Sure! Let's address each part of the question step-by-step.
### 6. Find the square of 32:
To find the square of a number, you multiply the number by itself.
[tex]\[
32^2 = 32 \times 32 = 1024
\][/tex]
So, the square of 32 is 1024.
### 7. Represent [tex]\(\frac{2}{7}\)[/tex] on the number line:
To represent [tex]\(\frac{2}{7}\)[/tex] on the number line, observe that it is a positive fraction slightly less than [tex]\(\frac{1}{3}\)[/tex]. On a number line, you divide the section between 0 and 1 into 7 equal parts. The fraction [tex]\(\frac{2}{7}\)[/tex] will be 2 parts out of those 7 parts. Numerically, [tex]\(\frac{2}{7}\)[/tex] approximates to:
[tex]\[
\frac{2}{7} \approx 0.2857
\][/tex]
So, [tex]\(\frac{2}{7}\)[/tex] would be placed slightly to the left of 0.3 on the number line.
### 8. Write Multiplicative inverse of 0:
The multiplicative inverse of a number [tex]\(a\)[/tex] is another number [tex]\(b\)[/tex] such that [tex]\(a \times b = 1\)[/tex].
For 0, there's no number that you can multiply by 0 that results in 1. Therefore,
The multiplicative inverse of 0 does not exist.
### 9. The product of a number and its reciprocal is:
A number's reciprocal is [tex]\( \frac{1}{a} \)[/tex]. When you multiply a number by its reciprocal, you get:
[tex]\[
a \times \left(\frac{1}{a}\right) = 1
\][/tex]
For instance, let's use the number 5 as an example. Its reciprocal is [tex]\(\frac{1}{5}\)[/tex]. Therefore,
[tex]\[
5 \times \left(\frac{1}{5}\right) = 1
\][/tex]
So, the product of a number and its reciprocal is 1.
### 10. Write in ascending and descending order:
Consider the fractions given:
[tex]\[
\frac{4}{5}, \frac{3}{7}, \frac{-1}{5}, \frac{2}{3}, \frac{5}{7}
\][/tex]
First, we convert these fractions into decimal form to easily compare them:
[tex]\[
\begin{align*}
\frac{4}{5} & = 0.8 \\
\frac{3}{7} & \approx 0.4286 \\
\frac{-1}{5} & = -0.2 \\
\frac{2}{3} & \approx 0.6667 \\
\frac{5}{7} & \approx 0.7143 \\
\end{align*}
\][/tex]
Ascending Order:
[tex]\[
\frac{-1}{5}, \frac{3}{7}, \frac{2}{3}, \frac{5}{7}, \frac{4}{5}
\][/tex]
In decimal form, this is:
[tex]\[
-0.2, 0.4286, 0.6667, 0.7143, 0.8
\][/tex]
Descending Order:
[tex]\[
\frac{4}{5}, \frac{5}{7}, \frac{2}{3}, \frac{3}{7}, \frac{-1}{5}
\][/tex]
In decimal form, this is:
[tex]\[
0.8, 0.7143, 0.6667, 0.4286, -0.2
\][/tex]
### Summary of Solutions:
1. The square of 32 is 1024.
2. [tex]\(\frac{2}{7}\)[/tex] on the number line is approximately 0.2857.
3. The multiplicative inverse of 0 does not exist.
4. The product of a number and its reciprocal is 1.
5. Ascending Order: [tex]\(-0.2, 0.4286, 0.6667, 0.7143, 0.8\)[/tex]
Descending Order: [tex]\(0.8, 0.7143, 0.6667, 0.4286, -0.2\)[/tex]
