(4/5) - 1/6

 Aug 14, 2017

I am coming to help! You want to know how to evaluate the expression \(\frac{4}{5}-\frac{1}{6}\):



To subtract (or add) fractions, we have to create a common denominator. What does that mean? It means that the denominators of both fractions must be the same before we can actually do any subtraction. 4/5 and 1/6 are not fractions with common denominators, so we will have to manipulate the fraction such that both have a common denominator. 


To do this, we must figure out the LCM (lowest common multiple) of both denominators in this expression. Normally, you could use a process to figure out the lowest common denominator, but we can actually use a shortcut here. If you are trying to find the LCM of two numbers that is 1 unit away from each other on a number line, then simply multiply both numbers together. This means that the LCM of 5 and 6 is 5*6, or 30:


This is the denominator that we want both fractions to have. Let's manipulate  4/5 first:


\(\frac{4}{5}*\frac{6}{6}\) Notice that we are actually multiplying the fraction by 1, which does not change the actual value of the fraction.




Now, let's change the other fraction such that the denominator is 30:


\(\frac{1}{6}*\frac{5}{5}\) Just like above, I am making the denominator to 30.


Now, let's subtracting the 2 fractions! It should be much easier now!


\(\frac{24}{30}-\frac{5}{30}\) When subtracting fractions, only subtract the numerator, but keep the denominator.
\(\frac{19}{30}\) 19 and 30 are co-prime, so the fraction cannot be simplified anymore.


Therefore, \(\frac{4}{5}-\frac{1}{6}=\frac{19}{30}\)

 Aug 14, 2017

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