Solve: 65-(4×3+2³÷4)-4³+5²÷5 Order of Operations Challenge

Q: Why do I need to solve what's inside parentheses first?

Parentheses have the highest priority in PEMDAS! Everything inside must be completed before you can use that result in the rest of the expression. In this problem, $ (4 × 3 + 2^3 ÷ 4) $ becomes 14 before we can subtract it from 65.

Q: What's the difference between ÷ and / symbols?

Both symbols mean division and work exactly the same way! $ 8 ÷ 4 = 8/4 = 2 $. The ÷ symbol is often used in arithmetic, while / is common in algebra.

Q: How do I handle multiple operations of the same priority?

When you have operations of equal priority (like multiplication and division), work left to right. For example: $ 2^3 ÷ 4 $ means calculate $ 2^3 = 8 $ first, then $ 8 ÷ 4 = 2 $.

Q: What if I forget PEMDAS during a test?

Remember the phrase "Please Excuse My Dear Aunt Sally" for PEMDAS! Write it down if needed. Also, look for parentheses and exponents first - they're usually the key to getting the right answer.

Q: How can I check if -8 is really correct?

Work through each step carefully and verify: $ 4 × 3 = 12 $, $ 2^3 = 8 $, $ 8 ÷ 4 = 2 $, so $ (12 + 2) = 14 $. Then: $ 65 - 14 - 64 + 5 = -8 $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Always solve the parentheses first

00:06 Even within the parentheses maintain proper order of operations

00:12 Calculate 2 to the power of 3 according to the laws of exponents

00:20 Insert this value into the exercise

00:26 Calculate 4 to the power of 3 according to the laws of exponents

00:36 Insert this value into the exercise

00:43 Represent the division as a fraction

00:52 Always solve division before addition

00:59 A number squared is the number multiplied by itself

01:04 Continue to solve the expression according to the proper order of operations

01:12 Reduce the fraction

01:20 Continue to solve the expression according to the proper order of operations

01:23 Given that all the operations are addition/subtraction

01:26 Arrange the exercise in a more manageable way to solve

01:32 Continue to solve the expression according to the proper order of operations

01:39 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve the following problem:

$65-(4\cdot3+2^3:4)-4^3+5^2:5=$

2

Step-by-step solution

Proceed to simplify the given expression whilst following the order of operations. The order of operations states that exponents precede multiplication and division, which in turn precede addition and subtraction, and that parentheses precede all of the above:

Therefore, we'll begin by simplifying the expressions inside of the parentheses. This should be carried out according to the order of operations mentioned above. We'll calculate the numerical value of the term with the exponent, which is the divided term inside of the parentheses. Simultaneously we'll calculate the result of the multiplication inside of the parentheses. Then we'll proceed to calculate the addition operation:

$65-(4\cdot3+2^3:4)-4^3+5^2:5= \\ 65-(12+8:4)-4^3+5^2:5=\\ 65-(12+2)-4^3+5^2:5=\\ 65-14-4^3+5^2:5=\\$ Simplify the resulting expression. Proceed to calculate the numerical value of the term with the exponent, which is the third term from the left. At the same time we will calculate the numerical value of the term with the exponent, which is divided by the fourth term from the left. We'll then continue to perform the division operation on this term. This is due to the fact that multiplication and division precede addition and subtraction:

$65-14-4^3+5^2:5=\\ 65-14-64+25:5=\\ 65-14-64+5$ We'll finish simplifying the given expression and perform the addition and subtraction operations:

$65-14-64+5 =\\ -8$ Let's summarize the steps of simplifying the given expression as shown below:

$65-(4\cdot3+2^3:4)-4^3+5^2:5= \\ 65-(12+8:4)-4^3+5^2:5=\\ 65-14-64+5 =\\ -8$ Therefore, the correct answer is answer C.

3

Final Answer

$-8$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)
Technique: Calculate $2^3 ÷ 4 = 8 ÷ 4 = 2$ inside parentheses first
Check: Work step-by-step: 65 - 14 - 64 + 5 = -8 ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations and calculating left to right
Don't solve 65 - 4 × 3 + 2³ ÷ 4 by going left to right = wrong answer of 1,028! This ignores that exponents and multiplication come before subtraction. Always follow PEMDAS: handle parentheses, then exponents, then multiplication/division, finally addition/subtraction.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

Why do I need to solve what's inside parentheses first?

+

Parentheses have the highest priority in PEMDAS! Everything inside must be completed before you can use that result in the rest of the expression. In this problem, $(4 × 3 + 2^3 ÷ 4)$ becomes 14 before we can subtract it from 65.

What's the difference between ÷ and / symbols?

+

Both symbols mean division and work exactly the same way! $8 ÷ 4 = 8/4 = 2$ . The ÷ symbol is often used in arithmetic, while / is common in algebra.

How do I handle multiple operations of the same priority?

+

When you have operations of equal priority (like multiplication and division), work left to right. For example: $2^3 ÷ 4$ means calculate $2^3 = 8$ first, then $8 ÷ 4 = 2$ .

Why is my answer negative when the problem starts with 65?

+

Don't worry! Even though we start with a large positive number, we're subtracting larger values than we're adding. Calculate: 65 - 14 - 64 + 5. The subtractions (78 total) are bigger than the additions (70 total), giving us -8.

What if I forget PEMDAS during a test?

+

Remember the phrase "Please Excuse My Dear Aunt Sally" for PEMDAS! Write it down if needed. Also, look for parentheses and exponents first - they're usually the key to getting the right answer.

How can I check if -8 is really correct?

+

Work through each step carefully and verify: $4 × 3 = 12$ , $2^3 = 8$ , $8 ÷ 4 = 2$ , so $(12 + 2) = 14$ . Then: $65 - 14 - 64 + 5 = -8$ ✓

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Solve: 65-(4×3+2³÷4)-4³+5²÷5 Order of Operations Challenge

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