Compare Expressions: 14+16:4×2 vs 14+16:(4×2) - Order of Operations

Order of Operations with Parentheses Impact

Fill in the correct sign:

14+16:4×2 14+16:4\times2

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14+16:(4×2) 14+16:(4\times2)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:11 First, let's look for the correct sign in the expression.
00:15 Next, calculate each side carefully.
00:19 Remember, always do multiplication and division before addition and subtraction.
00:25 Work through the expression from left to right, following this rule.
00:29 Calculate the product first, then keep solving the expression.
00:34 We've finished the left side, so now let's focus on the right side.
00:38 Always solve what's inside the parentheses first.
00:42 Remember to do multiplication and division before addition and subtraction here as well.
00:48 This is how we calculate the right side.
00:51 And there you have it! This is the final solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the correct sign:

14+16:4×2 14+16:4\times2

___

14+16:(4×2) 14+16:(4\times2)

2

Step-by-step solution

First, we solve the exercise14+16:4×2 14+16:4\times2 According to the order of operations, multiplication and division come before addition and subtraction, therefore we first divide 16 by 4 and then multiply the result by 2:

16:4=4 16:4=4

4×2=8 4\times2=8

Then, we solve the exercise:
14+8=22 14+8=22

Now, we solve the exercise:14+16:(4×2)= 14+16:(4\times2)=

According to the order of operations, the exercise within parentheses is first, so we first multiply 4 by 2 and then proceed to the division operation.

4×2=8 4\times2=8

16:8=2 16:8=2

In the last step we add:14+2=16 14+2=16

Since 22 is greater than 16, the corresponding result is> >

3

Final Answer

> >

Key Points to Remember

Essential concepts to master this topic
  • Rule: Follow PEMDAS/BODMAS - parentheses always come first
  • Technique: Calculate 16:4×2=4×2=8 16:4\times2 = 4\times2 = 8 vs 16:(4×2)=16:8=2 16:(4\times2) = 16:8 = 2
  • Check: First expression gives 22, second gives 16, so 22 > 16 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring how parentheses change the order
    Don't solve both expressions the same way = getting 22 = 22! Parentheses force you to multiply 4×2 first, changing 16÷4×2 into 16÷8. Always recognize that parentheses completely change which operations happen first.

Practice Quiz

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\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do parentheses make such a big difference here?

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Parentheses force the multiplication 4×2 to happen first! Without them, division and multiplication have equal priority and work left to right: 16÷4×2 = 4×2 = 8. With parentheses: 16÷(4×2) = 16÷8 = 2.

How do I remember the order of operations?

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Use PEMDAS (Parentheses, Exponents, Multiplication/Division left to right, Addition/Subtraction left to right) or BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction).

What if there are multiple sets of parentheses?

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Work from the innermost parentheses outward. Always complete everything inside parentheses before moving to operations outside them.

Do I always work left to right for multiplication and division?

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Yes! When operations have the same priority (like × and ÷), always work left to right. This is why 16÷4×2 equals 8, not 2.

How can I double-check my work?

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Calculate each expression step-by-step separately, then compare the final results. For this problem: 14+8=22 and 14+2=16, so 22 > 16.

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