What is the subtraction? Definition, method, examples, facts. (2023)

Subtraction: Introduction

Suppose we buy ice cream for a certain amount of money, say $140, and we give the cashier $200. Now the cashier returns the excess amount by doing a subtraction, e.g. B. $200 − 140 = $60. So the cashier returns $\$60$.

What's going on here?

The answer to this question is subtraction.

What is subtraction in mathematics?

Subtraction is one of the four basic operations in mathematics. The other three are addition, multiplication and division.

We can observe the applications of subtraction in different situations in our daily life.

For example, if we have 3 candies and our friend asks us for 1 candy, how many candies do we have left? Simply,

$ 3 − 1 = 2 $

Let's understand the concept with the following example of apples.

In the example above, if Harry has 6 apples and Jim gives 3 apples, how many apples does he have left?

We can calculate this by subtracting 3 from 6:

$ 6 − 3 = 3 $

Harry is left with 3 apples.

subtraction definition

The operation or process of finding the difference between two numbers or quantities is called subtraction. Subtracting a number from another number is also called "taking a number from another number". Some instances where we use subtraction are when making payments, transferring money to our friends, and more.

minus sign

In mathematics, we often use different symbols for different operators. We have symbols like $+, −, /, *$ and many more. The minus sign $"−"$ is one of the most important mathematical symbols we use. In the previous section we read about subtracting two numbers 6 and 3. If we look at this expression: $(6 − 3 = 3)$, then the symbol $(−)$ between the two numbers denotes the subtraction . This symbol is also known as the minus sign $(-)$.

remainder operation formula

In general, when we subtract two numbers, we use some terms used in a subtraction expression:

decreasing: A minuend is the number from which the other number is subtracted.

Subtract: A subtrahend is the number to be subtracted from the minuend.

Difference: A difference is the final result after subtracting the subtrahend from the minuend.

The subtraction formula is written as

decreasing$-$Subtract$=$Difference

For example,

$ 7 − 3 = 4 $

Here,

$7 =$ Descending

$3 =$ Subtract

$4 = $ difference

What's less in math?

Minus is a sign or symbol represented by a horizontal line.

We use less in math for multiple representations.

Use of the minus sign

Subtraktionsoperation

less stands for thearithmeticSubtraction operation between two numbers. We use the minus sign to denote, subtract, subtract, subtract, etc.

For example,

The minus sign also means how much more one value is than the other value.

For example, Darby has 8 Gingerbread and Olive has 3 Gingerbread.

Darby has more Gingerbread Cookies at $(8 − 3) = $5

Used to represent negative integers

Integers are numbers that are not in decimal or fractional form and contain positive and negative numbers and 0. We use the minus sign to represent negative integers, that is, integers less than zero (without fractions).

To represent a negative integer, we add a minus or minus sign in front of an integer. For example, the negative integer 5 is represented as: $(− 5)$

Use in measurement

We also use the minus sign in measurement, especially temperature.

For example, a temperature of $− 4^{\circ} \text{C}$ means 4 degrees below zero.

Another example: The temperature is $5^{\circ} \text{C}$ and then drops by $− 10^{\circ} \text{C}$. What is the temperature now?

The temperature is now $= 5 − 10 = − 5^{\circ} \text{C}$

To represent opposite directions

We also use the minus sign to represent a negative direction on graph paper to show the coordinates.

The graph also goes in the negative direction.

1. In the first quadrant, the coordinates have the form $(x,y)$.
2. In the second quadrant, the coordinates have the form $(−x,y)$.
3. In the third quadrant, the coordinates have the form $(−x,−y)$.
4. In the fourth quadrant, the coordinates have the form $(x,−y)$.

Mathematical operations on integers using the "minus" sign

• Multiplying two negative numbers results in a positive number.

Negative$\times$Negative$=$Positive

For example $(− 5) \times (− 15) = + 75$

• Multiplying a negative number by a positive number results in a negative number.

Negative$\times$Positive$=$Negative

For example $(− 5) \times (15) = − 75$

• Adding a negative number to a negative number always results in a negative number.

Negative$+$Negative$=$Negative

For example $(− 3) + (− 4) = (− 7)$

• Subtracting a positive number from a negative number always results in a negative number.

When we subtract a positive number from a negative number, we start with the negative number and count backwards.

Negative$-$Positive$=$Negative

For example: Let's say we have the problem $(− 2) − 3$.

Using the number line, let's start with $− 3$.

Now count down 3 units. So if we keep counting down three spaces from $−2$ on the number line, we get

The answer is $(− 2) − 3 = − 5$.

• Subtract a negative number from a negative number

A negative sign followed by a negative sign converts both signs to a positive sign. So instead of subtracting a minus, you add a plus. The answer can be positive or negative depending on the size of the numbers.

Negative$-$Negative$=$Negative$+$Positive

Basically, $−(−5)$ becomes $+ 5$, and then you add the numbers.

For example, we have $(− 2) − (− 5)$. We can read it as "minus two minus minus 5". We change the two negative signs to positive, so the equation now becomes $(- 2) + 5$.

