Arithmetic

Arithmetic

The teacher asked the class to find the value of \(3+7\times2\)

Mia and John were the first two to answer.

DMAS rules

Who do you think is correct?

It's Mia who got it right. Let's proceed to understand why her calculation is correct and what mistake John did. As we do so, we will explore the various concepts of arithmetic math and the operations involved. 

Lesson Plan

What Is Arithmetic?

Arithmetic is the branch of mathematics in which we study numbers and relations among numbers using various properties and use them to solve examples.

The word ‘Arithmetic’ comes from "arithmos", a Greek word meaning numbers. One of the oldest and fundamental principles of mathematics, Arithmetic is all about numbers and the elementary operations (addition, subtraction, multiplication, and division) that can be performed with those numbers.

basic operations of arithmetic

Arithmetic is all around you. If you take out two ice cubes from the ice tray, how many are left? To find this, you will have to subtract 2 from the total number of slots.

If each room in your house has 3 windows, and there are 4 rooms, to find the total windows in the house you will have to multiply 3 with 4. 


Basic Rules of Arithmetic

Let's just briefly go over the basic arithmetics operations.

four basic operations

Addition and Subtraction

Addition and subtraction are the most basic arithmetics operations. These concepts are building blocks of understanding and operating on numbers. We add and subtract numbers, amounts, and values in our everyday lives.

Addition can be visualized as 'putting together' of two or more quantities.

In arithmetics mathematics, subtraction means to take away some things from a group. In other words, subtraction is the process of removing things from a group.

subtraction

Multiplication and Division

Multiplication is one of the four basic arithmetic operations that can be applied to different math concepts like multiplying and dividing fractions, decimals, rationals, integers, etc. These operations form the building blocks for the other math concepts. 

And the last of basic arithmetic operations is division. In simple words, the division can be defined as the splitting of a large group into equal smaller groups. 

Equal to Sign : "="

Equal to sign is used to denote the outcome of the operations on numbers.

equal to sign

Inverse Operations 

  • The operations addition and subtractions are inverse operators of each other.
  • Similarly, the operations multiplication and division are inverse operators of each other.

Example 1

When we add 3 to 8 we get 11. i.e. 8+3 = 11

This would also mean:

  • If we take away 3 from 11, we get 8
  • If we take away 8 from 11, we get 3

inverse operation

Example 2

Multiplying 3 with 8 gives 24 i.e 8 x 3 = 24

This would also mean:

  • If we divide 24 by 3 we get 8
  • If we divide 24 by 8 we get 3

inverse operation

When there is more than 1 operator present, there is a rule called DMAS which is to be followed to operate them.

As per this rule: When we operate numbers with multiple operators, going from left to right we need to first operate numbers involving division or multiplication followed by operators addition and subtraction.

Let's take the example that we took in the beginning, \(3+7\times2\)

Here, we have 2 operators, multiplication and addition.

So, the first multiplication of 7 and 2 will be done and then the answer will be added to 3

DMAS example


Arithmetic Examples

Let's quickly see some arithmetic examples from our day-to-day life.

Example 1

Sia plucked 45 flowers from a garden and distributed them equally among 9 of her friends.

Can you find, how many flowers did each of her friends receive?

As we need to distribute 45 flowers equally among 9 children, we need to divide 45 by 9

\[45\div 9 = 5\]

So, each of her friends will receive 5 flowers.

Example 2

Mother bought 4 packets of candies each for John and Mia. There were 5 candies inside each packet. Can you find total how many candies were there?

Number of candies in 1 packet = 5

So, number of candies in 4 packets = \(4\times5=20\)

Thus, each child will get 20 candies.

Number of children = 2

So, total number of candies = \(20\times2=40\)

 
important notes to remember
Important Notes
  1. Arithmetic is a branch of mathematics that deals with operations on numbers. 
  2. There are four basic operations in arithmetic: Addition, Subtraction, Multiplication, and Division.
  3. The order of these operations is given by the DMAS rule.

Solved Examples

Example 1

 

 

A school library has 500 books out of which 120 reference books, 150 non-fiction books and the rest are fiction books. How many fiction books are there in the library?

Solution

Number of reference books = 120

Number of non-fiction books = 150

Total number of books = 500

\begin{align} \text {Number of fiction books} &= 500 - (120 +150) \\&=500-270\\&=230\end{align}

\(\therefore\) Number of fiction books = 230
Example 2

 

 

Peter has $25. He bought 3 cupcakes and a glass of milkshake. If a cupcake costs $2 and a glass of milkshake costs $7, how much money is he left with?

Solution

Cost of 1 cupcake = $ 2

Cost of 3 cupcakes \(3\times2=$ 6\)

Cost of a glass of milkshake = $7

\(\therefore\) Total amount spent = 6 + 7 = $13

So, the money left with him = 20 - 13 = $7

\(\therefore\) He has $7 left with him
Example 3

 

 

A box has some bananas, oranges, and apples. There are 30 bananas and the number of oranges is half of the bananas whereas the number of apples is 5 more than oranges. How many fruits are there in the box?

Solution

Number of bananas = 30

Number of oranges =\(\dfrac{1}{2}\) of 30 = 15

Number of apples = Number of oranges + 5 = 20

Total = 30 + 15 + 20 = 65

\(\therefore\)There are 65 fruits in the box
 
Challenge your math skills
Challenging Questions

Here is an image of a set of bowling pins.

Bowling Pins: Arithmetic Progression

  1. If we continue with the given arrangement, can you find how many bowling pins will be there in the 10th row?
  2. What will be the total number of bowling pins, if we consider the arrangement till the 10th row?

Interactive Questions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 

Let's Summarize

Starting from arithmetic definition to arithmetic sequence and arithmetic formula, this section covered various aspects of arithmetic math. You should now be in a good position to identify sequences and patterns on paper, as well as around you, and come up with the required answers.

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FAQs on Arithmetic

1.  What is the difference between arithmetic and algebra?

Arithmetics mathematics revolves around specific numbers and their computations using various basic arithmetic operations. On the other hand, algebra is about the rules and boundaries which stand true for whole numbers, integers, fractions, functions, and all other numbers in general. Algebra is built upon arithmetic math, following the arithmetic definition in all cases.

2. What topics come under arithmetic?

With arithmetic definition being extremely vast, there is a wide range of topics that come under its umbrella. They start from the basics like numbers, addition, subtraction, division, and move on to more complex subjects like exponents, variations, sequence, progression, and more. Some of the arithmetic formulas and arithmetic sequence did get covered in this section.

3. What is basic arithmetic math?

Basic arithmetic math covers four fundamental operations, which include addition, subtraction, multiplication, and division. In arithmetic math, the properties of numbers are associative, commutative, and distributive.

4. What are the 4 basic mathematical operations?

The four basic operations in maths are addition, subtraction, multiplication, and division.

5. Who is the father of arithmetic?

Brahmagupta is known as the father of arithmetic. He was a 7th Century Indian Mathematician, and also an astronomer.

6. Why is arithmetic important?

Arithmetic involves basic operations related to numbers that are used by every individual on a daily basis. It is an essential building block for advanced mathematics.

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