Compare Fractions: Determine the Correct Sign Between 5/25 and 1/5

Fraction Comparison with Simplification

Fill in the missing sign:

52515 \frac{5}{25}☐\frac{1}{5}

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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 5 to get a common denominator
00:09 Remember to divide both numerator and denominator
00:13 Now we have a common denominator between the fractions
00:16 We can see that the fractions are equal
00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing sign:

52515 \frac{5}{25}☐\frac{1}{5}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Simplify both fractions to their lowest terms.
  • Step 2: Compare the simplified fractions.

Now, let's work through each step:

Step 1: Simplification
Simplify 525 \frac{5}{25} :
- The greatest common divisor of 5 and 25 is 5.
- Divide the numerator and the denominator by 5: 525=5÷525÷5=15 \frac{5}{25} = \frac{5 \div 5}{25 \div 5} = \frac{1}{5} .
The fraction 525 \frac{5}{25} simplifies to 15 \frac{1}{5} .
The fraction 15 \frac{1}{5} stays the same as it is already in its simplest form.

Step 2: Comparison
Since both fractions simplify to 15 \frac{1}{5} , they are indeed equal.

Therefore, the solution to the problem is that the missing sign is = = .

3

Final Answer

= =

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always simplify fractions to lowest terms before comparing
  • Technique: Find GCD: 525=5÷525÷5=15 \frac{5}{25} = \frac{5 ÷ 5}{25 ÷ 5} = \frac{1}{5}
  • Check: Both fractions equal 15 \frac{1}{5} so they are equal ✓

Common Mistakes

Avoid these frequent errors
  • Comparing fractions without simplifying first
    Don't compare 525 \frac{5}{25} and 15 \frac{1}{5} directly = wrong comparison! Different-looking fractions can be equal when simplified. Always simplify both fractions to lowest terms first.

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 fractions need to be simplified?

+

Look for common factors in the numerator and denominator. If both can be divided by the same number (like 5 in this problem), then simplify!

What if the fractions look completely different?

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Don't worry! Fractions like 525 \frac{5}{25} and 15 \frac{1}{5} can be equivalent even though they look different. Always simplify to see their true relationship.

How do I find the greatest common divisor (GCD)?

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List the factors of both numbers and find the largest one they share. For 5 and 25: factors of 5 are {1, 5}, factors of 25 are {1, 5, 25}, so GCD = 5.

Can I convert to decimals instead?

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Yes! 525=0.2 \frac{5}{25} = 0.2 and 15=0.2 \frac{1}{5} = 0.2 , so they're equal. But simplifying fractions is usually faster and more accurate.

What if I can't find a common factor?

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If there's no common factor other than 1, the fraction is already in simplest form. Like 15 \frac{1}{5} - it can't be simplified further!

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