Question

How do you simplify\[\dfrac{1}{4} - \dfrac{2}{3}\]?

Answer 1

Hint: We can solve this by taking the Least common multiple (L.C.M) method. and the other method is the decimal method. We choose the L.C.M method which is easy compared to the decimal method. The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.

Complete step-by-step answer:
Let’s see the L.C.M. method.
Given, \[\dfrac{1}{4} - \dfrac{2}{3}\]
Now to take the L.C.M of ‘4’ and ‘3’.
The multiples of 4 are \[4,8,12,16,20,24,..\]
The multiples of 3 are \[3,6,9,12,15,16,...\]
We can see that the least common multiple of ‘4’ and ‘3’ is ‘12’.
Now, \[ = \dfrac{1}{4} - \dfrac{2}{3}\]
Multiply and divide by 12 we get,
\[ \Rightarrow \dfrac{{\left( {\dfrac{1}{4} - \dfrac{2}{3}} \right) \times 12}}{{12}}\]
\[ \Rightarrow \dfrac{{\dfrac{1}{4} \times 12 - \dfrac{2}{3} \times 12}}{{12}}\]
Cancelling the terms we have,
\[ \Rightarrow \dfrac{{3 - (2 \times 4)}}{{12}}\]
\[ \Rightarrow \dfrac{{3 - 8}}{{12}}\]
(When we subtract smaller numbers with bigger numbers we get a negative number.)
\[ \Rightarrow \dfrac{{ - 5}}{{12}}\].
Now, we have \[ \Rightarrow \dfrac{1}{4} - \dfrac{2}{3} = \dfrac{{ - 5}}{{12}}\] is the required result.

Now let’s see the decimal method.
We know \[\dfrac{1}{4} = 0.25\] and \[\dfrac{2}{3} = 0.6666\].
\[ \Rightarrow \dfrac{1}{4} - \dfrac{2}{3}\]
Substituting we have,
\[ \Rightarrow 0.25 - 0.6666\]
\[ \Rightarrow - 0.4166\]
Which is the same as, \[ - 0.4166 = \dfrac{{ - 5}}{{12}}\].
\[ \Rightarrow \dfrac{1}{4} - \dfrac{2}{3} = \dfrac{{ - 5}}{{12}}\] is the required result.
So, the correct answer is “ \[ \dfrac{{ - 5}}{{12}}\]”.

Note: We can see that in both the cases we can see that the answer. We also know the highest common factor (H.C.F). H.C.F is the greatest common divisor. In the above problem the H.C.F of ‘4’ and ‘3’ is 1. Because the factors of 4 is \[4 = 4 \times 1\] and factors of 3 is \[3 = 3 \times 1\]. We can see that 1 is the highest common factor for 3 and 4. Be careful in the calculation part. Remember also know when we subtract smaller numbers with bigger numbers we get a negative number