Question

Write equivalent fractions for 5/6,4/9 and 5/12 using the least common denominator

Answer 1

`\begin{gathered} (5)/(6)=(30)/(36) \\ (4)/(9)=(16)/(36) \\ (5)/(12)=(15)/(36) \end{gathered}`

Step-by-step explanation:

Given the below fractions;

`\begin{gathered} (5)/(6),(4)/(9),^\text{ and }(5)/(12) \\ \end{gathered}`

Let's go ahead and list the multiples of the denominators;

`\begin{gathered} Multiples\text{ of 6 are }6,12,18,24,30,36,... \\ Multiples\text{ of 9 are 9},18,27,36,45,... \\ Multiples\text{ of 12 are 12},24,36,48,60,... \end{gathered}`

We can see from the above that the least common multiple of 6, 9, and 12 is 36

So we can go ahead and express the given fractions to all have 36 as their denominator as seen below;

`\begin{gathered} (5)/(6)=(5*6)/(6*6)=(30)/(36) \\ (4)/(9)=(4*4)/(9*4)=(16)/(36) \\ (5)/(12)=(5*3)/(12*3)=(15)/(36) \end{gathered}`

So the equivalent fractions for 5/6, 4/9 and 5/12 using the least common denominator of 36 are 30/36, 16/36, and 15/36