Order of Operations: A Step-By-Step Guide | PEMDAS | Math with Mr. J

Summary

In 'Math with Mr. J.', the video focuses on the critical concept of the order of operations, essential for solving mathematical problems consistently. Mr. J. introduces the acronym PEMDAS to remember the sequence: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (also from left to right). He illustrates this with step-by-step examples, ensuring viewers understand how to apply these rules to reach the correct solution.

Takeaways

• 📝 The order of operations is a set of rules that ensures everyone solves math problems in the same way, leading to consistent solutions.
• 🔢 The acronym PEMDAS helps remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
• 🌟 Parentheses have the highest priority and should be solved first in any expression.
• 🚀 Exponents are the next priority after parentheses and indicate a number should be squared or raised to another power.
• ➗✖️ Multiplication and division are on the same level of priority, and if both are present, they are performed from left to right.
• 🔄 Addition and subtraction have the same priority and should be done from left to right when both are present in an expression.
• 📉 In the example 30 divided by (13 - 8), the problem inside the parentheses is solved first, resulting in 5, then the division is performed, yielding 6.
• 📈 In the problem 16 - 5 * 3 + 12, multiplication is performed first (5 * 3 = 15), followed by subtraction and addition from left to right, resulting in 13.
• 💫 The expression 7 squared minus 14 times 2 first calculates the exponent (7^2 = 49), then the multiplication (14 * 2 = 28), and finally the subtraction, giving 21.
• 🔄 For the problem 18 divided by (6 + 3) times 15, the operation inside the parentheses is solved first (6 + 3 = 9), followed by division (18 / 9 = 2), and finally multiplication (2 * 15 = 30).
• 👍 The video emphasizes the importance of following the order of operations step-by-step to arrive at the correct answer.

Q & A

What is the purpose of the order of operations in mathematics?

The order of operations ensures that everyone solves mathematical problems using the same set of rules, leading to consistent and correct solutions.

What does the acronym PEMDAS stand for in the context of the order of operations?

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Why is it important to start with parentheses when solving an expression?

Parentheses indicate the highest priority in the order of operations, so they must be solved first to determine the values that will be used in the rest of the expression.

How are multiplication and division treated in the order of operations?

Multiplication and division are on the same level of priority. If both are present in an expression, they are performed from left to right.

What is the correct order to perform addition and subtraction in an expression?

Addition and subtraction are also on the same level of priority, and they should be performed from left to right.

In the example 30 divided by (13 minus 8), what is the first step according to the order of operations?

The first step is to solve the expression within the parentheses, which is 13 minus 8.

What is the result of the calculation 16 minus 5 times 3 plus 12?

First, perform the multiplication (5 times 3), then the subtraction (16 minus the result), and finally the addition (plus 12), resulting in 13.

In the expression 7 squared minus 14 times 2, which operation should be performed first?

The exponent operation (7 squared) should be performed first, as it has the next highest priority after parentheses.

How is the expression 18 divided by (6 plus 3) times 15 simplified step by step?

First, solve the parentheses (6 plus 3), then perform the division (18 divided by the result), and finally the multiplication (times 15), resulting in 30.

What is the final answer to the example where the expression is 16 minus 5 times 3 plus 12?

Following the order of operations, the final answer is 13.

Can you provide an example of how the order of operations is applied in a real-world scenario?

In a real-world scenario, such as calculating the total cost of items with a discount and tax, the order of operations ensures that the discount is applied first, followed by the tax calculation, resulting in the correct final amount owed.

Outlines

00:00

📚 Introduction to Order of Operations

In the first paragraph, Mr. J introduces the concept of the order of operations, emphasizing its importance in solving mathematical problems with multiple steps. He explains that following a set of rules ensures consistency and accuracy in problem-solving. The order begins with parentheses, followed by exponents, and then moves to multiplication and division (which are of equal priority), and finally to addition and subtraction. The acronym PEMDAS is introduced as a mnemonic to remember the sequence. Mr. J then begins solving examples to demonstrate the application of these rules.

05:07

🔢 Applying PEMDAS to Example Problems

The second paragraph continues with Mr. J working through mathematical examples to illustrate the order of operations. He starts with a problem involving parentheses and division, correctly solving it to find the answer is 6. Moving on, he tackles a problem with multiplication and addition/subtraction, emphasizing the left-to-right rule for operations of equal priority. The example results in the answer 13. Mr. J then proceeds to problems involving exponents and mixed operations, solving each step-by-step and reinforcing the importance of following PEMDAS to arrive at the correct answers, which are 21 and 30, respectively.

