Compare Fractions: Find the Symbol Between 3/4 and 6/8

Q: How do I know when two fractions are equal?

Two fractions are equal when they simplify to the same form or represent the same decimal value. For example, $ \frac{6}{8} = \frac{3}{4} $ because both equal 0.75!

Q: What's the easiest way to compare fractions?

Start by simplifying both fractions to lowest terms. If they look the same after simplifying, they're equal! You can also convert to decimals or find a common denominator.

Q: How do I find the GCD to simplify fractions?

List the factors of both numbers and find the largest number that divides both evenly. For 6 and 8: factors of 6 are 1,2,3,6 and factors of 8 are 1,2,4,8, so GCD = 2.

Q: Can I cross-multiply to compare these fractions?

Yes! Cross-multiply: $ 3 \times 8 = 24 $ and $ 4 \times 6 = 24 $. Since both products equal 24, the fractions are equal!

Q: What if the fractions don't simplify to the same thing?

Then compare their decimal values or convert to equivalent fractions with the same denominator. The fraction with the larger numerator (when denominators match) is greater.

Comparing Fractions with Simplification

Fill in the missing sign:

$\frac{3}{4}☐\frac{6}{8}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 We want to reduce the fraction by 2 to get a common denominator

00:09 Remember to divide both numerator and denominator

00:14 Now we have a common denominator between the fractions

00:19 We can see that the fractions are equal

00:22 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

Fill in the missing sign:

$\frac{3}{4}☐\frac{6}{8}$

Step-by-step solution

To compare the fractions $\frac{3}{4}$ and $\frac{6}{8}$ , we will first simplify each fraction.

First, $\frac{3}{4}$ is already in simplest form since the GCD of 3 and 4 is 1.

Now, for the fraction $\frac{6}{8}$ , we find the GCD of 6 and 8, which is 2. Simplifying $\frac{6}{8}$ by dividing both the numerator and the denominator by 2 gives:

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

Both fractions, $\frac{3}{4}$ and $\frac{6}{8}$ , simplify to $\frac{3}{4}$ .

Since they simplify to the same form, they are equivalent:

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

Therefore, the correct missing sign is $\boxed{=}$ .

$=$

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify fractions to lowest terms before comparing values
Technique: Find GCD of 6 and 8 = 2, then $\frac{6÷2}{8÷2} = \frac{3}{4}$
Check: Both $\frac{3}{4}$ and $\frac{6}{8}$ equal 0.75 when converted to decimals ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators and denominators separately
Don't compare just 3 vs 6 and 4 vs 8 to conclude 3/4 < 6/8! This ignores the relationship between numerator and denominator within each fraction. Always simplify fractions first or convert to equivalent forms with common denominators.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{25}☐\frac{1}{5}$

FAQ

Everything you need to know about this question

How do I know when two fractions are equal?

Two fractions are equal when they simplify to the same form or represent the same decimal value. For example, $\frac{6}{8} = \frac{3}{4}$ because both equal 0.75!

What's the easiest way to compare fractions?

Start by simplifying both fractions to lowest terms. If they look the same after simplifying, they're equal! You can also convert to decimals or find a common denominator.

How do I find the GCD to simplify fractions?

List the factors of both numbers and find the largest number that divides both evenly. For 6 and 8: factors of 6 are 1,2,3,6 and factors of 8 are 1,2,4,8, so GCD = 2.

Can I cross-multiply to compare these fractions?

Yes! Cross-multiply: $3 \times 8 = 24$ and $4 \times 6 = 24$ . Since both products equal 24, the fractions are equal!

What if the fractions don't simplify to the same thing?

Then compare their decimal values or convert to equivalent fractions with the same denominator. The fraction with the larger numerator (when denominators match) is greater.

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