Number Line Pattern: Find the Missing Value in 0, 1/2, 1 Sequence

Q: How do I know what number to add each time?

Look at the first two given numbers to find the pattern! Here, $ \frac{1}{2} - 0 = \frac{1}{2} $ and $ 1 - \frac{1}{2} = \frac{1}{2} $, so we add $ \frac{1}{2} $ each time.

Q: What if I get mixed numbers in my answer?

Mixed numbers like $ 1\frac{1}{2} $ and $ 2\frac{1}{2} $ are perfectly correct! They show the exact position on the number line. Don't convert them to improper fractions unless asked.

Q: How do I add fractions to whole numbers?

When adding $ \frac{1}{2} $ to a whole number like 2, just write it as $ 2\frac{1}{2} $. Think of it as 2 and a half on the number line.

Q: Can I work backwards to check my pattern?

Yes! Start from any known number and subtract $ \frac{1}{2} $ to get the previous number. For example: $ 1 - \frac{1}{2} = \frac{1}{2} $ ✓

Q: What if the spaces on the number line aren't equal?

In arithmetic sequences, the spaces must be equal! If they look different, double-check your calculations. Each interval should represent the same value: $ \frac{1}{2} $.

Arithmetic Sequences with Half-Unit Intervals

Fill in the missing number

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Understand the problem

Fill in the missing number

Step-by-step solution

Let's begin by looking at the numbers from left to right:

$0,\frac{1}{2},1,1\frac{1}{2}$

We are able to deduce that the common operation is:

$+\frac{1}{2}$

$0+\frac{1}{2}=\frac{1}{2}$

$\frac{1}{2}+\frac{1}{2}=1$

$1+\frac{1}{2}=1\frac{1}{2}$

Therefore, the next sequence will be:

$1\frac{1}{2}+\frac{1}{2}=2$

$2+\frac{1}{2}=2\frac{1}{2}$

$2\frac{1}{2}+\frac{1}{2}=3$

Final Answer

$2,2\frac{1}{2},3$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Identify the constant difference between consecutive terms
Technique: Add $\frac{1}{2}$ repeatedly: $1\frac{1}{2} + \frac{1}{2} = 2$
Check: Verify each step maintains the same $+\frac{1}{2}$ pattern throughout ✓

Common Mistakes

Avoid these frequent errors

Changing the pattern halfway through
Don't switch from adding $\frac{1}{2}$ to adding 1 or doubling = breaks the sequence! This creates inconsistent spacing on the number line. Always maintain the same constant difference throughout the entire pattern.

Practice Quiz

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All negative numbers appear on the number line to the left of the number 0.

FAQ

Everything you need to know about this question

How do I know what number to add each time?

Look at the first two given numbers to find the pattern! Here, $\frac{1}{2} - 0 = \frac{1}{2}$ and $1 - \frac{1}{2} = \frac{1}{2}$ , so we add $\frac{1}{2}$ each time.

What if I get mixed numbers in my answer?

Mixed numbers like $1\frac{1}{2}$ and $2\frac{1}{2}$ are perfectly correct! They show the exact position on the number line. Don't convert them to improper fractions unless asked.

How do I add fractions to whole numbers?

When adding $\frac{1}{2}$ to a whole number like 2, just write it as $2\frac{1}{2}$ . Think of it as 2 and a half on the number line.

Can I work backwards to check my pattern?

Yes! Start from any known number and subtract $\frac{1}{2}$ to get the previous number. For example: $1 - \frac{1}{2} = \frac{1}{2}$ ✓

What if the spaces on the number line aren't equal?

In arithmetic sequences, the spaces must be equal! If they look different, double-check your calculations. Each interval should represent the same value: $\frac{1}{2}$ .

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