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

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What number is marked on the number axis?

000111

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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