Answer
385.8k+ views
Hint: We first try to describe the relation between the denominator and the numerator to find the simplified form. We use the G.C.D of the denominator and the numerator to divide both of them. We get the simplified form when the G.C.D is 1. We divide both sides of the equation $w=fd$ by $d$. That gives the value of $f$ in $w=fd$.
Complete step by step answer:
We need to solve for $f$ in $w=fd$. Here $w=fd$ has been expressed as the multiplication of $f$ and $d$. We divide both sides of the equation $w=fd$ with $d$.
So, \[\dfrac{w}{d}=\dfrac{fd}{d}\]. The right side of the equation becomes \[\dfrac{fd}{d}=f\]
This simplified part can be expressed as using their GCD.
Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.
This means we can’t eliminate any more common root from them other than 1.
For any fraction $\dfrac{p}{q}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number x then we need to divide the denominator and the numerator with x and get the simplified fraction form as $\dfrac{{}^{p}/{}_{x}}{{}^{q}/{}_{x}}$.
For our given fraction \[\dfrac{fd}{d}\], the G.C.D of the denominator and the numerator is $d$.
Now we divide both the denominator and the numerator with $d$ and get $\dfrac{{}^{fd}/{}_{d}}{{}^{d}/{}_{d}}=\dfrac{f}{1}=f$.
Therefore, the solution for $f$ in $w=fd$ is $\dfrac{w}{d}$.
Note:
The process is similar for both proper and improper fractions. In case of mixed fractions, we need to convert it into an improper fraction and then apply the case. Also, we can only apply the process on the proper fraction part of a mixed fraction.
Complete step by step answer:
We need to solve for $f$ in $w=fd$. Here $w=fd$ has been expressed as the multiplication of $f$ and $d$. We divide both sides of the equation $w=fd$ with $d$.
So, \[\dfrac{w}{d}=\dfrac{fd}{d}\]. The right side of the equation becomes \[\dfrac{fd}{d}=f\]
This simplified part can be expressed as using their GCD.
Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.
This means we can’t eliminate any more common root from them other than 1.
For any fraction $\dfrac{p}{q}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number x then we need to divide the denominator and the numerator with x and get the simplified fraction form as $\dfrac{{}^{p}/{}_{x}}{{}^{q}/{}_{x}}$.
For our given fraction \[\dfrac{fd}{d}\], the G.C.D of the denominator and the numerator is $d$.
Now we divide both the denominator and the numerator with $d$ and get $\dfrac{{}^{fd}/{}_{d}}{{}^{d}/{}_{d}}=\dfrac{f}{1}=f$.
Therefore, the solution for $f$ in $w=fd$ is $\dfrac{w}{d}$.
Note:
The process is similar for both proper and improper fractions. In case of mixed fractions, we need to convert it into an improper fraction and then apply the case. Also, we can only apply the process on the proper fraction part of a mixed fraction.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)