Solve (10+5+18)×4: Order of Operations Practice

Order of Operations with Parentheses First

(10+5+18)×4= (10+5+18)\times4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We'll make sure to open the parentheses properly
00:06 The outer term will multiply each term in parentheses
00:10 We'll use long multiplication to solve the product
00:18 We'll add all the products
00:22 We'll use long addition to find the solution
00:26 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(10+5+18)×4= (10+5+18)\times4=

2

Step-by-step solution

We will use the distributive property and multiply each term in parentheses by 4:

4×18+4×5+4×10= 4\times18+4\times5+4\times10=

We will solve the exercise from left to right.

We will solve the first multiplication exercise vertically. We will make sure to write correctly and multiply ones by ones, and ones by tens as follows:

4×18 4\\\times18

We get the result: 72.

Let's solve the remaining multiplication exercises:

4×5=20 4\times5=20

4×10=40 4\times10=40

Now we'll connect all the results in the following way:

72+20+40= 72+20+40=

We will solve the exercise vertically, making sure to write correctly and add ones with ones and tens with tens, as follows:

72+2040 72\\+20\\40

We'll add all the ones together and get: 2

We'll add all the tens together and get: 13

Therefore, we got the number:

132 132

3

Final Answer

132 132

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always solve expressions inside parentheses first
  • Technique: Add inside parentheses: 10+5+18=33, then multiply 33×4=132
  • Check: Verify by substituting back: (10+5+18)×4 = 33×4 = 132 ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying before adding inside parentheses
    Don't multiply 4 by each term separately first = gets 40+20+72=132 by luck! This ignores parentheses priority and usually gives wrong answers. Always solve what's inside parentheses completely before multiplying.

Practice Quiz

Test your knowledge with interactive questions

\( 20\div(4+1)-3= \)

FAQ

Everything you need to know about this question

Why can't I just multiply 4 by each number first?

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While the distributive property does work here, it's more complex and error-prone. Following PEMDAS (Parentheses first) is clearer: solve 10+5+18=33, then multiply by 4.

What if there were no parentheses in this problem?

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Without parentheses, you'd follow left-to-right for same operations. But parentheses change everything - they always come first in order of operations!

How do I remember the order of operations?

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Use PEMDAS: Please Excuse My Dear Aunt Sally

  • Parentheses
  • Exponents
  • Multiplication & Division (left to right)
  • Addition & Subtraction (left to right)

Is the distributive method shown in the explanation wrong?

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No, it's mathematically correct! The distributive property a(b+c+d)=ab+ac+ad a(b+c+d) = ab+ac+ad works. However, it's usually easier to add inside parentheses first: 33×4 is simpler than 4×10+4×5+4×18.

What if I get a different answer?

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Double-check each step: First add 10+5+18=33, then multiply 33×4=132. Common errors include forgetting to add all three numbers or making arithmetic mistakes.

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