Addition, Subtraction, Multiplication and Division

It can be helpful to understand how to use different mathematical operations as they can be used every day in many different situations, just like calculating how a bag of sweets can be divided equally between a group of people. 

Addition, Subtraction, Multiplication and Division Addition, Subtraction, Multiplication and Division

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Contents
Table of contents

    Addition, Subtraction, Multiplication and Division definition

    Addition, subtraction, multiplication and division are all types of operations used in mathematics.

    Addition

    Addition is a type of operation that results in the sum of two or more numbers. There is a sign to represent the operation addition, called a plus sign, which is a +.

    Subtraction

    Subtraction is a type of operation that results in finding the difference between two numbers. The sign to represent the operation subtract is called a minus sign and it looks like this -.

    Multiplication

    Multiplication is a type of operation that requires you to add in equal groups, multiplication results in a product. The sign that represents the operation multiplication can be called the multiplication sign and it looks like this ×.

    Division

    Division is the operation that is opposite to multiplication, it involves breaking a number down into equal parts. The sign that represents the operation division is simply called a division sign and looks like this ÷.

    Addition, Subtraction, Multiplication and Division rules

    There are different rules and methods that can be helpful when using each of these operations.

    Addition

    When adding two or more numbers together you can use a method called column addition. This involves putting the numbers one above the other in a column, you then work your way from right to left adding the numbers that are in the same column.

    Calculate 122+552

    Solution:

    To begin with, you can place the numbers on top of each other:

    122+552

    Now working from right to left, add the two horizontal numbers together starting with 2 and 2:

    122+5524

    Now moving onto 2 and 5:

    122+55274

    And finally 5 and 1:

    122+552672

    Therefore, 122+552=672

    If the two numbers you are adding are equal to more than 10, you can carry the number over.

    Subtraction

    When subtracting two numbers, you can also use a column method; the column subtraction method. This works in the same way as the column addition method, however, you subtract the numbers rather than add them.

    Calculate 538-214

    Solution:

    To begin with, you can place the numbers on top of each other, placing the number you are subtracting from on top:

    538-214

    Now working from right to left, subtract one number away from another, starting with 8 and 4:

    538-2144

    Now moving onto 3 and 1:

    538-21424

    And finally 5 and 2:

    538-214324

    Therefore, 538-214=324

    If the number you are subtracting is higher than the number subtracted from, you will need to take a digit from the column to the left.

    Multiplication

    When multiplying two numbers together there are different methods that can be used including the grid method. This involves breaking the two numbers down and placing them into a grid. You then complete individual multiplications and then add them all together.

    Calculate 23×42

    Solution:

    To begin with, draw out a grid, break down your numbers, and place them into the grid-like so:

    203
    40
    2

    To fill out the grid you simply multiply each number in the columns:

    203
    40800120
    2406

    Now you can add all of the values together to find the answer to the question, it may be easier to do this in steps:

    800+120=920

    40+6=46

    920+46=966

    Therefore, 23×42=966

    Division

    When dividing a number by another you can use a method called short division, this method works best when you are dividing a number by 10 or less. Short division involves dividing a number mentally into smaller stages.

    Calculate 306÷9

    Solution:

    To start with you can draw out your calculation, writing the number you're dividing by on the left and the number you're dividing written on the right as shown below:

    9306

    Now you need to work your way through the number you're dividing one unit at a time, start by figuring out how many times 9 can go into 3. Since this is not possible you need to carry the 3 over to the next unit:

    93306

    Now you can think about how many times 9 can go into 30. 9 goes into 30 three times with a remainder of three:

    9×3=27

    This can then be written into your division as below with the divisible number being written above the calculation and the remainder 3 being carried over to the 6:

    9333036

    Finally, you can calculate how many times 9 goes into 36:

    9×4=36

    93433036

    Therefore, 306÷9=34

    Addition, Subtraction, Multiplication and Division relationships

    It is possible for operations to have relationships with each other. There is a relationship between addition and subtraction as well as a relationship between multiplication and division.

    Addition & Subtraction

    Addition and subtraction can be considered the inverse of one another. This simply means that the operations are the opposite, you can undo an addition by subtracting the same number and vice versa!

    Multiplication & Division

    Multiplication and division are also considered the inverse of one another, if you want to undo a multiplication you can simply divide the number.

