Solve 4:2×(5+4+6): Order of Operations Challenge

Order of Operations with Mixed Division

4:2×(5+4+6)= 4:2\times(5+4+6)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:03 We always solve the parentheses first
00:06 Given that within the parentheses there's only addition we solve from left to right
00:13 Given that there's only multiplication and division we solve from left to right
00:22 This is the solution

Step-by-step written solution

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1

Understand the problem

4:2×(5+4+6)= 4:2\times(5+4+6)=

2

Step-by-step solution

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of them,

therefore we'll start by simplifying the expressions in parentheses first:
4:2(5+4+6)=4:215 4:2\cdot(5+4+6)= \\ 4:2\cdot15 Note that between multiplication and division operations there is no defined precedence for either operation, so we'll calculate the result of the expression obtained in the last stage step by step from left to right (which is the regular order in arithmetic operations), meaning we'll first perform the division operation, as it appears first from the left, and then we'll perform the multiplication operation that comes after it:

4:215=215=30 4:2\cdot15 =\\ 2\cdot15 =\\ 30 Therefore the correct answer is answer B.

3

Final Answer

30 30

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then multiplication and division left to right
  • Technique: Calculate (5+4+6) = 15, then 4÷2×15 = 2×15 = 30
  • Check: Verify by following order: parentheses → division → multiplication gives 30 ✓

Common Mistakes

Avoid these frequent errors
  • Doing multiplication before division
    Don't calculate 4÷(2×15) = 4÷30 = 2/15! This ignores left-to-right order for same-level operations and gives a completely wrong answer. Always work multiplication and division from left to right when they appear together.

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

Why do I calculate division before multiplication here?

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When multiplication and division appear together, they have equal priority. You must work from left to right. Since division (4÷2) comes first from the left, do it before multiplication.

What does the colon (:) symbol mean?

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The colon : is another way to write division, just like ÷. So 4:2 means the same as 4÷2, which equals 2.

Can I do the parentheses last instead?

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No! Parentheses always come first in PEMDAS. You must calculate (5+4+6)=15 (5+4+6) = 15 before doing any other operations.

What if I get a different order of operations?

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Always remember PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). This order never changes!

How can I avoid making calculation errors?

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Work step by step and write down each stage. Check: (5+4+6) = 15 ✓, then 4÷2 = 2 ✓, finally 2×15 = 30 ✓

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