How to use BODMAS (Order of Operations) #2

Summary

This script offers a clear explanation of the order of operations in mathematics, commonly remembered by the acronym BODMAS or BIDMAS. It illustrates how to solve equations by prioritizing operations within brackets, followed by orders (or indices), division, multiplication, addition, and finally subtraction. The script emphasizes the importance of performing division and multiplication, or addition and subtraction, from left to right. It guides through examples to demonstrate the process, highlighting the need to remember and apply this order to avoid common mistakes in mathematical calculations.

Takeaways

• 📚 The acronym BODMAS or BIDMAS is used to remember the order of operations in mathematics: Brackets, Order (exponents), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
• 🔢 Operations inside brackets should be performed first, and the order within the brackets follows the same BODMAS/BIDMAS principle.
• 💡 When dealing with exponents, perform the operation indicated by the exponent before moving on to other operations.
• ➗✖️ Division and multiplication should be performed from left to right, not necessarily completing all divisions before moving to multiplications.
• ➕➖ Addition and subtraction should also be done from left to right, starting with the first operation encountered.
• 👉 The script provides a step-by-step example of solving an equation using the BODMAS/BIDMAS order, emphasizing the importance of following the correct sequence.
• 📉 In the example, after dealing with brackets and exponents, the next step is to perform multiplication, followed by addition to reach the final answer.
• 📈 Another example is given to illustrate the process of simplifying equations with multiple brackets and operations, again emphasizing the step-by-step approach.
• 📝 The importance of remembering to apply BODMAS/BIDMAS when solving equations is highlighted as a common mistake people make is to forget the order of operations.
• 📊 The script suggests starting with the leftmost bracket and working to the right as a general rule for simplifying equations with multiple operations.
• 🔑 A final tip is provided to always think of BODMAS/BIDMAS when approaching equations to avoid common errors and ensure correct calculations.

Q & A

What does the acronym BODMAS or BIDMAS stand for and what is its purpose?

BODMAS or BIDMAS is a mnemonic to help remember the order of operations in mathematics. The letters stand for Brackets, Order (or Index), Division, Multiplication, Addition, and Subtraction, and they indicate the sequence in which operations should be performed.

Why is it important to follow the order of operations when solving mathematical expressions?

Following the order of operations ensures that mathematical expressions are solved correctly and consistently. Without it, the results could be incorrect, leading to mistakes in calculations.

What does the term 'Order' or 'Index' refer to in the context of BODMAS?

'Order' or 'Index' refers to the exponentiation in an expression, such as squaring or cubing a number, which is indicated by a small raised number and is also known as the power.

How should you handle operations inside brackets according to the BODMAS rule?

According to BODMAS, you should first solve the operations inside the brackets before moving on to the rest of the expression, as brackets take the highest priority.

What should you do if there are multiple sets of brackets in an expression?

You should solve the brackets one at a time, starting with the first one on the left and then moving to the right. The order of solving brackets is flexible, but it's generally easier to start from the left.

How does the script suggest dealing with division and multiplication in an expression?

The script suggests that when it comes to division and multiplication, you should start with the operations on the left and work your way to the right, rather than completing all divisions before moving on to multiplications.

What is the first step in solving the example expression '18 divided by 6 plus three squared times two'?

The first step is to solve the operation inside the brackets, which is the division of 18 by 6, resulting in 3.

What is the final result of the example expression after following the BODMAS rule?

The final result of the example expression is 21, after performing the operations in the correct order according to the BODMAS rule.

In the second example provided in the script, why is the order of two not considered initially?

The order of two is not considered initially because it is outside the brackets. The focus is first on the operations inside the brackets before considering operations outside.

What is the final result of the second example expression after applying the BODMAS rule?

The final result of the second example expression is 9, after simplifying the brackets, performing the order (exponentiation), division, and addition in the correct sequence.

What tip does the script give for effectively using the BODMAS rule?

The script suggests that the hardest thing with the BODMAS rule is remembering to use it. It advises to think of BODMAS whenever doing an equation and consider which operation should be done first to avoid mistakes.

