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Addition, Subtraction, Multiplication and Division

- Calculus
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Jetzt kostenlos anmeldenIt 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 are all types of operations used in mathematics.

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 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 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 $\times $.

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 $\xf7$.

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

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.

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.

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 $23\times 42$

**Solution:**

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

20 | 3 | |

40 | ||

2 |

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

20 | 3 | |

40 | 800 | 120 |

2 | 40 | 6 |

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, $23\times 42=966$

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 $306\xf79$

**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:

$9{\overline{)3}}^{3}06$

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

$9\times 3=27$

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:

$93{\overline{)3}}^{3}{0}^{3}6$

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

$9\times 4=36$

$934\overline{){3}^{3}}{0}^{3}6$

Therefore, $306\xf79=34$

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

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:

$647+278{}_{1}5\phantom{\rule{0ex}{0ex}}$

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

$647+278{}_{1}{}_{1}25$

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

$647+278{}_{1}{}_{1}925$

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:

${7}^{2}{\overline{)3}}^{1}2-4266\phantom{\rule{0ex}{0ex}}$

Now you can subtract 2 from 2:

${7}^{2}{\overline{)3}}^{1}2-42606$

Finally, you can subtract the 4 from 7:

${7}^{2}{\overline{)3}}^{1}2-426306$

Calculate $53\times 35$

**Solution:**

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

50 | 3 | |

30 | ||

5 |

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

50 | 3 | |

30 | 1500 | 90 |

5 | 250 | 15 |

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 $434\xf77$

**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:

$7{\overline{)4}}^{4}34$

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

$7\times 6=42$

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

$76{\overline{)4}}^{4}{3}^{1}4$

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

$7\times 2=14$

$762{\overline{)4}}^{4}{3}^{1}4$

Therefore, $434\xf77=62$

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:

${1}^{3}{\overline{)4}}^{1}2-548$

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:

${{\overline{)1}}^{1}}^{3}{\overline{)4}}^{1}2-5488$

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:

70 | 2 | |

3 | 210 | 6 |

$210+6=216$

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:

$4{\overline{)1}}^{1}88$

Now calculate how many times 4 can go into 18:

$4\times 4=16$

This leaves us with a remainder of 2:

$44{\overline{)1}}^{1}{8}^{2}8$

Finally, how many times can 4 go into 28:

$4\times 7=28$

$447{\overline{)1}}^{1}{8}^{2}8$

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

- 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.

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

Some examples of these operations include:

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

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