Finding the Fraction 6/5: Number Identification Problem

Fraction Positioning with Mixed Number Bounds

The number 65 \frac{6}{5} is found....

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Position the number
00:07 We'll position the number relative to 1
00:28 And we'll position the number relative to 1.5
00:36 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

The number 65 \frac{6}{5} is found....

2

Step-by-step solution

Let's first try to understand what numbers are greater and smaller than the number 65 \frac{6}{5} .

Since the denominator is 5, both the larger and smaller numbers will also have a denominator of 5:

?5<65<?5 \frac{?}{5}<\frac{6}{5}<\frac{?}{5}

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

55<65<7.55 \frac{5}{5}<\frac{6}{5}<\frac{7.5}{5}

Let's now simplify the fractions as follows:

5:55:5=11=1 \frac{5:5}{5:5}=\frac{1}{1}=1

7.5:55:5=1.51=1.5=112 \frac{7.5:5}{5:5}=\frac{1.5}{1}=1.5=1\frac{1}{2}

Therefore, the answer is:

1<65<112 1<\frac{6}{5}<1\frac{1}{2}

3

Final Answer

...between 1 1 to 112 1\frac{1}{2} .

Key Points to Remember

Essential concepts to master this topic
  • Compare: Convert improper fractions to decimal or mixed number form
  • Technique: Use 65=1.2 \frac{6}{5} = 1.2 to place between 1 and 1.5
  • Check: Verify 1<1.2<112 1 < 1.2 < 1\frac{1}{2} makes sense ✓

Common Mistakes

Avoid these frequent errors
  • Comparing numerators without considering denominators
    Don't just look at 6 > 5 and think 65 \frac{6}{5} is huge = wrong placement! The denominator matters just as much. Always convert to decimal form: 65=1.2 \frac{6}{5} = 1.2 to compare accurately.

Practice Quiz

Test your knowledge with interactive questions

What are the missing numbers (?) on the numer line below?

000??????111

FAQ

Everything you need to know about this question

How do I quickly know where 65 \frac{6}{5} fits?

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Convert to decimal: 65=6÷5=1.2 \frac{6}{5} = 6 ÷ 5 = 1.2 . Since 1.2 is between 1.0 and 1.5, it falls between 1 1 and 112 1\frac{1}{2} !

What if the fraction looks confusing with big numbers?

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Always use division! For any fraction ab \frac{a}{b} , just calculate a ÷ b to get the decimal. This makes comparing much easier than working with fractions.

Why can't 65 \frac{6}{5} be between 0 and 12 \frac{1}{2} ?

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Because 65=1.2 \frac{6}{5} = 1.2 and 12=0.5 \frac{1}{2} = 0.5 . Since 1.2 > 0.5, the fraction is actually greater than 12 \frac{1}{2} , not smaller!

How do I convert 112 1\frac{1}{2} to compare it?

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Mixed numbers convert easily: 112=1+12=1+0.5=1.5 1\frac{1}{2} = 1 + \frac{1}{2} = 1 + 0.5 = 1.5 . So you're comparing 1.0 < 1.2 < 1.5!

What's the easiest way to remember this method?

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  • Step 1: Convert everything to decimals
  • Step 2: Line up the numbers from smallest to largest
  • Step 3: See where your fraction fits in the sequence

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