Question

What is a common denominator for \[\dfrac{5}{6}\] and \[\dfrac{2}{9}\]?

Answer 1

Hint: In this question, we have to find out the common denominator of the given fractions.
For finding that, we have to find the lowest common multiple of the two denominators. First, we need to do prime factorization and then multiplying all the primes taking the common terms only once. After that we will get the common denominator.


Complete step-by-step solution:
We need to find out the common denominator for the given fractions \[\dfrac{5}{6}\] and \[\dfrac{2}{9}\].
We have to find out the lowest common multiple of the two denominators.
First, we need to do prime factorization for the two numbers \[6and9\].
We get,
\[6 = 2 \times 3\].
\[9 = 3 \times 3\].
Now the common prime number is \[3\], for finding the L.C.M we will multiply the common term once and the other terms.
Thus, the L.C.M of\[6and9\]=\[2 \times 3 \times 3 = 18\]
Now we can convert the fractions like the following way:
\[\dfrac{5}{6} \times 1\]and \[\dfrac{2}{9} \times 1\]
\[\Rightarrow \dfrac{5}{6} \times \dfrac{3}{3}\] and \[\dfrac{2}{9} \times \dfrac{2}{2}\]
i.e., \[\dfrac{{15}}{{18}}\] and \[\dfrac{4}{{18}}\]
Hence, \[18\] is a common denominator for\[\dfrac{5}{6}\] and \[\dfrac{2}{9}\].

Note: Proper fraction:
A fraction is where the numerator (the top number) is less than the denominator (the bottom number). For example, \[\dfrac{1}{4},\dfrac{3}{5}\] etc.
Improper fraction:
A fraction is where the numerator (the top number) is greater than the denominator (the bottom number).
For example,\[\dfrac{7}{5},\dfrac{3}{2}\] etc.
Mixed fraction:
A whole number and a proper fraction is combined into one “Mixed fraction”.
For example,\[5\dfrac{1}{2},7\dfrac{1}{5}\] etc.
L.C.D.:
In Mathematics, the lowest common denominator or least common denominator (LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.