**Category : **4th Class

**LEARNING OBJECTIVES**

**This lesson will help you to:—**

- be able to find the difference between two numbers.
- be able to solve real life problems based on subtraction.
- explore various facts of subtraction.
- be able to define subtraction.
- be able to define the terminology of subtraction.
- be able to explain the properties of subtraction.

** **

**Real Life Example**

Subtraction is used in every sphere of our life. It is used in our daily activities like purchasing grocery, all monetary transactions like banks etc.

More on top?????

No need to stop.

More on the floor?????

Go next door, get ten more.

Numbers the same?????

Zero’s the game.

** **

**QUICK CONCEPT REVIEW**

** **

**WHAT IS SUBTRACTION?**

Subtraction is taking away some objects from a given collection. It is taking one number away from another.

Some other names used in subtraction are Minus, Less, Difference, Decrease, Take Away, Deduct.

**TERMINOLOGY**

**Difference**

The result obtained after subtraction is called difference.

It the result obtained after subtracting one number from another.

**Minuend**

The number that is to be subtracted from is called minuend.

**Subtrahend**

The number that is to be subtracted is called subtrahend.

MINUEND – SUBTRAHEND = DIFFERENCE

For example, 50 - 20 = 30

Here, Minuend = 50

Subtrahend = 20

Difference = 30

**PROPERTY OF SUBTRACTION**

- When we subtract a number from itself, the answer is always Zero.

**For example:** 6884 – 6884 = 0

- When we subtract zero from a number, the answer is the number itself.

**For example:** Monty saw 9 mangoes on a mango tree.

He wants to eat the mangoes but could not reach them. How many mangoes were left on the tree?

There were 9 mangoes on the tree. Monty could not get any mango. It means still there were 9 mangoes on the tree.

This can be written as 9 – 0 = 9

Therefore, there were 9 mangoes left on the tree.

Hence, we can say that when we subtract zero from a number, the answer is the number itself.

**SUBTRACTION WITH NUMBER LINE**

72 – 45 =?

5 + 20 + 2 = 27

Therefore, 72 - 45 = 27

** **

**USES OF SUBTRACTION**

**1. To find out how many are left:** In a singing competition, 25 students out 75 qualified for the next round? How many students were left unselected?

Here we have to find the number of students who were left unselected. Whenever we have to find how many are left we use subtraction.

** **

**Amazing Fact**

The above question can solved with an amazing shortcut also.

5000 – 1832 =?

\begin{align}

& 5000\to 5000-1\to \,\,\,\,\,\,\,\,\,\,4999 \\

& -1832\to 1832-1\to -\underset{\begin{smallmatrix}

\_\_\_\_\_\_\_\, \\

\underset{\_\_\_\_\_\_\_\_\_\_}{\mathop{\,3168}}\,

\end{smallmatrix}}{\mathop{1831}}\, \\

\end{align}

Therefore, number of students left unselected = Total number of students - Number of students selected = 75 - 25 = 50

**2. To compare groups:** A Bakery had 52 pastries & 95 cookies. How many more cookies are there than pastries?

There are 2 groups:

(a) Pastries and

(b) Cookies

Now to compare the quantity of 2 groups, we will subtract the smaller group from the larger group.

This is shown as follows;

\begin{align}

& \underline{\begin{matrix}

\,\,\,\,9\,\,5\,\,\text{cookies} \\

-5\,\,2\,\,\text{cookies} \\

\end{matrix}} \\

& \,\,\,4\,\,3\,\,\text{more}\,\text{cookies}\,\text{than}\,\text{pastries}\text{.} \\

\end{align}

**3. To find what does not belong to a group:** Ben has 15 dogs. Out of them 5 are pugs. Find out how many dogs are not pugs.

Total number of dogs = 15

Number of Pugs = 5

To find the number of dogs which do not belong to the group of pugs, we will subtract the number of pugs from total number of dogs.

Therefore, 15 - 5 s 10 dogs are not pugs.

**4. To find what was taken away: **A farmer loaded a truck with 1129 apples. On the way, some apples fell on the road. On unloading, the farmer found that there are only 1000 apples. Find out how many apples fell from the truck.

Here we know the original number & the number which is left over. We need to find the number of apples taken away.

This can be written as follows:

\[\,\,-\,\,=\,\,\]

Therefore, the number of apples which fell from the truck are = 1129 – 1000 = 129

**5. To find how many more are needed:** A thirsty crow needs 1255 pebbles to put in the pot to raise the water level. But he has only 255 pebbles. How many more pebbles does he need?

\[\,\,+\,\,\,\,=\,\,\]

The number of pebbles required = 1255 – 255 = 1000 more pebbles.

**SUBTRACTING FOUR DIGIT NUMBER**

**1. Without Regrouping/Borrowing:** There are 2549 seats in a circus tent. 2138 people came to see the circus show. How many seats were left vacant?

To find out the number of vacant seats we will use subtraction as follows:

No. of vacant seats = Total no. of seats – no. of seats occupied by people.

= 2549 – 2138

\begin{align}

& \underline{\begin{align}

& \,\,\,\,Th\,\,H\,\,T\,\,\,O \\

& \,\,\,\,2\,\,\,\,\,5\,\,\,\,\,4\,\,\,\,\,9\, \\

& -\,2\,\,\,\,\,1\,\,\,\,\,3\,\,\,\,\,\,8 \\

\end{align}} \\

& \underline{\,\,\,\,0\,\,\,\,4\,\,\,\,\,\,1\,\,\,\,\,\,1\,} \\

\end{align}

Therefore, 411 seats were left vacant.

**2. By Regrouping/Borrowing:** Out of 2138 people who came to see the circus, 1619 were adults. Find out how many children were there? (See the previous circus figure.)

Total number of children = Total number of people – Total number of adults

= 2138 – 1619

This can also be written as:

\begin{align}

& \underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,\,\,T\,\,\,O \\

& \,\,\,\,\,\,1\,\,\,\,11\,\,\,\,\,2\,\,\,\,18\, \\

& \,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,\,8 \\

& -\,\,\,1\,\,\,\,\,\,6\,\,\,\,\,\,1\,\,\,\,\,\,\,9 \\

\end{align}} \\

& \underline{\,\,\,\,\,\,0\,\,\,\,\,5\,\,\,\,\,\,1\,\,\,\,\,\,\,\,9\,} \\

\end{align}

**SUBTRACTING WITH ZEROS**

5000 – 1832=?

**OR**

\[\underline{\begin{align}

& \,\,\,\,Th\,\,H\,\,T\,\,\,O \\

& \,\,\,\,5\,\,\,\,\,0\,\,\,\,\,0\,\,\,\,\,0\, \\

& -\,1\,\,\,\,\,8\,\,\,\,\,3\,\,\,\,\,\,2 \\

\end{align}}\]

There are not enough ones, tens or hundreds and we can't regroup from zero.

Therefore, we will make 0 into 10 & then regroup as shown below.

Reduce 5 by 1. 5 becomes 4 & 0 becomes 10. Now reduce 10 by 1.10 becomes 9 & 0 becomes 10. Repeat this process & subtract. The result is shown below.

*play_arrow*Subtraction

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