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 compare the numbers \( \frac{13}{4} \) and \( 1.5 \) using a horizontal number line, you can follow these steps:
1. **Convert the Fractions**: First, convert \( \frac{13}{4} \) to a decimal to make it easier to compare with \( 1.5 \).
\[
\frac{13}{4} = 3.25
\]
Now we have two numbers to compare: \( 3.25 \) and \( 1.5 \).
2. **Draw the Number Line**: Draw a horizontal line and label it with a range of numbers that will comfortably include both \( 1.5 \) and \( 3.25 \). You might choose to label whole numbers and some fractions/decimals in between (for example, from 0 to 4).
3. **Mark the Numbers**: Once the number line is drawn, locate where \( 1.5 \) and \( 3.25 \) would be placed:
- For \( 1.5 \), find the point between \( 1 \) and \( 2 \) (exactly halfway between them).
- For \( 3.25 \), find the point between \( 3 \) and \( 4 \). Since \( 3.25 \) is one quarter of the way between \( 3 \) and \( 4 \), you can mark it accordingly.
4. **Compare the Positions**: Once both numbers are marked on the number line, look at their positions. Since \( 1.5 \) is to the left of \( 3.25 \), it means that:
\[
1.5 < \frac{13}{4} \quad (\text{or } 1.5 < 3.25)
\]
5. **Conclude the Comparison**: From the placement of the two numbers on the number line, you can conclude that \( \frac{13}{4} \) is greater than \( 1.5 \).
In summary, by converting \( \frac{13}{4} \) to a decimal, placing both numbers on a number line, and observing their positions, you can easily compare the two numbers.
1. **Convert the Fractions**: First, convert \( \frac{13}{4} \) to a decimal to make it easier to compare with \( 1.5 \).
\[
\frac{13}{4} = 3.25
\]
Now we have two numbers to compare: \( 3.25 \) and \( 1.5 \).
2. **Draw the Number Line**: Draw a horizontal line and label it with a range of numbers that will comfortably include both \( 1.5 \) and \( 3.25 \). You might choose to label whole numbers and some fractions/decimals in between (for example, from 0 to 4).
3. **Mark the Numbers**: Once the number line is drawn, locate where \( 1.5 \) and \( 3.25 \) would be placed:
- For \( 1.5 \), find the point between \( 1 \) and \( 2 \) (exactly halfway between them).
- For \( 3.25 \), find the point between \( 3 \) and \( 4 \). Since \( 3.25 \) is one quarter of the way between \( 3 \) and \( 4 \), you can mark it accordingly.
4. **Compare the Positions**: Once both numbers are marked on the number line, look at their positions. Since \( 1.5 \) is to the left of \( 3.25 \), it means that:
\[
1.5 < \frac{13}{4} \quad (\text{or } 1.5 < 3.25)
\]
5. **Conclude the Comparison**: From the placement of the two numbers on the number line, you can conclude that \( \frac{13}{4} \) is greater than \( 1.5 \).
In summary, by converting \( \frac{13}{4} \) to a decimal, placing both numbers on a number line, and observing their positions, you can easily compare the two numbers.