    Addition, Subtraction, Multiplication and Division examples

    Calculate 647+278

    Solution:

    To begin with, you can place the numbers on top of each other:

    647+278

    Now working from right to left, add the two horizontal numbers together. Starting with 7 and 8, since they equal 15, you need to carry the 1 over:

    647+27815

    Now you need to add together 4, 7 and 1, again since this equals more than 10 you need to carry over the unit:

    647+2781125

    Finally, you can add together 6, 2 and 1:

    647+27811925

    Calculate 732-426

    Solution:

    To begin with, you can place the numbers on top of each other, placing the number you are subtracting from on top:

    732-426


    Now working from right to left, subtract one number away from another, starting with 2 and 6. Since 6 is bigger than two, you need to borrow a digit from the column to the left:

    72312-4266

    Now you can subtract 2 from 2:

    72312-42606

    Finally, you can subtract the 4 from 7:

    72312-426306

    Calculate 53×35

    Solution:

    To begin with, draw out a grid, break down your numbers, and place them into the grid-like so:

    503
    30
    5

    To fill out the grid you simply multiply each number in the columns:

    503
    30150090
    525015

    Now you can add all of the values together to find the answer to the question, it may be easier to do this in steps:

    1500+90=1590

    250+15=265

    1590+265=1855

    Calculate 434÷7

    Solution:

    Let's start by writing out the sum using the short division method:

    7434

    Now begin by calculating how many times 7 goes into 4, this is not possible so you can carry the 4 over to the 3:

    74434

    Next, you can look at how many times 7 can go into 43:

    7×6=42

    This leaves us with a remainder of 1 that can be carried over to the 4:

    7644314

    Finally, calculate how many times 7 can go into 14:

    7×2=14

    76244314

    Therefore, 434÷7=62

    Applications of Addition, Subtraction, Multiplication and Division

    These operations are often used in everyday life, let's work through some examples:

    Amy has 326 stickers in her sticker collection, Claire has 213 stickers. How many stickers would they have if they combined their collections?

    Solution:

    Start by placing the two numbers on top of one another:

    326+213

    Now you can add them together working from right to left, starting with 6 and 3:

    326+2139

    Work your way through the numbers:

    326+213539

    Therefore, if Amy and Claire combined their collections, they would have 539 stickers in the collection.

    Sam has 142 sweets, he gives his friend 54, how many sweets is Sam left with?

    Solution:

    To find out how many sweets Sam has, we can subtract 54 from 142. Start by placing the two numbers on top of each other:

    142-54

    Now working from right to left, subtract one number away from another. Don't forget, since 2 is smaller than 4 you need to take a unit from the column to the left:

    13412-548

    Now you can move on, again since 3 is smaller than 5 you will need to take a unit from the column to the left:

    113412-5488

    Therefore, Sam is left with 88 sweets.

    Dave is cooking for 12 people but his recipe serves only serves 4. If the recipe requires 72 grams of pasta, how much pasta will Dave need?

    Solution:

    To find out how much pasta Dave will need for his recipe we can use the operation multiplication. Since 4 goes into 12, 3 times, Dave will need three times more than what the recipe states. To do this we can use the grid method:

    702
    32106
    Now you can add the two numbers together:

    210+6=216

    Therefore, Dave will need 216 grams of pasta to serve 12 people.

    Barbara is out for a meal with 3 friends, the bill comes to £188 and they decide to split it evenly. How much does each person pay?

    Solution:

    To begin with, write the problem out using the short division method. The bill came to £188 and it is being split between 4 people, therefore it can be written as follows:

    4188

    Now take the first step and see how many times 4 can go into the first number on the left. Since 4 cannot go into 1, the 1 can be carried over:

    41188

    Now calculate how many times 4 can go into 18:

    4×4=16

    This leaves us with a remainder of 2:

    4411828

    Finally, how many times can 4 go into 28:

    4×7=28

    44711828

    This means that each person will need to pay £47.

    Addition, Subtraction, Multiplication and Division - Key takeaways

    • There are many different types of mathematical operations, these include:
      • Addition, which is an operation that results in the sum of two or more numbers.
      • Subtraction, which is an operation that results in finding the difference between two numbers.
      • Multiplication, which is an operation that requires you to add in equal groups, multiplication results in a product.
      • Division, which is an operation that is opposite to multiplication, it involves breaking a number down into equal parts.
    Frequently Asked Questions about Addition, Subtraction, Multiplication and Division

    What is the meaning of  Addition, Subtraction, Multiplication, and Division in maths?

    In maths addition, subtraction, multiplication, and division are types of operations. 

    What are examples of Addition, Subtraction, Multiplication, and Division in maths?

    Some examples of these operations include:

    • 23 + 17 = 40
    • 86 - 22 = 64
    • 10 × 42 = 420
    • 63 ÷ 7 = 9

    Which of the operators in maths comes first?

    When completing a sum where a number of the sums are used you can use a method called BIDMAS to find out which operation to calculate first. This method says to solve sums in the order of brackets, indices, multiplication/division then addition/subtraction. 

    How is the relationship between addition and subtraction similar to multiplication and division?

    The relationship between addition and subtraction is similar to the relationship between multiplication and division as they are both considered the inverse of one another. 

    What are the rules and applications of Addition, Subtraction, Multiplication, and Division?

    The rules of addition, subtraction, multiplication, and division refers to the order in which you use the operations. 

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