Question

How do you simplify \[\dfrac{5}{6} + \dfrac{8}{9}\] ?

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 answer:
We have, \[\dfrac{5}{6} + \dfrac{8}{9}\] .
To solve this we need to find the LCM of 6 and 9. We use factors of the 6 and 9 to find the LCM.
The factors of 6 are 1, 2 and 3. That is \[6 = 1 \times 2 \times 3\]
The factors of 9 are 1, 3 and 3. That is \[9 = 1 \times 3 \times 3\] .
We can see that the least common multiple of 6 and 9 is 18. That is \[ \Rightarrow 1 \times 2 \times 3 \times 3 = 18\]
Now we need to multiply 18 and divide by 18 to the given problem, we get:
 \[ = \dfrac{{\left( {\dfrac{5}{6} + \dfrac{8}{9}} \right) \times 18}}{{18}}\]
Now multiplying 3 for each fraction in the numerator we get,
 \[ = \dfrac{{\dfrac{5}{6} \times 18 + \dfrac{8}{9} \times 18}}{{18}}\]
Simplifying on the numerator we have,
 \[ = \dfrac{{\left( {5 \times 3} \right) + \left( {8 \times 2} \right)}}{{18}}\]
 \[ = \dfrac{{15 + 16}}{{18}}\]
 \[ = \dfrac{{31}}{{18}}\] .
Thus we have \[ \Rightarrow \dfrac{5}{6} + \dfrac{8}{9} = \dfrac{{31}}{{18}}\]
So, the correct answer is “Option C”.

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 the 6 and 9. Since we have the factors \[6 = 1 \times 2 \times 3\] and \[9 = 1 \times 3 \times 3\] . We can see that the highest common multiple (HCF) is 3.