Compare Fractions and Decimals: Is 3/5 Greater Than, Less Than, or Equal to 0.5?

Q: Should I convert the fraction to decimal or the decimal to fraction?

Either way works! You can convert $ \frac{3}{5} $ to 0.6, or convert 0.5 to $ \frac{5}{10} $. Choose the method that feels easier for you.

Q: How do I convert 3/5 to a decimal quickly?

Divide the numerator by denominator: 3 ÷ 5 = 0.6. Then compare: 0.6 > 0.5, so $ \frac{3}{5} > 0.5 $!

Q: Why did we use 10 as the common denominator?

Because 0.5 = $ \frac{5}{10} $, and 5 is a factor of 10. We can easily convert $ \frac{3}{5} $ to tenths by multiplying by $ \frac{2}{2} $.

Fraction Comparison with Decimal Conversion

Choose the appropriate sign:

$\frac{3}{5}~[?]~0.5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:04 Convert from decimal to fraction

00:18 Multiply the fraction by 2 to find the common denominator

00:21 Make sure to multiply numerator by numerator and denominator by denominator

00:29 Now let's compare the fractions

00:32 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

Choose the appropriate sign:

$\frac{3}{5}~[?]~0.5$

Step-by-step solution

First, let's convert 0.5 into a simple fraction.

Since there is only one digit after the decimal point, the number is divided by 10, therefore:

$0.5=\frac{5}{10}$

Now we have two simple fractions with different denominators.

Let's find the least common denominator between them, in this case the common denominator is 10.

We'll equate the denominators by multiplying by the appropriate numbers:

$\frac{3}{5}\times\frac{2}{2}=\frac{6}{10}$

$\frac{5}{10}\times\frac{1}{1}=\frac{5}{10}$

Now let's compare the numerators and we'll find that:

$\frac{6}{10}>\frac{5}{10}$

Final Answer

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Key Points to Remember

Essential concepts to master this topic

Rule: Convert to same format before comparing fractions and decimals
Technique: Convert $\frac{3}{5}$ to $\frac{6}{10}$ using common denominator 10
Check: Compare numerators when denominators match: 6 > 5 means $\frac{6}{10} > \frac{5}{10}$ ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators directly without common denominators
Don't compare 3 and 5 from $\frac{3}{5}$ vs 0.5 = wrong conclusion that 3 < 5! The denominators are different, so you can't compare numerators directly. Always convert to the same denominator or decimal format first.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Should I convert the fraction to decimal or the decimal to fraction?

Either way works! You can convert $\frac{3}{5}$ to 0.6, or convert 0.5 to $\frac{5}{10}$ . Choose the method that feels easier for you.

How do I convert 3/5 to a decimal quickly?

Divide the numerator by denominator: 3 ÷ 5 = 0.6. Then compare: 0.6 > 0.5, so $\frac{3}{5} > 0.5$ !

What if the denominators don't have an obvious common multiple?

You can always multiply the denominators together to get a common denominator. Or convert both to decimals by dividing - that's often faster for complex fractions!

Why did we use 10 as the common denominator?

Because 0.5 = $\frac{5}{10}$ , and 5 is a factor of 10. We can easily convert $\frac{3}{5}$ to tenths by multiplying by $\frac{2}{2}$ .

Can I just memorize that 3/5 = 0.6?

Yes! Common fraction-decimal equivalents are helpful to memorize:

$\frac{1}{2} = 0.5$
$\frac{3}{5} = 0.6$
$\frac{3}{4} = 0.75$

But always understand the conversion process too!

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