Question

6) Convert each fraction to its equivalent using the least common denominator. 1 3 1 4

Answer 1

The fractions are given as,

`(1)/(3)\text{ and }(1)/(4)`

The denominators of the fractions are 3 and 4.

The lowest common denominator is the lowest common multiple of the denominators,

`\text{LCD}=\text{LCM}(3,4)`

Since the numbers 3 and 4 have no common factors, their LCM will be equal to the product of the numbers,

`\text{LCM}(3,4)=3\cdot4=12`

Now, the purpose is to make the denominators of both the fractions as 12.

For this, we use the property that the fraction remains same if its numerator and denominator are multiplied by the same number,

`(a)/(b)=(a\cdot k)/(b\cdot k)`

Apply the property to the first fraction and make its denominator as 12,

`(1)/(3)=(1\cdot4)/(3\cdot4)=(4)/(12)`

Apply the property to the second fraction and make its denominator as 12,

`(1)/(4)=(1\cdot3)/(4\cdot3)=(3)/(12)`

Thus, the equivalent fraction of 1/3 and 1/4 are 4/12 and 3/12, respectively.

Therefore, options (e) and option (c), respectively, are correct choices.