Compare Fraction and Decimal: 3/4 ? 0.8 Inequality Problem

Q: Why not just convert both to decimals instead?

You absolutely can! $ \frac{3}{4} = 0.75 $ and 0.8, so 0.75 easier for you.

Q: How do I convert 0.8 to a fraction quickly?

Since 0.8 has one decimal place, put 8 over 10: $ \frac{8}{10} $. Then simplify by dividing both by 2: $ \frac{4}{5} $.

Q: What if the LCD is really big? Is there an easier way?

Yes! Convert the fraction to decimal instead. Divide: $ 3 ÷ 4 = 0.75 $. Then compare 0.75 and 0.8 directly - much simpler!

Q: How do I find the LCD of 4 and 5?

List multiples: 4, 8, 12, 16, 20... and 5, 10, 15, 20... The first number that appears in both lists is your LCD!

Q: Can I use cross multiplication here?

No - cross multiplication only works when comparing two fractions directly, like $ \frac{a}{b} $ vs $ \frac{c}{d} $. Here you need common denominators or decimal conversion.

Fraction-Decimal Comparison with Common Denominators

Choose the appropriate sign:

$\frac{3}{4}?0.8$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:07 Convert decimal number to fraction

00:14 Reduce as much as possible, make sure to divide both numerator and denominator

00:27 Multiply each fraction by the second denominator to find the common denominator

00:31 Make sure to multiply numerator by numerator and denominator by denominator

00:43 Now let's compare the fractions

00:47 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:

$\frac{3}{4}?0.8$

Step-by-step solution

First, let's convert 0.8 to a simple fraction.

Since there is only one number after the decimal point, the number is divided by 10 as follows:

$0.8=\frac{8}{10}$

Let's reduce the fraction:

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

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 20.

We'll multiply each one to reach the common denominator as follows:

$\frac{3}{4}\times\frac{5}{5}=\frac{15}{20}$

$\frac{4}{5}\times\frac{4}{4}=\frac{16}{20}$

Now we can compare the two fractions and see that:

$\frac{15}{20}<\frac{16}{20}$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert decimal to fraction for easier comparison
Technique: Find LCD - convert $\frac{3}{4}$ and $\frac{4}{5}$ using 20
Check: Verify $\frac{15}{20} < \frac{16}{20}$ means 0.75 < 0.8 ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators without same denominator
Don't compare 3 and 8 directly from $\frac{3}{4}$ and 0.8! This ignores denominators and gives wrong results. Always convert to same denominator or same decimal form first.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why not just convert both to decimals instead?

You absolutely can! $\frac{3}{4} = 0.75$ and 0.8, so 0.75 < 0.8. Both methods work - choose whichever feels easier for you.

How do I convert 0.8 to a fraction quickly?

Since 0.8 has one decimal place, put 8 over 10: $\frac{8}{10}$ . Then simplify by dividing both by 2: $\frac{4}{5}$ .

What if the LCD is really big? Is there an easier way?

Yes! Convert the fraction to decimal instead. Divide: $3 ÷ 4 = 0.75$ . Then compare 0.75 and 0.8 directly - much simpler!

How do I find the LCD of 4 and 5?

List multiples: 4, 8, 12, 16, 20... and 5, 10, 15, 20... The first number that appears in both lists is your LCD!

Can I use cross multiplication here?

No - cross multiplication only works when comparing two fractions directly, like $\frac{a}{b}$ vs $\frac{c}{d}$ . Here you need common denominators or decimal conversion.

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