Sure, let's work out the reciprocal of the fraction [tex]\(\frac{7}{10}\)[/tex] step-by-step.
Step 1: Understand the concept of a reciprocal.
- The reciprocal of a fraction [tex]\(\frac{a}{b}\)[/tex] is simply [tex]\(\frac{b}{a}\)[/tex].
Step 2: Apply this concept to the given fraction.
- For the fraction [tex]\(\frac{7}{10}\)[/tex], the reciprocal would be [tex]\(\frac{10}{7}\)[/tex].
Step 3: Express the reciprocal as a decimal (if needed).
To convert the fraction [tex]\(\frac{10}{7}\)[/tex] into a decimal, perform the division [tex]\(10 \div 7\)[/tex]. The result of this division is approximately:
[tex]\[ \frac{10}{7} \approx 1.4285714285714286 \][/tex]
Therefore, the reciprocal of [tex]\(\frac{7}{10}\)[/tex] is approximately [tex]\(1.4285714285714286\)[/tex].
