Identifying the Fraction 3/5: Mathematical Number Recognition

Fraction Comparison with Number Line Intervals

The number 35 \frac{3}{5} is found

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the range where the number is located
00:03 Let's draw the number line and plot the given number
00:10 Place each number in the range with common denominator (5)
00:15 Reduce the whole numbers and find the range
00:21 It appears the number is in this range
00:29 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 35 \frac{3}{5} is found

2

Step-by-step solution

Let's try to understand what is bigger and what is smaller than the number 35 \frac{3}{5}

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

?5<35<?5 \frac{?}{5}<\frac{3}{5}<\frac{?}{5}

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

05<35<55 \frac{0}{5}<\frac{3}{5}<\frac{5}{5}

Let's reduce the fractions as follows:

05=0 \frac{0}{5}=0

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

In other words, the fraction is between 0 and 1.

Let's try to find a smaller range, meaning consecutive numbers before and after the fraction's numerator as follows:

15<34<45 \frac{1}{5}<\frac{3}{4}<\frac{4}{5}

3

Final Answer

between 15 \frac{1}{5} to 45 \frac{4}{5}

Key Points to Remember

Essential concepts to master this topic
  • Position Rule: Compare fractions by finding their location between whole numbers
  • Technique: Use common denominators like 15<35<45 \frac{1}{5} < \frac{3}{5} < \frac{4}{5}
  • Check: Convert to decimals: 35=0.6 \frac{3}{5} = 0.6 is between 0.2 and 0.8 ✓

Common Mistakes

Avoid these frequent errors
  • Comparing fractions with different denominators incorrectly
    Don't compare 35 \frac{3}{5} to 12 \frac{1}{2} by just looking at numerators = wrong conclusions! This ignores that the parts have different sizes. Always convert to common denominators or decimals first.

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 do I know where 35 \frac{3}{5} fits on a number line?

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Think of it as 3 out of 5 equal parts. Since 35=0.6 \frac{3}{5} = 0.6 , it's more than halfway between 0 and 1, closer to 1 than to 0.

Why can't 35 \frac{3}{5} be between 0 and 12 \frac{1}{2} ?

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Because 35=0.6 \frac{3}{5} = 0.6 and 12=0.5 \frac{1}{2} = 0.5 ! Since 0.6 > 0.5, the fraction 35 \frac{3}{5} is larger than 12 \frac{1}{2} .

What's the easiest way to compare fractions?

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Convert them to decimals or find a common denominator. For example: 15=0.2 \frac{1}{5} = 0.2 , 35=0.6 \frac{3}{5} = 0.6 , 45=0.8 \frac{4}{5} = 0.8 .

How do I find what's between two fractions?

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Look at fractions with the same denominator first. Between 15 \frac{1}{5} and 45 \frac{4}{5} , you have 25 \frac{2}{5} and 35 \frac{3}{5} !

Can I use cross multiplication to compare fractions?

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Yes! To compare 35 \frac{3}{5} and 12 \frac{1}{2} : cross multiply 3×2=6 and 5×1=5. Since 6>5, we know 35>12 \frac{3}{5} > \frac{1}{2} .

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