Number Line Position: Identifying the Point at 2/3 Between 0 and 1

Q: How do I know how many parts to divide the number line into?

Look at the total number of equal segments from 0 to 1. In this problem, there are 3 equal segments, so we use thirds: $ \frac{1}{3} $, $ \frac{2}{3} $, $ \frac{3}{3} $.

Q: What's the difference between counting points and counting segments?

Points are the dots you see. Segments are the spaces between points. To find fractions on a number line, always count how many segments you move from 0, not how many points you pass.

Q: How can I double-check my answer?

Convert your fraction to a decimal: $ \frac{2}{3} $ ≈ 0.67. This should be closer to 1 than to 0, which matches the position shown on the number line.

Q: What if the segments aren't perfectly equal in the drawing?

In math problems, assume the segments are equal even if the drawing looks slightly off. Focus on the intended mathematical relationships rather than visual precision.

Fraction Positioning with Equal Segments

What is the missing number (?) marked on the number line below?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the highlighted number

00:03 It seems the axis is divided into 3 segments

00:11 And each segment equals one third, let's count them

00:18 Let's see which segment is highlighted

00:25 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

What is the missing number (?) marked on the number line below?

Step-by-step solution

Let's first count how many points there are, including the number 1, on the number line.

Since there are 3 in total, we'll define the 0 point as the fraction:

$\frac{0}{3}$

We will also define 1 as the following fraction:

$\frac{3}{3}$

Now let's fill in each point on the line to find out which numbers are missing:

Final Answer

$\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Division: Divide the number line into equal parts based on denominator
Technique: Count segments from 0: two out of three equals $\frac{2}{3}$
Check: Verify position is 2 segments past 0 and 1 segment before 1 ✓

Common Mistakes

Avoid these frequent errors

Counting points instead of segments
Don't count the dots on the number line = wrong fraction! Points are markers, not the actual divisions. Always count the segments (spaces) between points to find the correct fraction.

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 how many parts to divide the number line into?

Look at the total number of equal segments from 0 to 1. In this problem, there are 3 equal segments, so we use thirds: $\frac{1}{3}$ , $\frac{2}{3}$ , $\frac{3}{3}$ .

Why isn't the answer 1/2 if the point looks like it's halfway?

Visual estimation can be tricky! Always count the actual segments. The missing point is at the second segment out of three total segments, making it $\frac{2}{3}$ , not $\frac{1}{2}$ .

What's the difference between counting points and counting segments?

Points are the dots you see. Segments are the spaces between points. To find fractions on a number line, always count how many segments you move from 0, not how many points you pass.

How can I double-check my answer?

Convert your fraction to a decimal: $\frac{2}{3}$ . This should be closer to 1 than to 0, which matches the position shown on the number line.

What if the segments aren't perfectly equal in the drawing?

In math problems, assume the segments are equal even if the drawing looks slightly off. Focus on the intended mathematical relationships rather than visual precision.

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