Compare Fractions: Determine the Correct Symbol Between 2/5 and 6/15

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

Two fractions are equivalent when they simplify to the same reduced form. For example, $ \frac{2}{5} $ and $ \frac{6}{15} $ both equal $ \frac{2}{5} $ when simplified!

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

Yes! Cross-multiply: $ 2 \times 15 = 30 $ and $ 5 \times 6 = 30 $. Since both products equal 30, the fractions are equivalent.

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

Then they're not equal! You would use symbols instead. Compare the simplified fractions or convert to decimals to determine which is larger.

Q: Do I always need to simplify fractions before comparing?

Not always, but it's the safest method! You can also use cross-multiplication or convert to decimals, but simplifying helps you see the relationship most clearly.

Fraction Comparison with Equivalent Forms

Fill in the missing sign:

$\frac{2}{5}☐\frac{6}{15}$

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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 find a common denominator

00:06 Therefore we'll multiply the fraction by 3

00:09 Remember to multiply both numerator and denominator

00:12 Now we have a common denominator between the fractions

00:15 Notice that the fractions are equal

00:18 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:

$\frac{2}{5}☐\frac{6}{15}$

Step-by-step solution

To solve this problem, we'll take the following steps:

Step 1: Simplify the fraction $\frac{2}{5}$ .
Step 2: Simplify the fraction $\frac{6}{15}$ .
Step 3: Compare the simplified forms.

Let's go through these steps:

Step 1: $\frac{2}{5}$ is already in its simplest form because 2 and 5 have no common divisors other than 1.

Step 2: Simplify the fraction $\frac{6}{15}$ :
- The greatest common divisor (GCD) of 6 and 15 is 3.
- Divide both the numerator and the denominator by their GCD to simplify:
$\frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}$

Step 3: Compare the simplified forms:
Both $\frac{2}{5}$ and $\frac{6}{15}$ simplify to $\frac{2}{5}$ . Thus, they are equivalent.

Therefore, the correct mathematical sign between the fractions $\frac{2}{5}$ and $\frac{6}{15}$ is $=$ .

So, the missing sign is $\mathbf{=}$ .

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Simplification: Reduce fractions to lowest terms using greatest common divisor
Technique: $\frac{6}{15} = \frac{6 ÷ 3}{15 ÷ 3} = \frac{2}{5}$
Check: Both fractions simplify to same form means they are equal ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without simplifying first
Don't compare $\frac{2}{5}$ and $\frac{6}{15}$ directly by looking at numerators and denominators = wrong conclusion! Different-looking fractions can be equal. Always simplify both fractions to lowest terms before comparing.

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 equivalent?

Two fractions are equivalent when they simplify to the same reduced form. For example, $\frac{2}{5}$ and $\frac{6}{15}$ both equal $\frac{2}{5}$ when simplified!

What's the fastest way to find the GCD?

List the factors of both numbers and find the largest one they share. For 6 and 15: factors of 6 are 1, 2, 3, 6 and factors of 15 are 1, 3, 5, 15. The greatest common factor is 3.

Can I cross-multiply to compare these fractions?

Yes! Cross-multiply: $2 \times 15 = 30$ and $5 \times 6 = 30$ . Since both products equal 30, the fractions are equivalent.

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

Then they're not equal! You would use < or > symbols instead. Compare the simplified fractions or convert to decimals to determine which is larger.

Do I always need to simplify fractions before comparing?

Not always, but it's the safest method! You can also use cross-multiplication or convert to decimals, but simplifying helps you see the relationship most clearly.

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