Convert Mixed Number: Expressing 4⁴/₅ as a Decimal

Q: Why can't I just divide 4 by 5 to get the decimal?

You absolutely can! Dividing $ 4 ÷ 5 = 0.8 $ gives the same result as multiplying by $ \frac{2}{2} $ to get $ \frac{8}{10} $. Both methods work perfectly!

Q: What if the fraction doesn't convert to a nice decimal?

Some fractions like $ \frac{1}{3} $ give repeating decimals (0.333...). In those cases, you can either round to a specified number of decimal places or keep the exact fraction form depending on what the problem asks for.

Q: How do I know which number to multiply by to get 10 in the denominator?

Ask yourself: "What times 5 equals 10?" Since 5 × 2 = 10, multiply both numerator and denominator by 2. For other denominators, find what makes them equal 10, 100, or 1000.

Q: Can I convert mixed numbers to improper fractions instead?

Yes! $ 4\frac{4}{5} = \frac{24}{5} = 4.8 $. Both methods work, but converting the fraction part directly is often faster for decimal conversion problems.

Q: What's the easiest way to check my decimal answer?

Convert back to a fraction! $ 4.8 = 4\frac{8}{10} = 4\frac{4}{5} $ (after simplifying). If you get your original mixed number, you're correct!

Mixed Number Conversion with Fraction Simplification

$4\frac{4}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 Break down into whole number and fraction

00:06 We want to convert from fraction to decimal fraction, so we'll change the denominator to 10

00:10 Make sure to multiply both numerator and denominator

00:22 Convert fraction to decimal fraction

00:30 Let's 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

Understand the problem

$4\frac{4}{5}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert $\frac{4}{5}$ into a decimal.
Step 2: Add this decimal to the whole number part.

Now, let's work through each step:

Step 1: We start with the fractional part $\frac{4}{5}$ . To convert this into a decimal, we need a denominator of 10.

To get a denominator of 10, multiply both the numerator and the denominator by 2:

$\frac{4}{5} \times \frac{2}{2} = \frac{8}{10}$

This is equivalent to the decimal $0.8$ .

Step 2: Add this decimal to the whole number part 4:

$4 + 0.8 = 4.8$

Therefore, the solution to the problem is $4.8$ .

Final Answer

$4.8$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert fraction part to decimal, then add to whole number
Technique: Multiply $\frac{4}{5} \times \frac{2}{2} = \frac{8}{10} = 0.8$
Check: Verify that $4 + 0.8 = 4.8$ matches $4\frac{4}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Adding whole number to numerator instead of converting fraction first
Don't add 4 + 4 = 8 and write 8/5 = 1.6! This combines parts incorrectly and ignores the mixed number structure. Always convert the fraction part to decimal first, then add to the whole number.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

Why can't I just divide 4 by 5 to get the decimal?

You absolutely can! Dividing $4 ÷ 5 = 0.8$ gives the same result as multiplying by $\frac{2}{2}$ to get $\frac{8}{10}$ . Both methods work perfectly!

What if the fraction doesn't convert to a nice decimal?

Some fractions like $\frac{1}{3}$ give repeating decimals (0.333...). In those cases, you can either round to a specified number of decimal places or keep the exact fraction form depending on what the problem asks for.

How do I know which number to multiply by to get 10 in the denominator?

Ask yourself: "What times 5 equals 10?" Since 5 × 2 = 10, multiply both numerator and denominator by 2. For other denominators, find what makes them equal 10, 100, or 1000.

Can I convert mixed numbers to improper fractions instead?

Yes! $4\frac{4}{5} = \frac{24}{5} = 4.8$ . Both methods work, but converting the fraction part directly is often faster for decimal conversion problems.

What's the easiest way to check my decimal answer?

Convert back to a fraction! $4.8 = 4\frac{8}{10} = 4\frac{4}{5}$ (after simplifying). If you get your original mixed number, you're correct!

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