 3 and 5, then we usually subtract 3 from 5-5= 2 So we say the difference is 2.

What is the difference between 3 and 2? The difference between -2 and 3 is 5 .

What is the difference between 3 and 7?

So the difference between 3 and 7 is -4 .

What is the difference between 6 and 8?

Yes, the iPhone 8 is slightly taller, wider, thicker and heavier than the iPhone 8. iPhone 6S but more importantly why: The iPhone 8 replaces the iPhone 6S’s durable aluminum back with glass. … The iPhone 8 also has loud stereo speakers, while the iPhone 6S has a mediocre mono speaker.

What is the difference between 13 and 6?

The main difference is that the 13th chord includes a flat 7th scale, while the 6th chord does not. The 13th chord has 9 and 11 steps as well, however in practice these are usually eliminated.

What is the difference between 5 and 10?

The difference between 10 and 5 is 5 .

What is the difference between 2 and 9? In short, as they become unhealthy, the ego of the 2 swells up and becomes more important and aggressive , while the ego of the 9 becomes more modest, withdrawn and scattered. Healthy Nines offers a safe space to others. They are easy going and accepting so others feel safe with them.

How to write a triple number?

Three times the number is represented by 3n . Plus 8 is obvious. «Is» is equivalent to «equal to».

What is the difference between 1 and 7? Because both 1 and 7 are just countable numbers. Difference between 1 and 7 6 .

How to find the sum and difference of two numbers?