Outlines

00:00

📚 Understanding BODMAS/BIDMAS for Order of Operations

This paragraph introduces the concept of BODMAS (or BIDMAS), which is a mnemonic to remember the order of operations in mathematics: Brackets, Order (or Index), Division, Multiplication, Addition, and Subtraction. The video script explains how to apply this order to solve mathematical expressions, starting with brackets and then moving through the other operations in sequence. It emphasizes the importance of remembering to use BODMAS/BIDMAS to avoid common mistakes when solving equations.

05:02

🔍 Applying BODMAS/BIDMAS in Practice with Sample Problems

The second paragraph demonstrates the application of the BODMAS/BIDMAS rule through two sample problems. The first problem involves simplifying an expression with brackets and powers, leading to the final answer of 21. The second problem involves two sets of brackets and operations within them, resulting in a final answer of 9. The explanation stresses the importance of following the order of operations and suggests starting with the leftmost bracket and working to the right for simplicity. The paragraph concludes with a tip to always remember to use the BODMAS/BIDMAS rule when solving equations.

Keywords

💡BODMAS/BIDMAS

BODMAS and BIDMAS are acronyms used to remember the order of operations in mathematics. They stand for Brackets, Orders (or Indices), Division, Multiplication, Addition, and Subtraction. The video script emphasizes the importance of following this order when solving mathematical expressions to ensure accuracy. For example, the script mentions that one should 'always look at the brackets' first, followed by 'orders or index', and then proceed with division, multiplication, addition, and finally subtraction.

💡Brackets

Brackets in mathematics are used to group expressions or operations, indicating that the calculations within them should be performed before addressing the rest of the equation. In the script, the speaker instructs to 'look at the brackets' first, as in the example where '18 divided by six' is calculated to simplify the expression within the brackets.

💡Orders/Index

Orders or indices refer to the operation of exponentiation, where a number is raised to a power. The script explains that after dealing with brackets, one should address the 'order or index', such as squaring a number, which is often called 'power'. An example given is 'three squared times two', where 'three squared' means 3 multiplied by itself.

💡Division

Division is one of the fundamental operations in arithmetic, represented by the symbol '/'. The script mentions that after addressing the order or index, one should perform any division present in the expression. An instance from the script is '16 minus 6 times 2', where the multiplication is performed first, followed by the division.

💡Multiplication

Multiplication is the process of repeated addition and is denoted by the '×' symbol or simply juxtaposed numbers. The video script states that multiplication should be performed after division but before addition and subtraction. An example used is '6 times 2', which is calculated as part of simplifying the expression within brackets.

💡Addition

Addition is the process of combining two or more numbers into a single sum and is represented by the '+' symbol. The script explains that addition should be performed last in the sequence of operations, as seen in the final step of the example where '3 plus 18' is calculated to reach the final answer.

💡Subtraction

Subtraction is the operation of taking one number away from another and is denoted by the '-' symbol. The video script mentions that subtraction, like addition, should be performed from left to right when there are multiple operations of the same precedence.

💡Operations

In the context of the video, operations refer to the mathematical actions that need to be performed on numbers, such as addition, subtraction, multiplication, and division. The script emphasizes that each operation should be carried out in a specific order to solve equations correctly.

💡Equation

An equation in mathematics is a statement that asserts the equality of two expressions. The script discusses how to simplify and solve equations by following the BODMAS/BIDMAS order, such as transforming '18 divided by six' into 'three plus three squared times two'.

💡Simplification

Simplification in mathematics involves making a complex expression or equation easier to understand or solve by reducing it to its simplest form. The script provides examples of simplifying equations step by step, such as changing '4 squared divided by the bracket 4 divided by 2 times four plus seven' into the final answer of '9'.

💡Mistakes

The script mentions that common mistakes in solving mathematical equations occur when people forget to use the BODMAS/BIDMAS order. It suggests that remembering and applying this order is crucial to avoid errors and reach the correct solution.

Highlights

The importance of following a specific order in mathematical operations is emphasized.

Introduction to BODMAS/BIDMAS as a mnemonic for remembering the order of operations.

Explanation of the acronym BODMAS/BIDMAS and what each letter represents.

Clarification that the order of operations applies to both addition and subtraction, as well as multiplication and division.

Demonstration of how to solve a complex equation step by step using the BODMAS/BIDMAS rule.