Keywords

💡Order of Operations

The 'Order of Operations' is a fundamental rule set in mathematics that dictates the sequence in which operations should be performed to correctly solve an expression. In the video, it is the main theme, guiding viewers on how to approach problems with multiple operations. The script uses the acronym PEMDAS to help remember this order, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

💡Parentheses

Parentheses are symbols used in mathematical expressions to indicate that the operations within them should be performed first. In the video script, the first example starts with '13 minus 8 in parentheses,' which is solved before any other operation, emphasizing the priority of parentheses in the order of operations.

💡Exponents

Exponents represent the power to which a number is raised. In the script, '7 squared' is an example of an exponent, where 7 is multiplied by itself. The video explains that after solving within parentheses, exponents are the next priority according to the order of operations.

💡Multiplication and Division

Multiplication and Division are operations that involve scaling numbers. The script mentions that they are on the same level in the order of operations, meaning if both are present in an expression, they should be performed from left to right. An example from the script is '5 times 3,' which is solved before addition or subtraction.

💡Addition and Subtraction

Addition and Subtraction are basic arithmetic operations that increase or decrease a number, respectively. The video script explains that like multiplication and division, addition and subtraction are of equal priority and should be performed from left to right when both are present in an expression, as seen in the example '16 minus 15 plus 12.'

💡PEMDAS

PEMDAS is an acronym used to remember the order of operations. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. The script uses PEMDAS to help viewers recall the sequence in which to solve mathematical problems, ensuring consistency and accuracy in their solutions.

💡Left to Right

The term 'left to right' refers to the direction in which operations of equal priority are performed in an expression. In the script, it is used to explain that when both multiplication/division and addition/subtraction are present without parentheses or exponents, the operations should be carried out from left to right.

💡Expression

An 'expression' in mathematics is a combination of numbers, variables, and operators that represents a value. In the video, expressions are used to demonstrate the application of the order of operations, such as '30 divided by (13 - 8)' and '16 - 5 times 3 plus 12.'

💡Priority

In the context of the order of operations, 'priority' refers to the precedence given to certain operations over others. The script explains that multiplication and division have the same priority, as do addition and subtraction, and that operations within parentheses have the highest priority.

💡Solve

To 'solve' in mathematics means to find the value of an expression or equation. The video script guides viewers on how to solve expressions by following the order of operations, such as solving '13 - 8' within parentheses to get 5, which is then used in further calculations.

💡Acronym

An 'acronym' is a word formed from the initial letters or groups of letters of words in a phrase, used for ease of memory and communication. In the video, PEMDAS is introduced as an acronym to help remember the order of operations, which is a key tool for solving mathematical problems.

Highlights

Introduction to the order of operations as a set of rules for solving math problems.

Explanation of how the order of operations ensures consistent problem-solving and solutions.

The first step in the order of operations is to address parentheses.

Exponents come next in the order of operations after parentheses.

Multiplication and division are on the same level, to be performed from left to right.

Addition and subtraction are also on the same level, with operations done from left to right.

The acronym PEMDAS as a memory aid for the order of operations.

Example problem solving with parentheses first, then division: 30 divided by (13 - 8).

Demonstration of solving an expression with multiplication before subtraction: 16 - 5 * 3 + 12.

The importance of working from left to right when the same level of operations is present.

Solving an expression with exponents: 7 squared minus 14 times 2.

Addressing both multiplication and division from left to right in an expression: 18 divided by (6 + 3) times 15.

Final answer to the expression with parentheses and division: 18 / (6 + 3) * 15 equals 30.

Reinforcement of the PEMDAS order with a step-by-step approach to problem-solving.

Conclusion and summary of the importance of following the order of operations.

Transcripts

Welcome to Math with Mr. J.

In this video, I'm going to cover the order of operations and how to use the order

of operations. Now we can think of the order of operations as a set of rules or instructions

that we need to follow. When we have a problem with multiple operations and steps,

we use the order of operations that way everyone is working through problems the

same way and using the same rules. This helps us get to the same solutions or answers.

