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Sagot :
Certainly! Let's find the reciprocal of each given fraction step-by-step.
### Part (2): Reciprocal of [tex]\(\frac{1}{13}\)[/tex]
The reciprocal of a fraction is derived by interchanging the numerator and the denominator.
For [tex]\(\frac{1}{13}\)[/tex]:
- The numerator is 1.
- The denominator is 13.
To find the reciprocal:
[tex]\[ \text{Reciprocal of } \frac{1}{13} \text{ is } \frac{13}{1} = 13 \][/tex]
### Part (ii): Reciprocal of [tex]\(12 \frac{2}{5}\)[/tex]
First, we need to convert the mixed number [tex]\(12 \frac{2}{5}\)[/tex] into an improper fraction:
- [tex]\(12 \frac{2}{5}\)[/tex] means [tex]\(12 + \frac{2}{5}\)[/tex].
- The improper fraction form of [tex]\(12 \frac{2}{5}\)[/tex] is calculated as:
[tex]\[ 12 \times 5 + 2 = 60 + 2 = 62 \][/tex]
So, [tex]\(12 \frac{2}{5} = \frac{62}{5}\)[/tex].
Now, we find the reciprocal of [tex]\(\frac{62}{5}\)[/tex]:
To find the reciprocal:
[tex]\[ \text{Reciprocal of } \frac{62}{5} \text{ is } \frac{5}{62} \][/tex]
In decimal form:
[tex]\[ \frac{5}{62} \approx 0.08064516129032258 \][/tex]
### Part (iii): Reciprocal of 9
The number 9 can be written as a fraction:
[tex]\[ 9 = \frac{9}{1} \][/tex]
To find the reciprocal:
[tex]\[ \text{Reciprocal of } \frac{9}{1} \text{ is } \frac{1}{9} \][/tex]
In decimal form:
[tex]\[ \frac{1}{9} \approx 0.1111111111111111 \][/tex]
### Part (iv): Reciprocal of [tex]\(\frac{6}{7}\)[/tex]
For [tex]\(\frac{6}{7}\)[/tex]:
- The numerator is 6.
- The denominator is 7.
To find the reciprocal:
[tex]\[ \text{Reciprocal of } \frac{6}{7} \text{ is } \frac{7}{6} \][/tex]
In decimal form:
[tex]\[ \frac{7}{6} \approx 1.1666666666666667 \][/tex]
### Summary
- The reciprocal of [tex]\(\frac{1}{13}\)[/tex] is [tex]\(13.0\)[/tex].
- The reciprocal of [tex]\(12 \frac{2}{5}\)[/tex] is [tex]\(\approx 0.08064516129032258\)[/tex].
- The reciprocal of 9 is [tex]\(\approx 0.1111111111111111\)[/tex].
- The reciprocal of [tex]\(\frac{6}{7}\)[/tex] is [tex]\(\approx 1.1666666666666667\)[/tex].
I hope this helps you understand how to find the reciprocals of these fractions!
### Part (2): Reciprocal of [tex]\(\frac{1}{13}\)[/tex]
The reciprocal of a fraction is derived by interchanging the numerator and the denominator.
For [tex]\(\frac{1}{13}\)[/tex]:
- The numerator is 1.
- The denominator is 13.
To find the reciprocal:
[tex]\[ \text{Reciprocal of } \frac{1}{13} \text{ is } \frac{13}{1} = 13 \][/tex]
### Part (ii): Reciprocal of [tex]\(12 \frac{2}{5}\)[/tex]
First, we need to convert the mixed number [tex]\(12 \frac{2}{5}\)[/tex] into an improper fraction:
- [tex]\(12 \frac{2}{5}\)[/tex] means [tex]\(12 + \frac{2}{5}\)[/tex].
- The improper fraction form of [tex]\(12 \frac{2}{5}\)[/tex] is calculated as:
[tex]\[ 12 \times 5 + 2 = 60 + 2 = 62 \][/tex]
So, [tex]\(12 \frac{2}{5} = \frac{62}{5}\)[/tex].
Now, we find the reciprocal of [tex]\(\frac{62}{5}\)[/tex]:
To find the reciprocal:
[tex]\[ \text{Reciprocal of } \frac{62}{5} \text{ is } \frac{5}{62} \][/tex]
In decimal form:
[tex]\[ \frac{5}{62} \approx 0.08064516129032258 \][/tex]
### Part (iii): Reciprocal of 9
The number 9 can be written as a fraction:
[tex]\[ 9 = \frac{9}{1} \][/tex]
To find the reciprocal:
[tex]\[ \text{Reciprocal of } \frac{9}{1} \text{ is } \frac{1}{9} \][/tex]
In decimal form:
[tex]\[ \frac{1}{9} \approx 0.1111111111111111 \][/tex]
### Part (iv): Reciprocal of [tex]\(\frac{6}{7}\)[/tex]
For [tex]\(\frac{6}{7}\)[/tex]:
- The numerator is 6.
- The denominator is 7.
To find the reciprocal:
[tex]\[ \text{Reciprocal of } \frac{6}{7} \text{ is } \frac{7}{6} \][/tex]
In decimal form:
[tex]\[ \frac{7}{6} \approx 1.1666666666666667 \][/tex]
### Summary
- The reciprocal of [tex]\(\frac{1}{13}\)[/tex] is [tex]\(13.0\)[/tex].
- The reciprocal of [tex]\(12 \frac{2}{5}\)[/tex] is [tex]\(\approx 0.08064516129032258\)[/tex].
- The reciprocal of 9 is [tex]\(\approx 0.1111111111111111\)[/tex].
- The reciprocal of [tex]\(\frac{6}{7}\)[/tex] is [tex]\(\approx 1.1666666666666667\)[/tex].
I hope this helps you understand how to find the reciprocals of these fractions!
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