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# i need step-by-step instructions

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(4/5) - 1/6

Aug 14, 2017

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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. $$\frac{24}{30}$$

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. $$\frac{5}{30}$$

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, $$\frac{4}{5}-\frac{1}{6}=\frac{19}{30}$$

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Aug 14, 2017