Compare Fractions and Decimals: Is 2/4 = 0.5?

Q: Why can't I just compare 2 and 5 directly?

Because denominators matter! $ \frac{2}{4} $ means 2 pieces out of 4, while $ \frac{5}{10} $ means 5 pieces out of 10. The pieces are different sizes, so you need a common denominator to compare fairly.

Q: Is there a faster way than finding the LCD?

Yes! You can simplify first. $ \frac{2}{4} = \frac{1}{2} $ and $ 0.5 = \frac{1}{2} $. When fractions are in lowest terms, comparison becomes much easier!

Q: How do I convert 0.5 to a fraction?

Look at the decimal places! 0.5 has one decimal place, so put 5 over 10: $ 0.5 = \frac{5}{10} $. Then simplify: $ \frac{5}{10} = \frac{1}{2} $.

Q: Can I convert the fraction to decimal instead?

Absolutely! Divide the numerator by denominator: $ \frac{2}{4} = 2 ÷ 4 = 0.5 $. Sometimes this method is faster than finding common denominators.

Fraction-Decimal Comparison with Common Denominators

Choose the appropriate sign:

$\frac{2}{4}?0.5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's pick the right sign.

00:08 Now, simplify as much as you can. Divide both the top and bottom numbers.

00:21 Next, change from a decimal to a fraction.

00:33 Remember, keep simplifying by dividing both sides.

00:39 And that's how you find the answer!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign:

$\frac{2}{4}?0.5$

Step-by-step solution

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

Since there is only one number 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 20.

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

$\frac{2}{4}\times\frac{5}{5}=\frac{10}{20}$

$\frac{5}{10}\times\frac{2}{2}=\frac{10}{20}$

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

$\frac{10}{20}=\frac{10}{20}$

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert decimals to fractions using place value
Technique: Find LCD: $\frac{2}{4} \times \frac{5}{5} = \frac{10}{20}$
Check: Simplify both fractions to lowest terms: $\frac{2}{4} = \frac{1}{2} = 0.5$ ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions with different denominators directly
Don't compare $\frac{2}{4}$ and $\frac{5}{10}$ by just looking at numerators = wrong comparison! Different denominators mean different-sized pieces. Always convert to common denominators or simplify first.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

$0.1\stackrel{?}{=}0.10$

FAQ

Everything you need to know about this question

Why can't I just compare 2 and 5 directly?

Because denominators matter! $\frac{2}{4}$ means 2 pieces out of 4, while $\frac{5}{10}$ means 5 pieces out of 10. The pieces are different sizes, so you need a common denominator to compare fairly.

Is there a faster way than finding the LCD?

Yes! You can simplify first. $\frac{2}{4} = \frac{1}{2}$ and $0.5 = \frac{1}{2}$ . When fractions are in lowest terms, comparison becomes much easier!

How do I convert 0.5 to a fraction?

Look at the decimal places! 0.5 has one decimal place, so put 5 over 10: $0.5 = \frac{5}{10}$ . Then simplify: $\frac{5}{10} = \frac{1}{2}$ .

What if the LCD is really big?

Don't worry! Even with large LCDs, the comparison works the same way. Just multiply carefully and double-check your arithmetic. The LCD of 20 here isn't too bad!

Can I convert the fraction to decimal instead?

Absolutely! Divide the numerator by denominator: $\frac{2}{4} = 2 ÷ 4 = 0.5$ . Sometimes this method is faster than finding common denominators.

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