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Two pieces of carpet $ 3\dfrac{1}{4} $ meters and $ 2\dfrac{3}{4} $ meters long are joined together. How long is the joined carpet?

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Last updated date: 23rd Jul 2024
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Answer
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Hint: Here in this question, we are given a word problem related to the sum of two fractions. The length of two portions of carpet are given to us in the problem in the form of fractions. The two portions of the carpet are joined and we are required to find the total length of the carpet.

Complete step-by-step answer:
The length of two pieces of carpet are given to us in the problem as: $ 3\dfrac{1}{4} $ meters and $ 2\dfrac{3}{4} $ meters.
Now, the two pieces of carpet are joined together. We have to find the total length of the carpet.
Here in this question, we have to add the fractions. As we know $ + $ sign indicates the addition. The numbers are in the form of a fraction. In fraction we have 3 types: proper fraction, improper fraction and mixed fraction.
In the fraction, if the numerator is less than the denominator then it is the proper fraction. The numerator is greater than the denominator then it is an improper fraction. The fraction is a combination of whole number and fraction then it is mixed fraction.
Here in this question, both the fractions are mixed fractions.
So, the total length of the carpet is $ 3\dfrac{1}{4} + 2\dfrac{3}{4} $ meters.
We can add the mixed fractions by adding the whole parts and fractions parts separately.
So, we get,
 $ \Rightarrow \left( {3 + 2} \right) + \left( {\dfrac{1}{4} + \dfrac{3}{4}} \right) $
The denominator of both the fractions is the same. So, we get,
 $ \Rightarrow \left( 5 \right) + \left( {\dfrac{4}{4}} \right) $
Cancelling the common factors in numerator and denominator, we get,
 $ \Rightarrow 5 + 1 $
Adding up the terms, we get,
 $ \Rightarrow 6 $
Therefore, we get the total length of the carpet by joining both the portions as $ 6m $ .
So, the correct answer is “6 m”.

Note: While adding the two fractions we need to check the values of the denominator, if both denominators are having the same value then we can add the numerators. Suppose if the fractions have different denominators, we have to take LCM for the denominators and we simplify for further.