Question

How do you simplify \[\dfrac{4}{{11}} + \dfrac{6}{{11}}\]?

Answer 1

Hint: Fractions are a big part of our daily life and the mathematical world, so we must understand how to perform mathematical operations on two different fractions. In the given question, we have to add the two given fractions. The fractions having the same denominator can be added easily but when the denominators are different, then we first find the LCM of the terms in the denominator and then add the fractions. Using this approach, we can find out the correct answer.

Complete step by step solution:
We have, \[\dfrac{4}{{11}} + \dfrac{6}{{11}}\].
To solve this we need to find the LCM of 11 and 11. We use factors of the 11 and 11 to find the LCM.
The factors of 11 are 1 and 11. That is \[11 = 1 \times 11\]
The factors of 11 are 1 and 11. That is \[11 = 1 \times 11\].
We can see that the least common multiple of 11 and 11 is 11. That is \[ \Rightarrow 1 \times 11 = 11\]
Now we need to multiply 11 and divide by 11 to the given problem, we get:
\[\Rightarrow \dfrac{{\left( {\dfrac{4}{{11}} + \dfrac{6}{{11}}} \right) \times 11}}{{11}}\]
Now multiplying 11 for each fraction in the numerator we get,
\[\Rightarrow \dfrac{{\dfrac{4}{{11}} \times 11 + \dfrac{6}{{11}} \times 11}}{{11}}\]
Simplifying on the numerator we have,
\[\Rightarrow \dfrac{{4 + 6}}{{11}}\]
\[\Rightarrow \dfrac{{10}}{{11}}\].

Thus we have \[ \Rightarrow \dfrac{4}{{11}} + \dfrac{6}{{11}} = \dfrac{{10}}{{11}}\]

Note: If we have two primes and we need to find the LCM of this. Then we need to multiply these numbers, which gives us the LCM. That is The LCM of two or more prime numbers is equal to their product. We can also find the HCF of 11 and 11. Since we have the factors \[11 = 1 \times 11\] and \[11 = 1 \times 11\]. We can see that the highest common multiple (HCF) is 11.