Solve the Expression: 11:2 + 4½ Step by Step

Q: What does the colon (:) mean in math expressions?

The colon : is another way to write division! So $ 11:2 $ means exactly the same as $ 11 \div 2 $. It's commonly used in ratios and some textbooks.

Q: Should I convert everything to fractions or decimals?

Either way works perfectly! For this problem, decimals are easier: $ 5.5 + 4.5 = 10 $. But you could also use fractions: $ \frac{11}{2} + \frac{9}{2} = \frac{20}{2} = 10 $.

Q: What if I get a different decimal when dividing 11 by 2?

Double-check your division! $ 11 \div 2 = 5.5 $ because $ 2 \times 5 = 10 $, leaving 1 remaining, which becomes $ \frac{1}{2} = 0.5 $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Write division as a fraction

00:10 Break down 11 into 10 plus 1

00:18 Break down the fraction into a whole number and remainder

00:25 Convert from improper fraction to whole number

00:36 Add

00:41 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$11:2+4\frac{1}{2}=$

2

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Interpret the division operation $11:2$ as $11 \div 2$ .
Step 2: Divide 11 by 2 to get $5.5$ .
Step 3: Convert the mixed number $4\frac{1}{2}$ to its decimal form $4.5$ or as an improper fraction $\frac{9}{2}$ .
Step 4: Add the results from Step 2 and Step 3: $5.5 + 4.5 = 10$ .

Now, let's work through each step in detail:

Step 1: The division operation $11:2$ is equivalent to $11 \div 2$ . Performing the division, we have:

$11 \div 2 = 5.5$ .

Step 2: The mixed number $4\frac{1}{2}$ can be expressed as a decimal by converting it as follows:

$4\frac{1}{2} = 4 + 0.5 = 4.5$ .

Step 3: Add the results from Step 1 and Step 2:

$5.5 + 4.5 = 10$ .

Therefore, the solution to the problem is $10$ .

3

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Perform division first, then addition with mixed numbers
Technique: Convert $11:2 = 11 \div 2 = 5.5$ and $4\frac{1}{2} = 4.5$
Check: Verify $5.5 + 4.5 = 10$ by converting back to fractions ✓

Common Mistakes

Avoid these frequent errors

Adding before dividing or misunderstanding colon notation
Don't calculate $2 + 4\frac{1}{2}$ first = wrong order and 6.5 instead of 10! The colon (:) means division, not addition, and division must be done before addition. Always follow order of operations: division first, then addition.

Practice Quiz

Test your knowledge with interactive questions

$10\frac{1}{2}-\frac{1}{2}=$

FAQ

Everything you need to know about this question

What does the colon (:) mean in math expressions?

+

The colon : is another way to write division! So $11:2$ means exactly the same as $11 \div 2$ . It's commonly used in ratios and some textbooks.

Should I convert everything to fractions or decimals?

+

Either way works perfectly! For this problem, decimals are easier: $5.5 + 4.5 = 10$ . But you could also use fractions: $\frac{11}{2} + \frac{9}{2} = \frac{20}{2} = 10$ .

How do I convert a mixed number to a decimal?

+

Take the whole number and add the fraction as a decimal. For $4\frac{1}{2}$ : the whole part is 4, and $\frac{1}{2} = 0.5$ , so $4 + 0.5 = 4.5$ .

Why isn't the answer one of the fraction choices?

+

Because 10 is a whole number! When fractions or mixed numbers add up to a whole number, that's the correct answer. Don't force a fractional answer when the math gives you a clean whole number.

What if I get a different decimal when dividing 11 by 2?

+

Double-check your division! $11 \div 2 = 5.5$ because $2 \times 5 = 10$ , leaving 1 remaining, which becomes $\frac{1}{2} = 0.5$ .

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Solve the Expression: 11:2 + 4½ Step by Step

Division and Mixed Numbers with Decimal Conversion

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