Visual Representation of the Fraction 25/15: Choose the Correct Diagram

Q: How do I know when a fraction is improper?

A fraction is improper when the numerator is bigger than the denominator. In $ \frac{5}{3} $, since 5 > 3, it's improper and represents more than one whole.

Q: Why do we need to simplify fractions first?

Simplifying makes visualization easier! Instead of trying to draw 25 pieces out of 15, we can work with just 5 pieces out of 3, which is much clearer to understand and draw.

Q: How do I find the GCD quickly?

Use the Euclidean algorithm: Divide the larger by smaller, then use the remainder. For 25 and 15: 25 ÷ 15 = 1 remainder 10, then 15 ÷ 10 = 1 remainder 5, then 10 ÷ 5 = 2 remainder 0. The GCD is 5!

Q: What does the visual representation show exactly?

The correct diagram shows one completely shaded circle (representing 1 whole) plus two-thirds of another circle shaded. This perfectly represents $ 1\frac{2}{3} $ or $ \frac{5}{3} $.

Q: Can I convert improper fractions to mixed numbers?

Yes! $ \frac{5}{3} = 1\frac{2}{3} $ because 5 ÷ 3 = 1 with remainder 2. The quotient becomes the whole number and the remainder becomes the new numerator.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the correct visual representation for the given fraction

00:03 In black, we see the number of parts into which the whole is divided:

00:08 And in red is colored the given part, meaning the numerator

00:13 For each option, we'll find the mathematical representation and choose the appropriate one

01:19 Let's reduce what we can from the given fraction

01:30 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

Choose the option that visually represents the following fraction:

$\frac{25}{15}$

2

Step-by-step solution

To solve this problem, we need to find the visual representation corresponding to the fraction $\frac{25}{15}$ .

First, we simplify the fraction $\frac{25}{15}$ . To do this, find the greatest common divisor (GCD) of 25 and 15.
Upon using the Euclidean algorithm, we find that the GCD of 25 and 15 is 5.
We divide both the numerator and the denominator of $\frac{25}{15}$ by 5: $\frac{25 \div 5}{15 \div 5} = \frac{5}{3}$ .

The simplified fraction $\frac{5}{3}$ is an improper fraction, which means it can be expressed as a mixed number: $1\frac{2}{3}$ .

Visually, $\frac{5}{3}$ means 1 full unit and $\frac{2}{3}$ of another unit. The visual representation will show at least one full portion and a part of another.

By reviewing the visual options provided, the correct representation is the one displaying shaded portions that sum up to one whole and two-thirds of another, which is given by option 2. Therefore, the solution to the problem is the visual representation found in choice 2.

Thus, the correct answer is the option that displays option 2.

3

Final Answer

Key Points to Remember

Essential concepts to master this topic

Simplification: Find GCD to reduce fractions to lowest terms
Technique: Convert $\frac{25}{15}$ to $\frac{5}{3}$ by dividing by GCD of 5
Check: Improper fraction $\frac{5}{3} = 1\frac{2}{3}$ shows 1 whole plus $\frac{2}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Not simplifying fractions before visualizing
Don't try to visualize $\frac{25}{15}$ directly = confusing diagrams with 25 parts! Complex fractions make visual representation unnecessarily difficult. Always simplify first to get $\frac{5}{3}$ for clearer understanding.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction as a mixed number:

$\frac{10}{7}=$

FAQ

Everything you need to know about this question

How do I know when a fraction is improper?

+

A fraction is improper when the numerator is bigger than the denominator. In $\frac{5}{3}$ , since 5 > 3, it's improper and represents more than one whole.

Why do we need to simplify fractions first?

+

Simplifying makes visualization easier! Instead of trying to draw 25 pieces out of 15, we can work with just 5 pieces out of 3, which is much clearer to understand and draw.

How do I find the GCD quickly?

+

Use the Euclidean algorithm: Divide the larger by smaller, then use the remainder. For 25 and 15: 25 ÷ 15 = 1 remainder 10, then 15 ÷ 10 = 1 remainder 5, then 10 ÷ 5 = 2 remainder 0. The GCD is 5!

What does the visual representation show exactly?

+

The correct diagram shows one completely shaded circle (representing 1 whole) plus two-thirds of another circle shaded. This perfectly represents $1\frac{2}{3}$ or $\frac{5}{3}$ .

Can I convert improper fractions to mixed numbers?

+

Yes! $\frac{5}{3} = 1\frac{2}{3}$ because 5 ÷ 3 = 1 with remainder 2. The quotient becomes the whole number and the remainder becomes the new numerator.

How do I check if my visual answer is correct?

+

Count the total shaded parts! In the correct diagram, you should see 5 equal parts shaded out of every 3 parts total, which matches our fraction $\frac{5}{3}$ .

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Visual Representation of the Fraction 25/15: Choose the Correct Diagram

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