Locating the Negative Fraction: Finding -3/4 on the Number Line

Negative Fractions with Number Line Placement

The number −34 -\frac{3}{4} 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
00:04 Let's draw a number line and plot the given number
00:08 Let's write every number in the range with a common denominator (4)
00:17 Let's reduce the whole numbers and find the range
00:26 We can see that 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 −34 -\frac{3}{4} is found...

2

Step-by-step solution

Let's try to understand what is larger and what is smaller than the number −34 -\frac{3}{4} .

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

−?4<34<?4 -\frac{?}{4}<\frac{3}{4}<\frac{?}{4}

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

−44<−34<04 -\frac{4}{4}<-\frac{3}{4}<\frac{0}{4}

Let's then simplify the fractions as follows:

04=0 \frac{0}{4}=0

−4:44:4=−11=−1 -\frac{4:4}{4:4}=-\frac{1}{1}=-1

Therefore, the answer is:

−1<−34<0 -1<-\frac{3}{4}<0

3

Final Answer

...between −1 -1 and 0 0 .

Key Points to Remember

Essential concepts to master this topic
  • Position Rule: Negative fractions are located left of zero on number line
  • Technique: Compare −34 -\frac{3}{4} to whole numbers: −1<−34<0 -1 < -\frac{3}{4} < 0
  • Check: Convert to decimals: −34=−0.75 -\frac{3}{4} = -0.75 lies between -1 and 0 ✓

Common Mistakes

Avoid these frequent errors
  • Placing negative fractions on the positive side
    Don't ignore the negative sign and place −34 -\frac{3}{4} between 0 and 1 = wrong location! The negative sign means the fraction must be left of zero. Always remember negative numbers go left of zero on the number line.

Practice Quiz

Test your knowledge with interactive questions

What number is marked on the number axis?

000111

FAQ

Everything you need to know about this question

Why is −34 -\frac{3}{4} closer to zero than to -1?

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Since 34=0.75 \frac{3}{4} = 0.75 , the negative version −34=−0.75 -\frac{3}{4} = -0.75 is only 0.75 units away from zero, but 0.25 units away from -1!

How do I compare negative fractions to whole numbers?

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Use the same denominator! Convert whole numbers: −1=−44 -1 = -\frac{4}{4} and 0=04 0 = \frac{0}{4} . Then compare numerators: -4 < -3 < 0.

What if the fraction was positive instead?

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If we had +34 +\frac{3}{4} , it would be between 0 and 1 on the right side of zero. The negative sign flips it to the left side.

Can I convert to decimals to make it easier?

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Absolutely! Converting −34=−0.75 -\frac{3}{4} = -0.75 makes it clear that it's between -1.0 and 0.0 on the number line.

How do I remember which direction negative numbers go?

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  • Negative = Left of zero
  • Positive = Right of zero
  • Think of a thermometer: negative temperatures are below zero!

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