Compare Fractions and Decimals: 5/8 ? 0.6

Q: Why can't I just compare 5 and 6 from the fractions?

Because the denominators are different! $ \frac{5}{8} $ means 5 out of 8 parts, while $ \frac{6}{10} $ means 6 out of 10 parts. The size of each part is different, so you need equal denominators to compare fairly.

Q: Is it easier to convert fractions to decimals or decimals to fractions?

Both methods work! Converting fractions to decimals by division is often quicker: $ \frac{5}{8} = 5 ÷ 8 = 0.625 $. Then compare 0.625 vs 0.6 directly.

Q: How do I find the LCD of 8 and 10?

List the multiples: 8: 8, 16, 24, 32, 40, 48... and 10: 10, 20, 30, 40, 50... The smallest common multiple is 40, so LCD = 40.

Q: What if I get confused with which fraction is larger?

Use the cross-multiplication trick: For $ \frac{5}{8} $ vs $ \frac{6}{10} $, calculate 5×10 = 50 and 8×6 = 48. Since 50 > 48, we have $ \frac{5}{8} > \frac{6}{10} $!

Fraction-Decimal Comparison with Common Denominators

Choose the appropriate sign:

$\frac{5}{8}?0.6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the correct mathematical sign.

00:12 Start by changing the decimal number into a fraction.

00:24 Then, multiply each fraction by the other fraction's denominator, to find a common denominator.

00:31 Remember, multiply the numerators together, and the denominators together.

00:40 Okay, let's compare the fractions now.

00:45 And that's how we find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign:

$\frac{5}{8}?0.6$

Step-by-step solution

First, let's convert 0.6 into a simple fraction.

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

$0.6=\frac{6}{10}$

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 80.

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

$\frac{5}{8}\times\frac{10}{10}=\frac{50}{80}$

$\frac{6}{10}\times\frac{8}{8}=\frac{48}{80}$

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

$\frac{50}{80} > \frac{48}{80}$

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Conversion: Convert decimal to fraction using place value position
Technique: Find LCD: 8 and 10 gives 40, then compare numerators
Check: Convert both to decimals: 5/8 = 0.625, 0.6 = 0.600 ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators directly without same denominators
Don't compare 5 and 6 directly from 5/8 vs 6/10 = wrong conclusion! Different denominators make direct comparison invalid. Always convert to same denominator first or use decimal form.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why can't I just compare 5 and 6 from the fractions?

Because the denominators are different! $\frac{5}{8}$ means 5 out of 8 parts, while $\frac{6}{10}$ means 6 out of 10 parts. The size of each part is different, so you need equal denominators to compare fairly.

Is it easier to convert fractions to decimals or decimals to fractions?

Both methods work! Converting fractions to decimals by division is often quicker: $\frac{5}{8} = 5 ÷ 8 = 0.625$ . Then compare 0.625 vs 0.6 directly.

How do I find the LCD of 8 and 10?

List the multiples: 8: 8, 16, 24, 32, 40, 48... and 10: 10, 20, 30, 40, 50... The smallest common multiple is 40, so LCD = 40.

What if I get confused with which fraction is larger?

Use the cross-multiplication trick: For $\frac{5}{8}$ vs $\frac{6}{10}$ , calculate 5×10 = 50 and 8×6 = 48. Since 50 > 48, we have $\frac{5}{8} > \frac{6}{10}$ !

Why did we get 50/80 and 48/80 instead of 40?

The explanation used 80 as a common denominator (which also works since 80 is a multiple of both 8 and 10). Using the LCD of 40 gives: $\frac{5}{8} = \frac{25}{40}$ and $\frac{6}{10} = \frac{24}{40}$ .

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