Answer: The reciprocal of the given number is [tex]\frac{5}{16}[/tex]
Step-by-step explanation:
To write the reciprocal of the given number, we first simplify the given number.
As, it is a mixed fraction, the simplification of this occurs:
[tex]a\frac{b}{c}=\frac{(a\times c)+b}{c}[/tex]
So, simplifying the given mixed fraction, [tex]3\frac{1}{5}[/tex], we get:
[tex]3\frac{1}{5}=\frac{(3\times 5)+1}{5}=\frac{16}{5}[/tex]
To write the reciprocal, we exchange the positions of numerator and denominator, we get:
[tex]\frac{16}{5}=\frac{5}{16}[/tex]
Hence, the reciprocal of the given number is [tex]\frac{5}{16}[/tex]
The reciprocal of [tex]3\dfrac{1}{5}[/tex] is [tex]\boxed{\dfrac{5}{{16}}}[/tex].
Further Explanation:
The reciprocal of a number can be obtained by interchanging the denominator to numerator or we can simply say that flip the original number.
Mixed fraction can be defined as the sum of whole number and a fraction.
A number that is in the form of [tex]\dfrac{a}{b}[/tex] is called as fraction or proper fraction.
Given:
The number is [tex]3\dfrac{1}{5}[/tex].
Calculation:
Reciprocal of a mixed fraction [tex]x\dfrac{y}{z}[/tex] can be obtained as,
[tex]x\dfrac{y}{z} = \dfrac{{(z \times x) + y}}{z}[/tex]
Now to obtain the reciprocal of the number [tex]3\dfrac{1}{5}[/tex] change the mixed fraction into proper fraction than can be obtained as,
[tex]\begin{aligned}F &= 3\frac{1}{5}\\&= \frac{{\left( {5 \times 3} \right) + 1}}{5} \\&= \frac{{16}}{5} \\\end{aligned}[/tex]
The original fraction is [tex]\dfrac{{{\text{numerator}}}}{{{\text{denominator}}}}[/tex].
The reciprocal fraction is [tex]\dfrac{{{\text{denominator}}}}{{{\text{numerator}}}}[/tex].
Now flip the fraction [tex]\dfrac{{16}}{5}[/tex] to obtain the reciprocal of the number.
[tex]{\text{Reciprocal}} = \dfrac{5}{{16}}[/tex]
Hence, the reciprocal of [tex]3\dfrac{1}{5}[/tex] is [tex]\boxed{\frac{5}{{16}}}[/tex].
Learn more:
1. Learn more about addition of two numbers https://brainly.com/question/894273
2. Learn more about multiplication https://brainly.com/question/4892332
Answer details:
Grade: Junior School
Subject: Mathematics
Chapter: Number system
Keywords: number, reciprocal, [tex]3\dfrac{1}{5}[/tex], fraction, mixed fraction, proper fraction, denominator, numerator, flip, original number, reciprocal number, interchange, whole number.
