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[00:00:00]If you have the expression 8 + open parentheses 90 / 9 * 2 close parentheses and multiplied by 2 ^ 2, then what is the correct answer of this question?

[00:00:14]Many people when solving this question go straight to the expression inside the parentheses and they start with the division between 90 and 9.

[00:00:22]So, instead of this expression, they write 8 + open parentheses 10 * 2 close parentheses and multiplied by 2 ^ 2.

[00:00:35]In the next step, they go for the multiplication between 10 and 2 and write this equation as 8 + 20 * 2 ^ 2.

[00:00:46]Then, they go for the addition between 8 and 20 and write this equation as 28 * 2 ^ 2.

[00:00:56]In the final step, they go for the exponent and write this equation as 28 * 4 which finally gives them the answer 112.

[00:01:07]However, that's definitely wrong.

[00:01:11]Also, some other people when solving this question again go straight to the expression inside the parentheses, but this time they start with the multiplication between 9 and 2 because they think multiplication has a higher priority than division.

[00:01:27]So, instead of this expression, they write 8 + open parentheses 90 / 18 close parentheses and multiplied by 2 ^ 2.

[00:01:41]In the next step, they go for the division between 90 and 18 and write this equation as 8 + 5 * 2 ^ 2.

[00:01:52]Then, they go for the exponent and write write equation as 8 + 5 * 4.

[00:02:00]And the final step, they go for the multiplication between 5 and 4 because they think multiplication has priority over addition.

[00:02:10]So, they write this expression as 8 + 20.

[00:02:15]Which finally gives them the answer 28.

[00:02:18]However, this answer is absolutely wrong.

[00:02:22]All right. Now, let me show you how to solve this equation properly.

[00:02:27]To solve this question, they must follow a rule that is called PEMDAS. And in this rule, P stands for parentheses, E stands for exponent, M stands for multiplication, D stands for division, A stands for addition, and S stands for subtraction.

[00:02:46]As you can see on the screen, in this expression, first we have an addition sign, then parentheses, followed by a multiplication, and finally exponent. According to the PEMDAS rule, first you go for the expression inside the parentheses because P or parentheses have the highest priority than the other operation.

[00:03:08]And inside the parentheses, we have one division sign followed by a multiplication sign.

[00:03:14]It's really important to understand that multiplication and division have equal precedence, and we must perform these two operations from left to right.

[00:03:24]So, first you go for the division between 90 and 9. And instead of this expression, we can write 8 + (10 * 2) * 2².

[00:03:40]In the next step, we go for the multiplication between 10 and 2. And write this equation as 8 + 20 * 2².

[00:03:52]Then, we go for the exponent because in the PEMDAS rule, after parentheses, exponent has a higher priority than the other operations.

[00:04:01]So, instead of this equation, we can write 8 + 20 multiplied by 4.

[00:04:09]And the final step, we go for the multiplication between 20 and 4 because multiplication has priority over addition.

[00:04:18]So, we write this equation as 8 + 80 which finally gives us the answer 80 8.

[00:04:27]Okay, now let's solve another math question together.

[00:04:31]What is the value of the expression 7 + 2 inside the parentheses + 45 / 9 * 5?

[00:04:41]Many people when solving this question first go for the expression inside the parentheses and instead of this equation, they write 9 + 45 / 9 * 5.

[00:04:56]In the next step, they go for the addition between 9 and 45 and write this equation as 50 4 / 9 * 5.

[00:05:08]Then, they go for the division between 54 and 9 and instead of this equation, they write 6 * 5 which finally gives them the answer 30.

[00:05:20]However, it's not the correct answer to this question.

[00:05:24]Also, some other people when solving this question again go straight to the expression inside the parentheses and instead of this equation, they write 9 + 45 / 9 * 5.

[00:05:39]In the next step, they go for the multiplication between 9 and 5 because they think multiplication has a higher priority than division.

[00:05:49]So, instead of this expression, they write 9 + 45 / 45.

[00:05:59]Then, they go for the division between 45 and 45 because they believe division has priority over addition.

[00:06:07]So, they rewrite this equation as 9 + 1, which finally gives them the answer 10.

[00:06:14]But, that's definitely wrong.

[00:06:17]To solve this question, we must follow the order of operations step by step from top to bottom.

[00:06:24]As you can see on this screen, in this expression, first we have parentheses, then an addition sign, followed by a division, and finally a multiplication.

[00:06:34]According to the PEMDAS rule, first we go for the expression inside the parentheses, and instead of this expression, we can write 9 + 45 / 9 * 5.

[00:06:49]In the next step, we move on to the division and multiplication because these two operations have a higher priority than addition.

[00:06:57]However, it's really important to understand that multiplication and division are at the same level of precedence, and we must perform these two operations from left to right.

[00:07:08]So, first we go for the division between 45 and 9, and instead of this expression, we can write 9 + 5 * 5.

[00:07:20]In the final step, we go for the multiplication between 5 and 5 because multiplication has priority over addition.

[00:07:28]So, instead of this expression, we can write 9 + 25, which finally gives us the answer 34.

[00:07:38]All right. Now, let's solve the final math question together.

[00:07:42]What is the value of the expression 3 ^ 2 - ( 9 + 1) * ( 9 - 7) inside the parentheses? And what's left by 9 - 7 inside the parentheses?

[00:07:55]Many people when solving this question first go for the exponent and instead of this equation they write 9 - ( 9 + 1) * ( 9 - 7) inside the parentheses.

[00:08:10]And what's left by And in the next step, they go to the expression inside the first parentheses and write this equation as 9 - 10 * ( 9 - 7) inside the parentheses.

[00:08:26]Then, they go for the subtraction between 9 and 10 and write this equation as -1 * ( 9 - 7) inside the parentheses.

[00:08:38]And in the final step, they go to the expression inside the parentheses and write this equation as -1 * 2, which finally gives them the answer -2.

[00:08:49]However, this answer is actually incorrect.

[00:08:53]To solve this question, we must follow a rule that is called PEMDAS.

[00:08:58]As you can see on the screen, in this equation, first we have an exponent, then a subtraction sign, followed by parentheses, then a multiplication, and finally another parentheses.

[00:09:11]According to the PEMDAS rule, first you go for the expression inside the parentheses. And instead of this equation, we can write 3 ^ 2 - 10 * 2.

[00:09:23]And in the next step, we go for the exponent because in the PEMDAS rule, after parentheses, exponent has a higher priority than the other operations.

[00:09:33]So, we rewrite this equation as 9 minus 10 multiplied by 2.

[00:09:40]And the final step, we go for the multiplication between 10 and 2 because multiplication has priority over subtraction.

[00:09:49]So, we rewrite this equation as 9 minus 20, which finally gives us the answer -11.