Question

How do you write \[\dfrac{4}{{12}}\] in simplest form?

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.

Formula Used:
We are going to use the relation between LCM, HCF and the product of two numbers.
\[LCM\left( {a,b} \right) \times HCF\left( {a,b} \right) = a \times b\]

Complete step-by-step answer:
The given fraction to be reduced into the simplest form is \[\dfrac{4}{{12}}\].
First, we are going to find the HCF of the two numbers (numerator \[\left( 4 \right)\] 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.
\[\begin{array}{l}2\left| \!{\overline {\,
 {4,12} \,}} \right. \\2\left| \!{\overline {\,
 {2,6} \,}} \right. \\3\left| \!{\overline {\,
 {1,3} \,}} \right. \\{\rm{ }}\left| \!{\overline {\,
 {1,1} \,}} \right. \end{array}\]
Hence, the LCM is \[2 \times 2 \times 3 = 12\]
Now, we divide the product of the numbers by their LCM to find their HCF,
\[HCF = \dfrac{{4 \times 12}}{{12}} = 4\]
Now, we divide the two numbers by their HCF,
\[4 \div 4 = 1\] and \[12 \div 4 = 3\]
Hence, in lowest terms, \[\dfrac{4}{{12}}\] is \[\dfrac{1}{3}\].

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: In the given question, we had to find the lowest term of the given fraction. To reduce a fraction into simplest form, it means that there should be no common factor in the numerator and the denominator. For doing that, we first found the LCM of the two numbers, then multiplied the numbers and then divided their product by the LCM. This gave us the HCF. Then we divided the both numbers (numerator and denominator) by the HCF.