Compare Fractions: Find the Missing Symbol Between 2/5 and 6/15

Q: How do I know if two fractions are equal without calculating?

The quickest way is to cross-multiply! For $ \frac{2}{5} $ and $ \frac{6}{15} $, multiply 2×15 and 5×6. If both products equal 30, the fractions are equal!

Q: Why can't I just compare 2/5 and 6/15 by looking at them?

Because they have different denominators! You need a common reference point. Think of it like comparing 2 slices of a 5-piece pizza to 6 slices of a 15-piece pizza - you need equal-sized pieces to compare fairly.

Q: What does 'simplest form' actually mean?

A fraction is in simplest form when the numerator and denominator have no common factors except 1. For example, $ \frac{6}{15} $ becomes $ \frac{2}{5} $ because we divided both by their GCF of 3.

Q: How do I double-check my simplification is correct?

Multiply your simplified fraction back up! If $ \frac{2}{5} $ came from $ \frac{6}{15} $, then 2×3 should equal 6 and 5×3 should equal 15. It works!

Comparing Fractions with Simplification Methods

Fill in the missing symbol:

$\frac{2}{5}☐\frac{6}{15}$

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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 reduce the fraction by 3 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

00:23 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 symbol:

$\frac{2}{5}☐\frac{6}{15}$

Step-by-step solution

To solve this problem, we follow these steps:

Simplify each fraction to its simplest form.
Compare the simplified fractions to determine their relationship.

Let's simplify the fractions:

$\frac{2}{5}$ is already in its simplest form since 2 and 5 have no common factors other than 1.

For $\frac{6}{15}$ , find the greatest common factor (GCF) of 6 and 15, which is 3.

Divide both the numerator and the denominator by their GCF:

$\frac{6 \div 3}{15 \div 3} = \frac{2}{5}$

Now both fractions simplify to $\frac{2}{5}$ .

Since the fractions $\frac{2}{5}$ and $\frac{2}{5}$ are equal, we use the symbol $=$ .

Therefore, the correct symbol to fill in the blank is = .

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Simplification: Reduce both fractions to lowest terms before comparing
Technique: Find GCF of 6 and 15, which is 3
Check: Verify $\frac{6}{15} = \frac{2}{5}$ by cross-multiplying: 6×5 = 15×2 = 30 ✓

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 denominators make direct comparison impossible. Always simplify both fractions to lowest terms first, then compare the simplified forms.

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 if two fractions are equal without calculating?

The quickest way is to cross-multiply! For $\frac{2}{5}$ and $\frac{6}{15}$ , multiply 2×15 and 5×6. If both products equal 30, the fractions are equal!

What if I can't find the GCF easily?

List the factors of both numbers! For 6: 1, 2, 3, 6. For 15: 1, 3, 5, 15. The largest common factor is 3, so that's your GCF.

Why can't I just compare 2/5 and 6/15 by looking at them?

Because they have different denominators! You need a common reference point. Think of it like comparing 2 slices of a 5-piece pizza to 6 slices of a 15-piece pizza - you need equal-sized pieces to compare fairly.

What does 'simplest form' actually mean?

A fraction is in simplest form when the numerator and denominator have no common factors except 1. For example, $\frac{6}{15}$ becomes $\frac{2}{5}$ because we divided both by their GCF of 3.

How do I double-check my simplification is correct?

Multiply your simplified fraction back up! If $\frac{2}{5}$ came from $\frac{6}{15}$ , then 2×3 should equal 6 and 5×3 should equal 15. It works!

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