Sure! Let's solve this problem step-by-step.
We are asked to find the multiplication of a non-zero rational number and its reciprocal.
1. Understanding the reciprocal:
- The reciprocal of a number [tex]\(a\)[/tex] (where [tex]\(a \neq 0\)[/tex]) is [tex]\( \frac{1}{a} \)[/tex].
2. Choose a non-zero rational number:
- Let's consider a non-zero rational number. For instance, let this number be [tex]\( 5 \)[/tex].
3. Find the reciprocal:
- The reciprocal of [tex]\( 5 \)[/tex] is [tex]\( \frac{1}{5} \)[/tex].
4. Multiply the number by its reciprocal:
- Now, we multiply [tex]\( 5 \)[/tex] by its reciprocal [tex]\( \frac{1}{5} \)[/tex]:
[tex]\[
5 \times \frac{1}{5}
\][/tex]
5. Perform the multiplication:
- When you multiply [tex]\( 5 \)[/tex] by [tex]\( \frac{1}{5} \)[/tex], you get:
[tex]\[
5 \times \frac{1}{5} = 1
\][/tex]
Hence, the multiplication of a non-zero rational number and its reciprocal is [tex]\( 1 \)[/tex].
So, the final answer is:
1