Everyone is on the same page, so to speak, and going through problems the same way.

As far as the order of operations. We start with parentheses, so parentheses are

priority number one. If we see parentheses in an expression, we start there. Then

we have exponents. Then multiplication and division. Now I do want to mention, multiplication

and division are on the same level, they are the same priority in the order of operations.

So if we have both, we work from left to right. And then addition and subtraction.

Now addition and subtraction are on the same level, they are the same priority. So

if we have both, we work from left to right. This will all make a lot more sense

as we go through our examples. Just think of the order of operations like a a set

of instructions that we follow step-by-step. Now we have an acronym that we can think

of in order to remember that order, PEMDAS. So parentheses,

exponents, multiplication and division, and then addition and subtraction. So PEMDAS

just represents the order of operations. Let's jump into our examples and see exactly

how all of this works, starting with number one, where we have 30 divided by and

then in parentheses 13 minus 8. So let's work through the order of operations. Do

we have any parentheses in this expression? Yes. So we start there, we have 13 minus

8 in parentheses. 13 minus 8 is 5. Then we need to bring down everything we did not

use. So we have 30 and then divided by 5. So now we have 30 divided by 5. We only

have one operation here, division, so that's what we need to do. 30 divided by 5

is 6. So our final answer, 6. So for number one, we worked through the order of operations.

We started with parentheses, then we brought down everything we did not use and we

ended with 30 divided by 5, which gave us 6. Let's move on to number two, where we

have 16 minus 5, times 3, plus 12. Let's work through the order of operations. Do

we have any parentheses? No. So let's move on to exponents. Do we have any exponents?

No. So let's move on to multiplication and division. Do we have any multiplication

or division? Yes. So that's where we start. We have multiplication. We have 5 times 3.

That is 15. Now we need to bring down everything we did not use, so we have 16

minus 15 and then plus 12. So we have 16 minus 15, plus 12 and we need to continue

to work through the order of operations. Any parentheses? No. Any exponents? No.

Any multiplication or division? No. Any addition or subtraction. Yes. We have both

addition and subtraction. Since we have both addition and subtraction, we need to

work from left to right. Addition and subtraction are on the same level, they are

the same priority in our order of operations. So again, we need to work left to right.

When working from left to right, we need to do subtraction first here. So 16 minus

15 is 1. Bring down everything we did not use, so plus 12. And now we have 1 plus

12. We only have one operation left. So that's what we need to do. We need to add.

1 plus 12 is 13 and that is our final answer. Let's move on to numbers three and

four. Here are numbers three and four. Let's start with number three, where we have

7 squared, minus 14, times 2. Let's work through the order of operations. Are there

any parentheses in this expression? No. So let's move on to exponents. Are there

any exponents in this expression? Yes. So let's start there. We have 7 squared, which means 7 times 7.

That's 49. Bring down everything we did not use.

So now we have 49 minus 14, times 2. Let's continue to work through the order of operations.

Any parentheses? No. Any exponents? No. Any multiplication or division? Yes, we have

multiplication, so that's what we need to do next. We have 14 times 2, which is 28.

Bring down everything we did not use, so 49 minus 28. We have one operation left,

subtraction. So we need to subtract. 49 minus 28

is 21. So our final answer, 21. Let's move on to number 4 where we have 18 divided

by and then in parentheses, 6 plus 3, end parentheses times 15. Let's work through

the order of operations. Any parentheses in this expression? Yes, so we need to start

there. We have 6 plus 3 in parentheses. That's 9. And then we need to bring down everything we did not use.

So now we have 18 divided by 9, times 15. Any parentheses? No. Any exponents? No.

Any multiplication or division? Yes, we actually have both multiplication and division.

Since we have both, we need to work from left to right. Multiplication and division

are on the same level so to speak, they are the same priority. So when that happens,

we work from left to right. When working from left to right division comes first.

We have 18 divided by 9. So let's do that. 18 divided by 9 is 2. Bring down everything

we did not use. So times 15 there and now we have 2 times 15. 2 times 15 gives us

30. Our final answer, 30. So there you have it. There's how to use the order of operations.

Just remember, PEMDAS, parentheses, exponents, multiplication and division, and then

addition and subtraction. Just work through step-by-step. I hope that helped. Thanks

so much for watching. Until next time. Peace.