Solve (14+8-2)/(4×5)×2+3: Order of Operations Practice

Order of Operations with Fraction Division

Check the correct answer:

14+82452+3= \frac{14+8-2}{4\cdot5}\cdot2+3=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's solve from left to right, we want to calculate the fraction
00:07 Now let's calculate the numerator product
00:13 Let's continue calculating the numerator
00:20 Let's reduce what we can
00:26 Always solve multiplication and division before addition and subtraction
00:30 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

Check the correct answer:

14+82452+3= \frac{14+8-2}{4\cdot5}\cdot2+3=

2

Step-by-step solution

First, we will solve the multiplication exercise that was broken:

4×5=20 4\times5=20

Now, we will solve the exercise that was broken:

14+82=222=20 14+8-2=22-2=20

We receive the solution:

2020=1 \frac{20}{20}=1

Now, we receive the exercise:

1×2+3= 1\times2+3=

According to the order of operations, we will first solve the multiplication exercise and then proceed:

1×2=2 1\times2=2

2+3=5 2+3=5

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
  • Technique: Solve numerator 14+8-2=20, denominator 4×5=20
  • Check: Substitute back: 2020×2+3=1×2+3=5 \frac{20}{20}×2+3 = 1×2+3 = 5

Common Mistakes

Avoid these frequent errors
  • Solving operations from left to right without grouping
    Don't solve 14+8-2÷4×5×2+3 from left to right = wrong order! This ignores parentheses and fraction bars which group operations together. Always solve what's inside parentheses and above/below fraction bars first.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do I solve the numerator and denominator separately first?

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The fraction bar acts like parentheses! Everything above it (14+8-2) must be solved completely before dividing by everything below it (4×5).

Can I just work from left to right?

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No! Order of operations (PEMDAS) must be followed. Parentheses and fraction bars create groups that must be solved first, regardless of their position.

What if I get the numerator and denominator both equal to 20?

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Perfect! When numerator equals denominator, 2020=1 \frac{20}{20} = 1 . This simplifies your expression significantly for the remaining calculations.

How do I handle the multiplication and addition at the end?

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After getting 1×2+3 1×2+3 , multiply first (1×2=2), then add (2+3=5). Multiplication always comes before addition in PEMDAS!

What's the most common mistake in this type of problem?

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Students often ignore the fraction bar grouping and try to work left to right. Remember: fraction bars group operations just like parentheses do!

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