Question
Nico wants to use a horizontal number line to compare 13
4
and 1.5. He is unsure how to do it and asks you for help. How would you explain the process?
4
and 1.5. He is unsure how to do it and asks you for help. How would you explain the process?
Answers
GPT-4o mini
To help Nico compare \( \frac{13}{4} \) and \( 1.5 \) using a horizontal number line, you can follow these steps:
### Step 1: Convert to a Common Format
Since we are comparing two numbers, it's helpful to express both numbers in the same format. We can convert \( 1.5 \) into a fraction:
\[
1.5 = \frac{15}{10} = \frac{3}{2}
\]
However, to keep it simple, let’s convert \( 1.5 \) back into an improper fraction with a common denominator with \( \frac{13}{4} \).
### Step 2: Get a Common Denominator
The fraction \( \frac{13}{4} \) already has a denominator of 4. We can express \( 1.5 \) using the same denominator:
1. Convert \( 1.5 \) into a fraction with 4 as the denominator:
\[
1.5 = \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4}
\]
### Step 3: Compare the Two Fractions
Now we can compare the two fractions:
- \( \frac{13}{4} \)
- \( \frac{6}{4} \)
To compare:
- \( \frac{13}{4} \) is greater than \( \frac{6}{4} \) because the numerator (13) is greater than 6 while the denominators are the same.
### Step 4: Plot on a Number Line
Now we can plot these fractions on a horizontal number line:
1. Draw a horizontal line.
2. Mark points for \( 0 \), \( 1 \), \( 2 \), \( 3 \), and \( 4 \) (you could extend the line further, but those are key points).
3. Plot \( \frac{6}{4} \) (which is equivalent to \( 1.5 \)) somewhere between \( 1 \) and \( 2 \).
4. Plot \( \frac{13}{4} \) which is \( 3.25 \) (since \( 13 \div 4 = 3.25 \)), which is located between \( 3 \) and \( 4 \).
### Conclusion
From the positions on the number line:
- \( 1.5 \) or \( \frac{6}{4} \) is to the left of \( \frac{13}{4} \) or \( 3.25 \).
Thus, \( \frac{13}{4} > 1.5 \).
To summarize: on a horizontal number line, \( 1.5 \) is to the left of \( \frac{13}{4} \), illustrating that \( \frac{13}{4} \) is greater than \( 1.5 \).
### Step 1: Convert to a Common Format
Since we are comparing two numbers, it's helpful to express both numbers in the same format. We can convert \( 1.5 \) into a fraction:
\[
1.5 = \frac{15}{10} = \frac{3}{2}
\]
However, to keep it simple, let’s convert \( 1.5 \) back into an improper fraction with a common denominator with \( \frac{13}{4} \).
### Step 2: Get a Common Denominator
The fraction \( \frac{13}{4} \) already has a denominator of 4. We can express \( 1.5 \) using the same denominator:
1. Convert \( 1.5 \) into a fraction with 4 as the denominator:
\[
1.5 = \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4}
\]
### Step 3: Compare the Two Fractions
Now we can compare the two fractions:
- \( \frac{13}{4} \)
- \( \frac{6}{4} \)
To compare:
- \( \frac{13}{4} \) is greater than \( \frac{6}{4} \) because the numerator (13) is greater than 6 while the denominators are the same.
### Step 4: Plot on a Number Line
Now we can plot these fractions on a horizontal number line:
1. Draw a horizontal line.
2. Mark points for \( 0 \), \( 1 \), \( 2 \), \( 3 \), and \( 4 \) (you could extend the line further, but those are key points).
3. Plot \( \frac{6}{4} \) (which is equivalent to \( 1.5 \)) somewhere between \( 1 \) and \( 2 \).
4. Plot \( \frac{13}{4} \) which is \( 3.25 \) (since \( 13 \div 4 = 3.25 \)), which is located between \( 3 \) and \( 4 \).
### Conclusion
From the positions on the number line:
- \( 1.5 \) or \( \frac{6}{4} \) is to the left of \( \frac{13}{4} \) or \( 3.25 \).
Thus, \( \frac{13}{4} > 1.5 \).
To summarize: on a horizontal number line, \( 1.5 \) is to the left of \( \frac{13}{4} \), illustrating that \( \frac{13}{4} \) is greater than \( 1.5 \).