Solve 20×4:5×(3+0×7-1): Order of Operations Challenge

Q: Why do I solve the parentheses first even though there's multiplication outside?

PEMDAS rules say parentheses come before everything else! Even if you see multiplication or division outside, you must always finish what's inside the parentheses completely first.

Q: What happens when I multiply by zero in the middle of a problem?

When you see $ 0\times7 $, it equals zero immediately. This makes $ 3+0\times7-1 = 3+0-1 = 2 $. Don't overthink it - zero times anything is always zero!

Q: Should I do 20×4÷5×2 from left to right or multiplication first?

Go left to right when operations have the same priority! Since multiplication and division are equal in PEMDAS, solve: 20×4=80, then 80÷5=16, then 16×2=32.

Q: How do I remember to check my work with order of operations?

After solving, trace through each step and ask: "Did I do parentheses first? Then left to right for same-priority operations?" Substitute your final answer to see if it makes sense!

Q: What if I get confused by the colon symbol (:)?

The colon means division in many countries! So $ 20\times4:5 $ is the same as $ 20\times4\div5 $. Just remember: colon = division symbol.

Order of Operations with Parentheses and Zero

$20\times4:5\times(3+0\times7-1)=$

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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 Always solve the parentheses first

00:07 Multiplication and division precede addition and subtraction

00:10 0 multiplied by any number always equals 0

00:17 Continue to solve the expression according to the correct order of operations

00:24 Calculate the parentheses and then continue

00:32 Solve from left to right, one operation at a time

00:44 This is the solution

00:48 New Chapter

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$20\times4:5\times(3+0\times7-1)=$

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 these,

Therefore, we'll start by simplifying the expression in parentheses, since multiplication comes before addition and subtraction, we'll first perform the multiplication in this expression and then the addition and subtraction operations

$20\cdot4:5\cdot(3+0\cdot7-1)= \\ 20\cdot4:5\cdot(3+0-1)= \\ 20\cdot4:5\cdot2 \\$ Let's continue simplifying the expression we got in the last step, note that between division and multiplication operations there is no precedence derived from the aforementioned order of operations, therefore we'll perform the operations one after another from left to right - this is the natural order of operations,

$20\cdot4:5\cdot2 = \\ 80:5\cdot2 =\\ 16\cdot2 =\\ 32$ Therefore the correct answer is answer B.

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then multiplication and division left to right
Zero Property: Any number multiplied by zero equals zero: $0\times7 = 0$
Verification: Work step-by-step: 80÷5×2 = 16×2 = 32 ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations and calculating left to right
Don't solve 20×4÷5×(3+0×7-1) as 80÷5×2 = 16×2 without doing parentheses first! This skips PEMDAS and can give wrong results. Always solve what's in parentheses before anything else, following order of operations inside them too.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I solve the parentheses first even though there's multiplication outside?

PEMDAS rules say parentheses come before everything else! Even if you see multiplication or division outside, you must always finish what's inside the parentheses completely first.

What happens when I multiply by zero in the middle of a problem?

When you see $0\times7$ , it equals zero immediately. This makes $3+0\times7-1 = 3+0-1 = 2$ . Don't overthink it - zero times anything is always zero!

Should I do 20×4÷5×2 from left to right or multiplication first?

Go left to right when operations have the same priority! Since multiplication and division are equal in PEMDAS, solve: 20×4=80, then 80÷5=16, then 16×2=32.

How do I remember to check my work with order of operations?

After solving, trace through each step and ask: "Did I do parentheses first? Then left to right for same-priority operations?" Substitute your final answer to see if it makes sense!

What if I get confused by the colon symbol (:)?

The colon means division in many countries! So $20\times4:5$ is the same as $20\times4\div5$ . Just remember: colon = division symbol.

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