To solve the problem, we need to compare the given numbers and arrange them in order from greatest to least. Let's break it down step by step.
Step 1: Identify and convert all numbers to a comparable form
The numbers given are:
- $ -\frac{19}{2} $
- $ -3\frac{1}{4} $
- $ -1.2 $
- $ \frac{38}{6} $
- $ 7 $
#### Convert each number:
1.
$ -\frac{19}{2} $:
\[
-\frac{19}{2} = -9.5
\]
2.
$ -3\frac{1}{4} $:
\[
-3\frac{1}{4} = -3.25
\]
3.
$ -1.2 $:
\[
-1.2 \text{ (already in decimal form)}
\]
4.
$ \frac{38}{6} $:
\[
\frac{38}{6} = 6.333\ldots \approx 6.33
\]
5.
$ 7 $:
\[
7 \text{ (already in integer form)}
\]
Step 2: Compare the numbers
Now, we have the following numbers in decimal form:
- $ -9.5 $
- $ -3.25 $
- $ -1.2 $
- $ 6.33 $
- $ 7 $
Step 3: Arrange the numbers from greatest to least
- The greatest number is $ 7 $.
- The next greatest is $ 6.33 $.
- Then comes $ -1.2 $.
- Next is $ -3.25 $.
- The least is $ -9.5 $.
So, the order from greatest to least is:
\[
7, \, 6.33, \, -1.2, \, -3.25, \, -9.5
\]
Step 4: Match the order with the given options
Now, let's match this order with the provided options:
-
Option F: $ -\frac{19}{2}, \, -3\frac{1}{4}, \, -1.2, \, \frac{38}{6}, \, 7 $
\[
-9.5, \, -3.25, \, -1.2, \, 6.33, \, 7
\]
This is not in order from greatest to least.
-
Option G: $ 7, \, \frac{38}{6}, \, -\frac{19}{2}, \, -3\frac{1}{4}, \, -1.2 $
\[
7, \, 6.33, \, -9.5, \, -3.25, \, -1.2
\]
This is not in order from greatest to least.
-
Option H: $ -\frac{19}{2}, \, 7, \, \frac{38}{6}, \, -3\frac{1}{4}, \, -1.2 $
\[
-9.5, \, 7, \, 6.33, \, -3.25, \, -1.2
\]
This is not in order from greatest to least.
-
Option J: $ 7, \, \frac{38}{6}, \, -1.2, \, -3\frac{1}{4}, \, -\frac{19}{2} $
\[
7, \, 6.33, \, -1.2, \, -3.25, \, -9.5
\]
This is in order from greatest to least.
Final Answer:
\[
\boxed{J}
\]
Parent Tip: Review the logic above to help your child master the concept of 6th grade rational numbers worksheet.
