Question

Is the fraction \[\dfrac{5}{{12}}\] in its lowest term? If not, how do you simplify it?

Answer 1

Hint: In the given question, we have been given a fraction. We have to reduce the fraction in the simplest form. To reduce a fraction into simplest form, it means that there should be no common factor in the numerator and the denominator. To do that, we find the HCF of the two numbers (numerator and denominator). For finding the HCF, we use the relation between LCM, HCF and the product of two numbers.

Complete step by step solution:
The given fraction is \[\dfrac{5}{{12}}\].
Now, if it is in its lowest form, then its HCF is going to be \[1\].
First, we are going to find the HCF of the two numbers (numerator \[\left( 5 \right)\] and the denominator \[\left( {12} \right)\]), then we are going to divide the two numbers by the HCF.
To find the HCF, we calculate the LCM.
\[\begin{array}{l}2\left| \!{\overline {\,
 {5,12} \,}} \right. \\2\left| \!{\overline {\,
 {5,6} \,}} \right. \\3\left| \!{\overline {\,
 {5,3} \,}} \right. \\5\left| \!{\overline {\,
 {5,1} \,}} \right. \\{\rm{ }}\left| \!{\overline {\,
 {1,1} \,}} \right. \end{array}\]
Hence, the LCM is \[2 \times 2 \times 3 \times 5 = 60\]
Now, we divide the product of the numbers by their LCM to find their HCF,
\[HCF = \dfrac{{5 \times 12}}{{60}} = 1\]
Hence, the fraction is already in its lowest form.

Additional Information: HCF of two numbers is the largest number which divides both of the two numbers. It is called the Highest Common Factor. It is also written as GCD; Greatest Common Divisor. While, LCM of two numbers or the least common multiple is the smallest number which is divisible by the two numbers.

Note: When we are given a fraction which is to be converted to the lowest term, we find the HCF or the Highest Common Factor of the numerator and the denominator by applying the above used method. The possible point of error is when we find the LCM or when we apply the formula to calculate the HCF. We need to make sure that we are thorough with our calculations and cross-check them so that there is no possibility of a mistake and so that we get the correct answer.