Locating the Fraction 1/4: Precise Number Identification

Q: How can all answers be correct at the same time?

Think of nested ranges! Since $ \frac{1}{4} = 0.25 $, it fits between 0 and 1, between 0 and $ \frac{2}{4} $ (0.5), and between 0 and $ \frac{3}{4} $ (0.75). Each range contains the previous ones!

Q: Why don't I just pick the smallest range?

The question asks where the fraction lies, not for the smallest possible range. If a fraction is between 0 and 0.5, it's also automatically between 0 and 0.75, and between 0 and 1!

Q: How do I compare fractions with the same denominator?

When denominators are the same, just compare the numerators! Since all fractions have denominator 4: \( \frac{0}{4}

Q: What if the fractions had different denominators?

Convert them to the same denominator first! For example, to compare $ \frac{1}{4} $ and $ \frac{1}{2} $, write $ \frac{1}{2} = \frac{2}{4} $, then compare: \( \frac{1}{4}

Q: Should I convert fractions to decimals?

You can! $ \frac{1}{4} = 0.25 $, $ \frac{2}{4} = 0.5 $, $ \frac{3}{4} = 0.75 $. This makes it easier to see that 0.25 is between 0 and 0.5, between 0 and 0.75, and between 0 and 1.

Fraction Positioning with Multiple Number Ranges

Identify where $\frac{1}{4}$ lies?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the domain where the number is located

00:03 Draw the number line and mark the given number

00:08 Place every number in the domain with a common denominator (4)

00:15 Narrow down to whole numbers and find the domain

00:19 We can see that the number is found in all these domains

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

Identify where $\frac{1}{4}$ lies?

Step-by-step solution

Let's try to understand what is bigger and what is smaller than the number $\frac{1}{4}$

Since the denominator is 4, both the larger and smaller numbers will have a denominator of 4:

$\frac{?}{4}<\frac{1}{4}<\frac{?}{4}$

Now let's complete the numerators with numbers that will help us reach whole numbers in fractions as follows:

$\frac{0}{4}<-\frac{3}{4}<\frac{4}{4}$

Let's proceed to reduce the fractions as follows:

$\frac{0}{4}=0$

$\frac{4:4}{4:4}=-\frac{1}{1}=1$

This means the fraction is between 0 and 1

But since the consecutive numbers for the fraction's numerator are:

$\frac{0}{4} < \frac{1}{4} < \frac{2}{4}$

$\frac{0}{4} < \frac{1}{4} < \frac{3}{4}$

We can see that all the answers are correct

Final Answer

All answers are correct

Key Points to Remember

Essential concepts to master this topic

Rule: Fractions between 0 and 1 can belong to multiple ranges
Technique: Convert fractions to common denominators: $\frac{2}{4} = \frac{1}{2}$ , $\frac{3}{4}$
Check: Verify $0 < \frac{1}{4} < \frac{2}{4} < \frac{3}{4} < 1$ shows all ranges work ✓

Common Mistakes

Avoid these frequent errors

Thinking only one answer can be correct
Don't choose just the smallest range like 0 to 1/2 = missing other valid ranges! A fraction can lie within multiple overlapping intervals simultaneously. Always check if the fraction satisfies all given ranges before eliminating options.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

How can all answers be correct at the same time?

Think of nested ranges! Since $\frac{1}{4} = 0.25$ , it fits between 0 and 1, between 0 and $\frac{2}{4}$ (0.5), and between 0 and $\frac{3}{4}$ (0.75). Each range contains the previous ones!

Why don't I just pick the smallest range?

The question asks where the fraction lies, not for the smallest possible range. If a fraction is between 0 and 0.5, it's also automatically between 0 and 0.75, and between 0 and 1!

How do I compare fractions with the same denominator?

When denominators are the same, just compare the numerators! Since all fractions have denominator 4: $\frac{0}{4} < \frac{1}{4} < \frac{2}{4} < \frac{3}{4} < \frac{4}{4}$

What if the fractions had different denominators?

Convert them to the same denominator first! For example, to compare $\frac{1}{4}$ and $\frac{1}{2}$ , write $\frac{1}{2} = \frac{2}{4}$ , then compare: $\frac{1}{4} < \frac{2}{4}$

Should I convert fractions to decimals?

You can! $\frac{1}{4} = 0.25$ , $\frac{2}{4} = 0.5$ , $\frac{3}{4} = 0.75$ . This makes it easier to see that 0.25 is between 0 and 0.5, between 0 and 0.75, and between 0 and 1.

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