Question

Subtract the following fraction and reduce to the lowest term $\dfrac{7}{{15}}{\text{ from }}\dfrac{{13}}{{20}}$

Answer 1

Hint- In order to solve the problem, first start with the basic subtraction of fraction by taking LCM of the denominator, find the answer and finally convert it to lowest term by cancellation.

Complete Step-by-Step solution:
Given fractions are: $\dfrac{7}{{15}}{\text{ and }}\dfrac{{13}}{{20}}$
Let $a = \dfrac{7}{{15}}{\text{ and }}b = \dfrac{{13}}{{20}}$
Now let us subtract b from a by taking LCM of the denominator.
$
   \Rightarrow a - b \\
   \Rightarrow \dfrac{7}{{15}} - \dfrac{{13}}{{20}} \\
   \Rightarrow \dfrac{{28 - 39}}{{60}}{\text{ }}\left[ {\because {\text{LCM of 15,20 = 60}}} \right] \\
   \Rightarrow \dfrac{{ - 11}}{{60}} \\
 $
The numerator is -11 and the denominator is 60.
Since 11 is a prime number. So HCF between -11 and 60 is 1.
So, the answer is already in lowest terms.
Hence, the subtraction result for the problem is $\dfrac{{ - 11}}{{60}}$

Note- In order to find the fraction in lowest term the best way to find the HCF of the numbers in numerator and denominator and divide them by HCF. Do not find the fraction in lowest term before the subtraction as after subtraction, again you may need to convert the fraction in lowest term.