Number Comparison: Identifying the Smallest Value Among Given Numbers

Q: Why do I get different answers when I work left to right?

Working left to right ignores the order of operations (PEMDAS)! You must do multiplication and division first, then addition and subtraction, regardless of position in the expression.

Q: What does the colon symbol mean in math?

The colon (:) means division, just like the ÷ symbol. So $ 20\colon4 $ means $ 20 ÷ 4 = 5 $.

Q: How do I remember to do operations in the right order?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Write it out if needed!

Q: Should I use parentheses to show my work?

Yes! Writing $ 100-3\times20 = 100-(3\times20) = 100-60 = 40 $ shows you're following order of operations correctly.

Q: What if two expressions give the same value?

That's totally normal! In this problem, both $ 100-3\times20 $ and $ 10\colon5\times20 $ equal 40. You're looking for the smallest unique value.

Order of Operations with Mixed Expressions

Which has the smallest value?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's begin with the first exercise. It's a great starting point!

00:21 Now, we have a simple exercise. Let's solve it together!

00:26 Next, move on to the second exercise. Ready, set, go!

00:32 Remember, multiplication and division are equal in the operation order. Solve them from left to right.

00:45 Let's proceed to the third exercise. You're doing great!

00:51 Multiplication and division come before addition and subtraction in any operation.

00:57 All that's left is a simple subtraction. You can do it!

01:00 This is the solution to the third exercise. Well done!

01:08 Remember, multiplication and division take priority over adding and subtracting. Keep it up!

01:18 In the fourth exercise, the answer is the smallest of all. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which has the smallest value?

Step-by-step solution

$100-3\times20=100-(3\times20)=100-60=40$

$10:5\times20=2\times20=40$

$50-4\times3=50-(4\times3)=50-12=38$

D':

$20:4+10=(20:4)+10=5+10=15$

Final Answer

$20\colon4+10$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Division/multiplication before addition/subtraction in all expressions
Technique: Calculate $20\colon4+10 = 5+10 = 15$ step by step
Check: Compare all four calculated values to find smallest: 15 ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following order of operations
Don't calculate $20\colon4+10$ as $(20\colon4)+10$ but then do $100-3\times20$ as $(100-3)\times20 = 1940$ ! This inconsistent approach leads to wrong comparisons. Always follow PEMDAS for every expression: multiply/divide first, then add/subtract.

Practice Quiz

Test your knowledge with interactive questions

$8 + 3 \times 2 =$

FAQ

Everything you need to know about this question

Why do I get different answers when I work left to right?

Working left to right ignores the order of operations (PEMDAS)! You must do multiplication and division first, then addition and subtraction, regardless of position in the expression.

What does the colon symbol mean in math?

The colon (:) means division, just like the ÷ symbol. So $20\colon4$ means $20 ÷ 4 = 5$ .

How do I remember to do operations in the right order?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Write it out if needed!

Should I use parentheses to show my work?

Yes! Writing $100-3\times20 = 100-(3\times20) = 100-60 = 40$ shows you're following order of operations correctly.

What if two expressions give the same value?

That's totally normal! In this problem, both $100-3\times20$ and $10\colon5\times20$ equal 40. You're looking for the smallest unique value.

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Number Comparison: Identifying the Smallest Value Among Given Numbers

Order of Operations with Mixed Expressions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I get different answers when I work left to right?

What does the colon symbol mean in math?

How do I remember to do operations in the right order?

Should I use parentheses to show my work?

What if two expressions give the same value?

🌟 Unlock Your Math Potential

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