Answer
385.5k+ views
Hint: To solve this question, first we will discuss the simplest form and the steps to convert in simplest form. And then solve the question by taking the common denominator as their L.C.M. And after calculation, we will get our final answer.
Complete step by step solution:
Before solving the given question, the first question that arises here is what we mean by simplest form. So, when the numerator and denominator can no longer be reduced to any smaller number separately, we get the fraction in its simplest form.
And the steps for finding the simplest form:
$ * $ Search for common factors in the numerator and denominator.
$ * $ Check whether one of the numbers in the fraction is a prime number.
$ * $ Divide by a fraction equivalent to 1. For eg.. $\dfrac{2}{2}$ , $\dfrac{3}{3}$ , $\dfrac{{10}}{{10}}$ etc..
Now, we will solve the given expression in the simplest form:
Given two fractions with equal denominators simply keep the same denominator and add the numerators to get the sum.
$\dfrac{4}{3} + \dfrac{4}{3} = \dfrac{{4 + 4}}{3} = \dfrac{8}{3}$
To convert to a mixed fraction, note that:
$\dfrac{8}{3} = \dfrac{{6 + 2}}{3} = \dfrac{6}{3} + \dfrac{2}{3} = 2 + \dfrac{2}{3}$ or as written: $2\dfrac{2}{3}$
We can also write $\dfrac{8}{3}$ as $\dfrac{3}{3} + \dfrac{3}{3} + \dfrac{2}{3}$ and $\dfrac{3}{3} = 1$
So, $1 + 1 + \dfrac{2}{3} = 2\dfrac{2}{3}$
Hence, the simplest form of $\dfrac{4}{3} + \dfrac{4}{3}$ is $\dfrac{8}{3}$ or $2\dfrac{2}{3}$.
Note:
If the denominator is different, then we cannot directly pick the denominator as the L.C.M. Then we should conclude the L.C.M first and then match the multiple with respect to the numerators.
Complete step by step solution:
Before solving the given question, the first question that arises here is what we mean by simplest form. So, when the numerator and denominator can no longer be reduced to any smaller number separately, we get the fraction in its simplest form.
And the steps for finding the simplest form:
$ * $ Search for common factors in the numerator and denominator.
$ * $ Check whether one of the numbers in the fraction is a prime number.
$ * $ Divide by a fraction equivalent to 1. For eg.. $\dfrac{2}{2}$ , $\dfrac{3}{3}$ , $\dfrac{{10}}{{10}}$ etc..
Now, we will solve the given expression in the simplest form:
Given two fractions with equal denominators simply keep the same denominator and add the numerators to get the sum.
$\dfrac{4}{3} + \dfrac{4}{3} = \dfrac{{4 + 4}}{3} = \dfrac{8}{3}$
To convert to a mixed fraction, note that:
$\dfrac{8}{3} = \dfrac{{6 + 2}}{3} = \dfrac{6}{3} + \dfrac{2}{3} = 2 + \dfrac{2}{3}$ or as written: $2\dfrac{2}{3}$
We can also write $\dfrac{8}{3}$ as $\dfrac{3}{3} + \dfrac{3}{3} + \dfrac{2}{3}$ and $\dfrac{3}{3} = 1$
So, $1 + 1 + \dfrac{2}{3} = 2\dfrac{2}{3}$
Hence, the simplest form of $\dfrac{4}{3} + \dfrac{4}{3}$ is $\dfrac{8}{3}$ or $2\dfrac{2}{3}$.
Note:
If the denominator is different, then we cannot directly pick the denominator as the L.C.M. Then we should conclude the L.C.M first and then match the multiple with respect to the numerators.
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)