Solve for y: 23-12×(-5)+y÷7+[21-4]=107 Order of Operations Challenge

Order of Operations with Mixed Operations

What is the number that should replace y?

2312×(5)+y ⁣:7+[214]=107 23-12\times(-5)+y\colon7+\lbrack21-4\rbrack=107

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:12 Let's start by solving the parts in parentheses and doing the multiplication first.
00:43 Remember, subtracting a negative is like adding a positive.
00:58 Now, add up the numbers given in the problem.
01:32 Next, subtract one hundred from both sides to get the variable by itself.
01:48 Finally, multiply by seven to figure out the value of Y. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the number that should replace y?

2312×(5)+y ⁣:7+[214]=107 23-12\times(-5)+y\colon7+\lbrack21-4\rbrack=107

2

Step-by-step solution

We begin by solving the multiplication exercise:

12×(5)=60 12\times(-5)=-60

and subsequently the exercises within brackets:

214=17 21-4=17

We obtain the following:

23(60)+y:7+17=107 23-(-60)+y:7+17=107

Keep in mind that a negative times a negative becomes a positive:

23+60+y:7+17=107 23+60+y:7+17=107

Next we simplify and add:

23+60=83 23+60=83

83+17=100 83+17=100

We obtain the following calculation:

100+y:7=107 100+y:7=107

We then rearrange the sections:

y:7=107100 y:7=107-100

y7=7 \frac{y}{7}=7

Lastly we multiply by 7:

y=7×7=49 y=7\times7=49

3

Final Answer

49

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Brackets first, then multiplication/division, finally addition/subtraction
  • Technique: Calculate 12×(5)=60 12\times(-5)=-60 and [214]=17 [21-4]=17 first
  • Check: Substitute y=49: 23+60+49÷7+17=107 23+60+49÷7+17=107

Common Mistakes

Avoid these frequent errors
  • Working left to right without following PEMDAS
    Don't solve 23-12 first then multiply by -5 = wrong grouping! This ignores multiplication priority and gives incorrect intermediate results. Always complete all multiplications and bracket operations before any addition or subtraction.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why do I multiply 12 by -5 before subtracting from 23?

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Because multiplication comes before subtraction in PEMDAS! The expression means 23 - (12×(-5)), not (23-12)×(-5). Order of operations is crucial for getting the right answer.

What does the colon (:) symbol mean in y:7?

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The colon means division, just like ÷. So y:7 is the same as y7 \frac{y}{7} or y÷7. It's common notation in some countries.

How do I handle the negative times negative part?

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When you have minus a negative number, it becomes positive! So 23-(-60) becomes 23+60. Remember: subtracting a negative = adding a positive.

Should I solve for y at the very beginning?

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No! First simplify everything else using PEMDAS. Get the equation down to something simple like 100+y7=107 100 + \frac{y}{7} = 107 , then solve for y.

What if I get a different answer when I check?

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Go back and check each step carefully! Common errors include: forgetting PEMDAS order, making arithmetic mistakes, or incorrectly handling negative numbers. Take your time with each calculation.

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