Solve the Expression: 10:(5×1/2) Using Order of Operations

Q: Why can't I just work from left to right?

The order of operations (PEMDAS) is a mathematical rule that ensures everyone gets the same answer! Parentheses always come first, no matter where they appear in the expression.

Q: What does the colon symbol mean in this problem?

The colon (:) is another way to write division, just like ÷. So $ 10:(5\times\frac{1}{2}) $ means $ 10 \div (5\times\frac{1}{2}) $

Q: Can I convert everything to decimals first?

Yes! Converting $ \frac{1}{2} = 0.5 $ makes it $ 10 \div (5 \times 0.5) = 10 \div 2.5 = 4 $. Just remember to still follow the order of operations!

Q: How do I check if 4 is really the right answer?

Work backwards! If the answer is 4, then $ 4 \times 2.5 = 10 $. Since $ 5 \times \frac{1}{2} = 2.5 $, we get $ 4 \times 2.5 = 10 $ ✓

Order of Operations with Parentheses and Fractions

$10:(5\times\frac{1}{2})=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Division is also multiplication by the reciprocal

00:07 Therefore when opening the parentheses, it will end up as divided by C

00:11 We will use this formula in our exercise

00:14 We will solve according to the order of operations from left to right

00:21 Division is also multiplication by the reciprocal

00:27 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$10:(5\times\frac{1}{2})=$

Step-by-step solution

To solve the problem $10 \div (5 \times \frac{1}{2})$ , we'll follow these steps:

Step 1: Evaluate the expression inside the parentheses. Multiply $5$ by $\frac{1}{2}$ .
Step 2: Use the result from Step 1 for division with $10$ .

Now, let's work through each step:

Step 1: Calculate the multiplication inside the parentheses:
$5 \times \frac{1}{2} = \frac{5}{2} = 2.5$ .

Step 2: Divide $10$ by the result from Step 1:
$10 \div 2.5 = 4$ .

Hence, the solution to the given expression is $4$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always evaluate expressions inside parentheses first
Technique: Calculate $5 \times \frac{1}{2} = 2.5$ before dividing
Check: Verify $10 \div 2.5 = 4$ by multiplying $4 \times 2.5 = 10$ ✓

Common Mistakes

Avoid these frequent errors

Dividing 10 by 5 first, then multiplying by 1/2
Don't work left to right ignoring parentheses: 10 ÷ 5 × 1/2 = 1! This violates order of operations and gives the wrong answer. Always solve what's inside parentheses first: (5 × 1/2) = 2.5, then 10 ÷ 2.5 = 4.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

FAQ

Everything you need to know about this question

Why can't I just work from left to right?

The order of operations (PEMDAS) is a mathematical rule that ensures everyone gets the same answer! Parentheses always come first, no matter where they appear in the expression.

How do I multiply 5 by 1/2?

To multiply by a fraction, multiply the whole number by the numerator: $5 \times \frac{1}{2} = \frac{5 \times 1}{2} = \frac{5}{2} = 2.5$

What does the colon symbol mean in this problem?

The colon (:) is another way to write division, just like ÷. So $10:(5\times\frac{1}{2})$ means $10 \div (5\times\frac{1}{2})$

Can I convert everything to decimals first?

Yes! Converting $\frac{1}{2} = 0.5$ makes it $10 \div (5 \times 0.5) = 10 \div 2.5 = 4$ . Just remember to still follow the order of operations!

How do I check if 4 is really the right answer?

Work backwards! If the answer is 4, then $4 \times 2.5 = 10$ . Since $5 \times \frac{1}{2} = 2.5$ , we get $4 \times 2.5 = 10$ ✓

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