On the number line it starts at $− 2$.

So we advance 5 units: $+ 5$.

The answer is $− 2 − (− 5) = 3$.

• Subtracting a negative number from a positive number always gives a positive number.

When we subtract a negative number from a positive number, we change the minus sign followed by a negative sign to a plus sign. So instead of subtracting a minus, you add a plus. So the equation becomes a simple addition problem.

Positive – Negative = Positive + Positive

For example, suppose we have the problem $2 − (− 4)$. The reading is "two minus minus four". The $− (− 4)$ becomes $+ 4$.

On the number line we start at 2.

So we advance three units: $2 + $4.

The answer is 2$ − (− 4) = 6$.

rest methods

There are several subtraction methods. In this article, we will discuss three of them.

visual representation

One method is to use a chart showing what you start with, what's taken away, and what's left.

For example we have 5 balls, now a friend asks for 2 balls, we can easily calculate that we have 2 balls left using the concept of subtraction and represent it by a chart like this:

Another method of subtraction is to use a number line.

Subtraction on number lines

If we want to calculate 5 minus 2, we start at 5. Since we need 2 to stay, we go back 2 steps. Finally we notice that we are at 3.

This is how $5 − $2 is evaluated on the number line.

This is a number line representation of the expression.

column method

The most commonly used method is the column subtraction method where we separate the numbers into units, tens, hundreds, etc. and we write the minuend above the subtrahend, where all ones are in one column, all tens in another column and short. With this method, we always start the subtraction with ones and proceed from right to left.

regroup into math

Regrouping in mathematics can be defined as the process of forming/ungrouping by performing operations such as addition and subtraction. Regrouping means groups are rearranged in place to perform an operation. We use rearrangement in subtraction when the digits in the minuend are smaller than the digits in the same place in the subtrahend.

This process is called rearrangement because we rearrange numbers, or rearrange them according to their place value, to perform this process. When we use regrouping in subtraction, it is sometimes called borrowing.

Subtraction with rearrangement

When doing subtraction, we sometimes use the concept of rearranging numbers. When subtracting numbers using the column method and the bottom digit is greater than the top digit, we regroup the numbers to subtract.

Let's understand subtraction using this rearrangement example, which involves finding the answer to the expression $31 − 19$.

Here we first subtract the ones place of the number in the bottom box with the top box. When the number in the bottom slot is greater than the number in the top slot, a regrouping, also known as a loan, occurs. In this case we subtract one from the tens place of the number in the top box and write the remaining number above it, that is we subtract 1 from 3 so 2 is what we write above 3 while subtracting that 1 is "borrowed" . ” to the unit's location, convert it to 10 and add it to the existing unit's location number, giving us a two-digit number. In simpler terms, 10 is borrowed from the tens place and added to the ones place. In the example above, 10 is added to the ones place, which is 1, and we write 11 over the ones place.

Now we come to the actual subtraction of the two numbers. The position number of the top slot unit can now be subtracted from the position number of the bottom slot unit, i. $2 − 1$, which gives us 1 and leaves us with 12 as the final answer.

Here's how we regroup the hundreds and tens to subtract 182 from 427:

subtraction properties

Here are some important properties of subtraction in our daily lives.

• Commutative law of subtraction:

The commutative law states that swapping numbers does not change the result. But in subtraction we cannot get the same result if we put the minuend instead of the subtrahend and vice versa. Therefore, the commutative law is not possible in subtraction.

For example, $8 − $5 is not equal to $5 − $8.

• Subtraction Identity Property:

The identity property states that when we subtract "0" from a number, the result is the number itself.

For example $5 − 0 = $5.

• Inverse Property of Subtraction (subtraction of a number itself):

When we subtract a number from itself, the result is always "0".

$\text{A} − \text{A} = 0$

For example $9 − 9 = $0.

• Subtraction property of equality

According to the property, if we subtract any number from both sides of an equation, the equality of the equation remains.

For the given algebra equation;

$\right arrow \times − 3 = 5$

If we subtract the same number from both sides, the equation will still be true. Here we will subtract 8 from both sides.

$\Right Arrow \times − 3 − 8 = 5 − 8$

$\Right Arrow \times − 11 = − 3$

• Distribution property of subtraction

By property, multiplication of subtraction of numbers is equal to subtraction of multiplication of single numbers.

$\text{A} \times (\text{B} − \text{C}) = \text{A} \times \text{B} − \text{A} \times \text{C}$

For example: $3 \times (5 − 2) = 3 \times 3 = $9 and $3 \times 5 − 3 \times 2 = 15 − 6 = $9

Diploma

In this article we will learn about subtraction, its definition with examples, the symbols used for it and the common methods of subtraction. We also learned about the minus sign. The minus sign is used for various purposes. Let's practice our understanding with some worked out examples and practice problems and worked out examples.

worked examples

1. In a soccer match, Team A scored 5 goals and Team B scored 9 goals. Which team scored the most goals and how many?

Solution:

Gols do Time $\text{A} = 5$;

Goals scored by team $\text{B} = 9$

We can clearly see that Team B scored more goals. To calculate the number of goals Team B has surmounted, we subtract 5 from 9.

