How to use BODMAS (Order of Operations) #2
Summary
TLDRThis 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
- π 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).
- π’ Operations inside brackets should be performed first, and the order within the brackets follows the same BODMAS/BIDMAS principle.
- π‘ When dealing with exponents, perform the operation indicated by the exponent before moving on to other operations.
- ββοΈ Division and multiplication should be performed from left to right, not necessarily completing all divisions before moving to multiplications.
- ββ Addition and subtraction should also be done from left to right, starting with the first operation encountered.
- π 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.
- π In the example, after dealing with brackets and exponents, the next step is to perform multiplication, followed by addition to reach the final answer.
- π Another example is given to illustrate the process of simplifying equations with multiple brackets and operations, again emphasizing the step-by-step approach.
- π 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.
- π The script suggests starting with the leftmost bracket and working to the right as a general rule for simplifying equations with multiple operations.
- π 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
π 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.
π 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.
Mindmap
Keywords
π‘BODMAS/BIDMAS
π‘Brackets
π‘Orders/Index
π‘Division
π‘Multiplication
π‘Addition
π‘Subtraction
π‘Operations
π‘Equation
π‘Simplification
π‘Mistakes
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
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