# Sum

Sum

 1 Concept Video on Addition - Cuemath Way 2 Introduction to Sum 3 What is Sum? 4 What is the Sum of Two Numbers? 5 Important Notes on Sum 6 Solved Examples on Sum 7 Thinking out of the Box! 8 Practice Questions on Sum 9 Maths Olympiad Sample Papers 10 Frequently Asked Questions (FAQs)

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## Concept Video on Addition - Cuemath Way

Do you know how to add numbers?

If you don't, you can watch this video to learn how to add numbers the Cuemath way.

In this Cuemath video, you will learn how to add by building number combinations using Base Ten Blocks.

## Introduction to Sum

Addition is an important concept in Math.

We use it regularly in our daily lives.

Let's learn what it means to add or to find the sum of numbers.

When you take two or more numbers to add them, you have a total sum of two or more numbers.

For instance, if this cat gives birth to 3 kittens, she is adding to her family.

Here, we have 1 cat and her 3 kittens.

There are 4 cats in total.

This can be written as: $$1 + 3 = 4$$

This is a mathematical equation which is read as "one plus three equals four".

## What is Sum?

### Sum: Definition

Sum is a way of putting things together.

The sum brings two or more numbers together to make a new total.

The terms such as "all together, "put together," "how many in all," "total," and "sum"  indicates that you will need to add two or more numbers.

The plus sign (+) is used when two things are added together.

## What is the Sum of Two Numbers?

The sum of two numbers is just putting two numbers together.

Finding the sum of small numbers is not hard.

Let's look at an example to understand how to add numbers using our fingers.

Alaya is standing near a traffic signal.

She is trying to count the number of vehicles that have stopped at the red light signal.

She sees three buses at the signal.

She counts them by opening three fingers of one hand.

Next, she sees two more buses that have stopped at the signal.

She counts them by opening two more fingers.

Now, Alaya counts all the fingers opened in her hand to count the number of buses at the signal.

There are five open fingers which means that there are 5 buses at the signal.

Now, let's see how to find a sum using a number line.

We will find the sum of 3 and 2 using a number line.

First, draw a number line and encircle the first addend 3 on it.

Now, make two jumps to the right of 3

The number you reach is 5

This is the sum.

### Sum: Calculator

Do you want to view more examples on how to add numbers?

You can explore this simulation to find the sum of two numbers.

Drag the points on the red line and blue line to change the number of candies.

You can observe that as the number of candies change, the sum of them changes too.

### Fun Facts

Do you know that two numbers and their sum form a "fact family"?

For example, the numbers 4, 5, and 9 form a fact family.

This is because $$4 + 5 = 9$$; $$5 + 4 = 9$$; $$9 - 4 = 5$$; and $$9 - 5 = 4$$

So, now you know how the numbers interact with each other.

The sum of any two natural numbers is greater than either of them.

Important Notes
1. Adding 0 to a number gives the sum as the number itself.
2. When 1 is added to a number, the sum equals the successor of the number.
3. Changing the order of addend in the sum does not make any difference to the sum.
4. The sum of opposite sides of a dice is always 7

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## Sum: Examples

 Example 1

Nora's granny lives in the next village.

She has to cross a river to reach her granny's house.

She wants to take $$14\;\text{kg}$$ of sugarcane, $$5\;\text{kg}$$ of jaggery and $$10\;\text{kg}$$ of tomatoes with her in the boat.

She can carry a maximum weight of $$30\;\text{kg}$$ with her in the boat..

Can she carry all of them with her in the boat?

Solution:

We need to calculate the total weight of sugarcane, jaggery and tomatoes.

Weight of sugarcane = $$14\;\text{kg}$$

Weight of jaggery =  $$5\;\text{kg}$$

Weight of tomatoes = $$10\;\text{kg}$$

Total weight of these things

= $$14\;\text{kg} + 5\;\text{kg} + 10\;\text{kg} = 29\;\text{kg}$$

$$29\;\text{kg}$$ is less than the weight the boat can carry.

 $$\therefore$$ Nora can carry all of them in the boat.
 Example 2

Two friends, Jacob and Mia, are playing with a bat and a ball.

Turn by turn, they toss the ball on their bats until it falls.

Each player gets two chances.

Jacob tossed the ball $$14$$ times in his first chance and $$9$$ times in his second chance, whereas Mia tossed the ball $$8$$ times in her first chance and $$10$$ times in her second chance.

Who won the game?

Solution:

Let's count the total number of tosses by Jacob.

\begin{align}\text{Total tosses by Jacob}\end{align}

\begin{align}\!&=\!\!\text{Tosses in first chance}\!+\!\text{Tosses in second chance}\\&=14+9\\&=23\end{align}

Now, let's count the total number of tosses by Mia.

\begin{align}\text{Total tosses by Mia}\end{align}

\begin{align}\!\!&=\!\!\text{Tosses in first chance}\!+\!\text{Tosses in second chance}\\&=8+10\\&=18\end{align}

Jacob made more tosses than Mia.

 $$\therefore$$ Jacob won the game.
 Example 3

Emma and Olivia are playing a game using a number strip shown below.

It has numbers $$-8$$ to $$8$$ marked in equal intervals.

They keep their token on the number $$0$$

They have a red and a blue coloured die in a bag.

They pick a die randomly from the bag and throw it.

If it is a red-coloured die, they will move to the right as per the number shown on the die.

If it is a blue-coloured die, they will move to the left as per the number shown on the die.

At the first attempt, Emma gets a red die and a number 4 after throwing it.

Olivia happens to get a blue die.

She gets a number $$5$$ after throwing it.

At the second attempt, Emma gets 6 points with the blue die and Olivia secures 6 points with the red die.

At what number are their tokens placed after both the attempts?

Solution:

The number Emma reaches on first attempt

= $$0+4=4$$

The number Olivia reaches on first attempt

= $$0+(-5)=-5$$

The number Emma reaches on second attempt

= $$4+(-6)=-2$$

The number Olivia reaches on second attempt

= $$(-5)+6=1$$

 $$\therefore$$ Emma is at $$-2$$ and Olivia is at $$1$$ after their second attempt.

Think Tank
 1. A snake moves from one hole to another to eat the insects hidden inside the holes. The number in each hole below represents the number of insects in that hole. The snake starts from the blue hole and moves along only these lines. What path can this snake take to eat exactly 20 insects and then arrive at the blue hole?

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## Practice Questions

Here are few activities for you to practice.

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

## 1. What is sum?

When two or more numbers are added, the resultant is called a sum.

## 2. What is an example of sum?

The most common example of sum is when working with money.

Going shopping means that money will be spent.

We can use addition to find the sum of the money to be paid to the shopkeeper.

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
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