9 $ − 5 = 4 $

Therefore, Team B scored 4 more goals than Team A.

2. Jeff has 120 pens. Your friend Tim has 50 fewer pens than Jeff. How many pens does Tim have?

Solution:

As we know, the term "less than" refers to the subtraction operation.

given,

Jeff $ = 120 $

Tim $ = 120 − 50 = 70 $

Tim also has 70 Founders.

3. During an annual Easter egg hunt, participants found 52 eggs in the clubhouse, 14 of which were broken. Can you find the exact number of whole eggs?

Solution:

The number of easter eggs found in the clubhouse $= 52$;

Number of broken Easter eggs $= 14$;

The total number of whole eggs $=$ ?

Now let's subtract the number of broken eggs from the total number of eggs.

Therefore, the number of whole eggs is 38.

4. Jerry collected 194 fish and Evan collected 132 fish. Who collected the most fish and how much?

Solution:

Number of fish collected by Jerry $= 194$;

Number of fish collected by Evan $= 132$

This shows Jerry collected more fish. Let's subtract $194 − $132 to get the difference.

As a result, Jerry caught 62 more fish than Evan.

5. How much less is 5251 than 6556?

Solution:

The data shows that 6556 is greater than 5251.

Now subtract 5251 from 6556.

6556 $ − 5251 $ = 1305 $

So 5251 is less than 6556 times 1305.

6. What is the value of 794 minus 658?

Solution:794 $ − 658 $ = 136 $

7. When Steve woke up his temperature was$101^{\circ} \text{F}$. Two hours later it was the third lowest value. What was his temperature after two hours?

Solution:Temperature when Steve woke up $= 101^{\circ} \text{F}$

Temperature after 2 hours $= 101^{\circ} \text{F} − 3^{\circ} \text{F} = 98^{\circ} \text{F}$

8. What are the coordinates of A if$x = −5$mi$y = − 7$. Which A quadrant will you be in?

Solution:Given $x = − 5$ and $y = − 7$, the coordinates of A are $(− 5, − 7)$. Since both coordinates are negative, i.e. $( − x, − y)$, A lies in the third quadrant.

9. There is an elevator on the eighteenth floor. Go down 13 floors. What floor is the elevator on now?

Solution:The floor where the elevator is located is now $= 18 − 13 = 5th floor

10. es$(4 − 6) = (6 − 4)$?

Solution:Let's find the solution for both.

On the left $4 − 6 = − $2

On the right, however, $6 − 4 = $2

We can clearly see that $2 \neq − 2$.

Therefore $(4 − 6)$ is not equal to $(6 − 4)$.

practical problems

frequently asked questions

Why is the answer to a subtraction problem called difference?

Because when you subtract a smaller number from a larger number, the result is the difference between the two numbers.

Example: Subtract 2 from 6

$ 6 − 2 = 4 $

But the number 6 is also 4 greater than 2. It's the difference between the two numbers.

What other operation has the output less than the input?

Another operation where the output is less than the input is division.

Is subtraction associative?

No, subtraction is not associative. Let's see an example: $10 − (5 − 1) \neq (10 − 5) − 1$

Can we subtract a larger number from a smaller number?

Yes, we can subtract a larger number from a smaller number. The result is a negative number.

Mathematically, why does the "counting" of subtraction work?

If we subtract 2 numbers we can do it in two ways. Let's take an example of subtracting 5 from 8. You can take 8 and subtract 5 from it, or you can start with 5 and count to 8. If you start with 5 and count to 8, you do this 3 times: 6, 7 , and 8. So 3 is the difference between 5 and 8.

What is the difference between the minus sign and the plus sign?

The minus sign is denoted by a horizontal symbol, i.e. $−$, and means to subtract or take away. While the plus sign is denoted by the intersection of horizontal and vertical lines, that is, $ + $, which means add or find the sum.

Is the commutative property true for subtraction?

The commutative property does not apply to subtraction. Average for any two integers, $\text{A} − \text{B} \neq \text{B} − \text{A}$. For example: $3 − 5 = − 2$ and $5 − 3 = 2$ and $− 2 \neq 2$.

Is the associative law true for subtraction?

The associative law does not apply to subtraction. Average for any three integers A, B, and C.

$\text{A} – (\text{B} – \text{C}) \neq (\text{A} – \text{B}) – \text{C}$ For example: $(2 – ) – 5 = – 1 – 5 = – 6$ and $2 – (3 – 5) = 2 + 2$ and $– 6 \neq 4$.

What is a minuend and a subtrahend?

In a subtraction equation, the minuend is the highest number from which a component would be subtracted. A subtrahend is the term denoting the number being subtracted from another.

Who discovered the minus sign?

(Video) Grade 1 Math 5.6, Use related facts, add & subtract

Robert Recorde introduced the modern use of minus to Britain in 1557. The first appearance of the minus sign was given by Johannes Widmann in 1489 and can be found in his book entitled "Mercantile Arithmetic".