
Express the following as a fraction and simplify:
(a)
(b)
(c)
(d)
(e)
(f)
Answer
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Hint: Here, we need to express the given decimals as a fraction in the simplest form. We will write the decimals as a fraction, and then simplify it by dividing the numerator and denominator by the same number until they become co-prime. A fraction is in the simplest form if and are co-prime.
Complete step-by-step answer:
(a)
First, we will write the given decimal as a fraction.
Rewriting as a fraction, we get
Now, we will write in the simplest form.
A fraction is in the simplest form if and are co-prime.
We will divide the numerator and denominator by the same number till they become co-prime.
We know that a number with 0 or 5 in the unit’s place is divisible by 5.
Therefore, 275 and 100 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 55 and 20 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 11 and 4 do not have any common factor, 11 and 4 are co-prime numbers.
Therefore, we have expressed as a fraction in simplest form as .
(b)
Rewriting as a fraction, we get
Now, we will write in the simplest form.
We can observe that 3625 and 1000 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 725 and 200 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 145 and 40 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 29 and 8 do not have any common factor, 29 and 8 are co-prime numbers.
Therefore, we have expressed as a fraction in simplest form as .
(c)
Rewriting as a fraction, we get
Now, we will write in the simplest form.
We can observe that 125 and 100 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 25 and 20 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 5 and 4 do not have any common factor, 5 and 4 are co-prime numbers.
Therefore, we have expressed as a fraction in simplest form as .
(d)
Rewriting as a fraction, we get
Now, we will write in the simplest form.
We can observe that 65 and 10 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 13 and 2 do not have any common factor, 13 and 2 are co-prime numbers.
Therefore, we have expressed as a fraction in simplest form as .
(e)
Rewriting as a fraction, we get
Now, we will write in the simplest form.
We can observe that 4125 and 1000 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 825 and 200 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 165 and 40 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 33 and 8 do not have any common factor, 33 and 8 are co-prime numbers.
Therefore, we have expressed as a fraction in simplest form as .
(f)
Rewriting as a fraction, we get
Now, we will write in the simplest form.
We can observe that 35 and 10 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 7 and 2 do not have any common factor, 7 and 2 are co-prime numbers.
Therefore, we have expressed as a fraction in simplest form as .
Note: We used the term fractions and co-prime numbers in the solution. A fraction is a number which represents a part of a group. It is written as , where is called the numerator and is called the denominator. The group is divided into equal parts.
Two numbers are called co-prime numbers if they do not share a common factor other than 1. For example, the factors of 49 are 1, 7, and 49. The factors of 20 are 1, 2, 4, 5, 10, 20. We can observe that 49 and 20 are co-prime since they have no common factor other than 1.
Complete step-by-step answer:
(a)
First, we will write the given decimal as a fraction.
Rewriting
Now, we will write
A fraction
We will divide the numerator and denominator by the same number till they become co-prime.
We know that a number with 0 or 5 in the unit’s place is divisible by 5.
Therefore, 275 and 100 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 55 and 20 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 11 and 4 do not have any common factor, 11 and 4 are co-prime numbers.
Therefore, we have expressed
(b)
Rewriting
Now, we will write
We can observe that 3625 and 1000 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 725 and 200 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 145 and 40 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 29 and 8 do not have any common factor, 29 and 8 are co-prime numbers.
Therefore, we have expressed
(c)
Rewriting
Now, we will write
We can observe that 125 and 100 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 25 and 20 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 5 and 4 do not have any common factor, 5 and 4 are co-prime numbers.
Therefore, we have expressed
(d)
Rewriting
Now, we will write
We can observe that 65 and 10 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 13 and 2 do not have any common factor, 13 and 2 are co-prime numbers.
Therefore, we have expressed
(e)
Rewriting
Now, we will write
We can observe that 4125 and 1000 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 825 and 200 are divisible by 5.
Dividing the numerator and denominator by 5, we get
The numbers 165 and 40 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 33 and 8 do not have any common factor, 33 and 8 are co-prime numbers.
Therefore, we have expressed
(f)
Rewriting
Now, we will write
We can observe that 35 and 10 are divisible by 5.
Dividing the numerator and denominator by 5, we get
Since 7 and 2 do not have any common factor, 7 and 2 are co-prime numbers.
Therefore, we have expressed
Note: We used the term fractions and co-prime numbers in the solution. A fraction is a number which represents a part of a group. It is written as
Two numbers are called co-prime numbers if they do not share a common factor other than 1. For example, the factors of 49 are 1, 7, and 49. The factors of 20 are 1, 2, 4, 5, 10, 20. We can observe that 49 and 20 are co-prime since they have no common factor other than 1.
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