Example of simplifying an equation by first addressing operations inside brackets.

Illustration of calculating powers or indices before moving to multiplication and division.

Process of eliminating brackets after simplifying the operations inside them.

Explanation of how to handle multiple sets of brackets in an equation.

The concept of working from left to right when dealing with similar operations.

Strategy for tackling equations with numerous addition and subtraction operations.

Final step of solving an equation by performing the remaining addition or subtraction.

Application of the BODMAS/BIDMAS rule to a second example equation.

Step-by-step breakdown of solving nested brackets and powers in a complex equation.

Emphasis on the importance of remembering and applying the BODMAS/BIDMAS rule to avoid mistakes.

Encouragement to use the BODMAS/BIDMAS mnemonic whenever solving equations.

Advice for sharing the video with friends to help them understand the order of operations.

Closing remarks expressing hope for the video's usefulness and an invitation to future content.

Transcripts

if we take a look at a question like

this one

there's a lot of stuff going on

there's an addition

some brackets

division

and index or order

and the multiplication

we call each of these things an

operation

and we have to do them all in a specific

order

we can't just start on the left and work

our way through

to help us remember this order we can

use something called bodmas

or bidmas

which are both exactly the same

except for this second letter

which can be an o or an i

depending on which one you've learned

each letter stands for different

operation

and the order of the letters tells us

the order in which we should do the

operations

so first we should always look at the

brackets

then we should look at the order or

index

which is the little raised number when

you square or cube something and is

often called the power

then any division

multiplication

addition

and finally subtraction

one important thing though is that when

it comes to division and multiplication

or addition and subtraction

you should start with the ones on the

left and work your way to the right

so if you have a question like this one

with loads of plus and minuses

you would just start on the left and

work your way through to the right

you wouldn't have to do all of the

additions before the subtractions

getting back to our example though

the first thing that we would do is look

at the brackets

and as the only operation inside the

brackets

is a divide

we do that straight away

so 18 divided by six which equals three

and now that the three is the only thing

inside the brackets we can just get rid

of the brackets

and our equation is now three plus three

squared times two

the next thing on our list is the order

or index

which is this power of two

this means that we have to do three

times by itself

so three times three

which equals nine

so we now have three plus nine times two

next up is division

but there isn't any division in our

equation

so we can skip that and go into

multiplication

which we do have

as 9 times 2

which is 18

leaving us with 3 plus 18

and now the only thing left is this

addition

so we do 3 plus 18 to get 21 as our

final answer

let's try one more

so first of all we need to look for any

brackets

and this time there are two sets of

brackets

so we'll have to look at one of them and

then the other one

it's completely up to you which one you

want to do first

but in general i would say it's just

easier to start on the left and then

work to the right

so we'll start with this one on the left

now notice that we haven't highlighted

this order of two up here

that's because the order is outside of

the bracket

so we don't consider it yet

we're only focusing on what's inside the

bracket for now

within the bracket the first thing we

have to do is the order of 2 on the 4

so 4 squared

which is 16

giving us 16 minus 6 times 2

inside the bracket

there isn't any division in the bracket

so the next thing we do is

multiplication

6 times 2

which is 12.

and then the only thing left

is the subtraction

so 16 minus 12 which gives us 4

at this point we finished simplifying

this first bracket

so we can rewrite our equation as 4

squared divided by the bracket 4 divided

by 2 times four

plus seven

and then next we're going to deal with

this other bracket

and the only operations inside it are a

division and a multiplication

so we do the division first four divided

by two which is two

and then we can multiply that two by the

four

to get eight

so now we have four squared divided by

eight

plus seven

now that we've got rid of all the

brackets

the next thing to do is this order on

the four

so four squared which is sixteen

next we do the division

so 16 divided by 8 which is 2

and finally the addition

so 2 plus 7

which gives us 9 as our final answer

and that's it that's everything that you

need to know about body mass

if i could give you one tip i'd say the

hardest thing with this topic is just

remembering to use it

so whenever you do an equation just

think of bot mass and think which of

these operations should i do first

because most people just completely

forget to use it and that's why they

make all their mistakes

anyway i hope you enjoyed the video and

found it useful in some way

if you did then please do share with

your friends

and hopefully we'll see you again soon