Answer :
Certainly! Let’s determine which point on the number line could represent [tex]\( -2 \frac{1}{4} \)[/tex].
### Step-by-step Solution:
#### Step 1: Understand the Mixed Fraction
The given number is [tex]\( -2 \frac{1}{4} \)[/tex]. A mixed fraction consists of a whole number and a fractional part. In this case:
- The whole number part is [tex]\(-2\)[/tex].
- The fractional part is [tex]\( \frac{1}{4} \)[/tex].
#### Step 2: Convert the Mixed Fraction to an Improper Fraction
To understand it better on the number line, we can first convert [tex]\( -2 \frac{1}{4} \)[/tex] to a decimal.
#### Step 3: Convert the Fraction to Decimal
The fractional part [tex]\( \frac{1}{4} \)[/tex] can be converted to a decimal as follows:
[tex]\[ \frac{1}{4} = 0.25 \][/tex]
#### Step 4: Combine the Whole Number and the Decimal Part
Since the number is negative, combining the whole number [tex]\(-2\)[/tex] with the decimal part [tex]\(0.25\)[/tex] gives:
[tex]\[ -2 \frac{1}{4} = -2.25 \][/tex]
#### Step 5: Locate [tex]\(-2.25\)[/tex] on the Number Line
To locate [tex]\(-2.25\)[/tex] on the number line:
- We start at 0 and move left to [tex]\(-2\)[/tex].
- Then, we move an additional [tex]\(0.25\)[/tex] units to the left to reach [tex]\(-2.25\)[/tex].
So, the point on the number line that represents [tex]\( -2 \frac{1}{4} \)[/tex] is closest to [tex]\(-2.25\)[/tex].
### Conclusion
When looking at the points labeled on a number line, the point closest to [tex]\(-2.25\)[/tex] would be the one representing [tex]\( -2 \frac{1}{4} \)[/tex].
### Step-by-step Solution:
#### Step 1: Understand the Mixed Fraction
The given number is [tex]\( -2 \frac{1}{4} \)[/tex]. A mixed fraction consists of a whole number and a fractional part. In this case:
- The whole number part is [tex]\(-2\)[/tex].
- The fractional part is [tex]\( \frac{1}{4} \)[/tex].
#### Step 2: Convert the Mixed Fraction to an Improper Fraction
To understand it better on the number line, we can first convert [tex]\( -2 \frac{1}{4} \)[/tex] to a decimal.
#### Step 3: Convert the Fraction to Decimal
The fractional part [tex]\( \frac{1}{4} \)[/tex] can be converted to a decimal as follows:
[tex]\[ \frac{1}{4} = 0.25 \][/tex]
#### Step 4: Combine the Whole Number and the Decimal Part
Since the number is negative, combining the whole number [tex]\(-2\)[/tex] with the decimal part [tex]\(0.25\)[/tex] gives:
[tex]\[ -2 \frac{1}{4} = -2.25 \][/tex]
#### Step 5: Locate [tex]\(-2.25\)[/tex] on the Number Line
To locate [tex]\(-2.25\)[/tex] on the number line:
- We start at 0 and move left to [tex]\(-2\)[/tex].
- Then, we move an additional [tex]\(0.25\)[/tex] units to the left to reach [tex]\(-2.25\)[/tex].
So, the point on the number line that represents [tex]\( -2 \frac{1}{4} \)[/tex] is closest to [tex]\(-2.25\)[/tex].
### Conclusion
When looking at the points labeled on a number line, the point closest to [tex]\(-2.25\)[/tex] would be the one representing [tex]\( -2 \frac{1}{4} \)[/tex].
