Compare Fraction and Decimal: 6/8 ? 0.75

Q: Which is easier - converting fraction to decimal or decimal to fraction?

Converting fraction to decimal is usually faster! Just divide the numerator by denominator: $ \frac{6}{8} = 6 ÷ 8 = 0.75 $. Use a calculator if needed.

Q: How do I convert 0.75 to a fraction?

Since 0.75 has 2 decimal places, write it as $ \frac{75}{100} $, then simplify by dividing both by 25 to get $ \frac{3}{4} $.

Q: Why do I need to find a common denominator?

Common denominators help when both numbers are fractions. In this problem, converting to decimals or reducing fractions is actually easier than finding common denominators!

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

Some decimals like 0.333... create repeating decimals. In those cases, it's easier to convert the fraction to decimal instead for comparison.

Q: How can I double-check my comparison?

Convert both ways! If $ \frac{6}{8} = 0.75 $ and $ 0.75 = \frac{3}{4} $, and $ \frac{6}{8} = \frac{3}{4} $ when simplified, then they're definitely equal!

Fraction-Decimal Comparison with Conversion Methods

Choose the appropriate sign:

$\frac{6}{8}?0.75$

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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 number to fraction

00:20 Reduce as much as possible, make sure to divide both numerator and denominator

00:40 Reduce this fraction as much as possible

00:48 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:

$\frac{6}{8}?0.75$

Step-by-step solution

First, let's convert 0.75 to a simple fraction.

Since there are two numbers after the decimal point, the number is divided by 100, therefore:

$0.75=\frac{75}{100}$

Let's reduce the fraction by dividing by 25:

$\frac{75:25}{100:25}=\frac{3}{4}$

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 8.

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

$\frac{6}{8}\times\frac{1}{1}=\frac{6}{8}$

$\frac{3}{4}\times\frac{2}{2}=\frac{6}{8}$

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

$\frac{6}{8}=\frac{6}{8}$

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert decimal to fraction or fraction to decimal
Method: $\frac{6}{8} = 0.75$ by dividing 6 ÷ 8
Verification: Both forms equal $\frac{3}{4}$ when simplified ✓

Common Mistakes

Avoid these frequent errors

Comparing without converting to same form
Don't compare 6/8 and 0.75 directly without converting = wrong comparison! Different forms make it hard to see they're equal. Always convert both numbers to the same form (both fractions or both decimals) before comparing.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Which is easier - converting fraction to decimal or decimal to fraction?

Converting fraction to decimal is usually faster! Just divide the numerator by denominator: $\frac{6}{8} = 6 ÷ 8 = 0.75$ . Use a calculator if needed.

How do I convert 0.75 to a fraction?

Since 0.75 has 2 decimal places, write it as $\frac{75}{100}$ , then simplify by dividing both by 25 to get $\frac{3}{4}$ .

Why do I need to find a common denominator?

Common denominators help when both numbers are fractions. In this problem, converting to decimals or reducing fractions is actually easier than finding common denominators!

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

Some decimals like 0.333... create repeating decimals. In those cases, it's easier to convert the fraction to decimal instead for comparison.

How can I double-check my comparison?

Convert both ways! If $\frac{6}{8} = 0.75$ and $0.75 = \frac{3}{4}$ , and $\frac{6}{8} = \frac{3}{4}$ when simplified, then they're definitely equal!

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