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## Main Question or Discussion Point

What is the easiest method for adding and subtracting rational numbers

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What is the easiest method for adding and subtracting rational numbers

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Mark44

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You need to be more specific. Do you mean rational numbers represented as fractions, like ##\frac{1}{2} + \frac{3}{5}## or rational numbers represented as decimal fractions, like .5 + .6?What is the easiest method for adding and subtracting rational numbers

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represented as fractions

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1What is the easiest method for adding and subtracting rational numbers

2. Add/Subtract the numerators (the top numbers) and put the answer over the common denominator you've found

And if needed,

3. Simplify the fraction by dividing both top and bottom by the same amount, to keep the value of the fraction the same

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##\frac{1}{2} + \frac{3}{7}##

Well, what is the smallest number that is a multiple of both 2 and 7? It's 14. So now, how do we write the original fractions with denominators of 14? Well, we multiply 2 by 7 to get 14, so we do the same to the numberator, 1. Likewise, we multiply 7 by 2 to get 14, so we multiply 3 by 2 to get 6. So we may write

##\frac{1}{2} + \frac{3}{7} = \frac{7}{14} + \frac{6}{14} = \frac{13}{14}##

Which doesn't reduce. So, very roughly speaking,

##\frac{a}{bc} + \frac{d}{ef} = \frac{(aef)+(bcd)}{bcef}##

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Mark44

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To elaborate on what AMenendez is saying, we are multiplying each fraction by 1 in some form so as to get the denominator we want.So, the standard way of adding / subtracting numbers is to first identify a ``least common denominator". So, say I had:

##\frac{1}{2} + \frac{3}{7}##

Well, what is the smallest number that is a multiple of both 2 and 7? It's 14. So now, how do we write the original fractions with denominators of 14? Well, we multiply 2 by 7 to get 14, so we do the same to the numberator, 1. Likewise, we multiply 7 by 2 to get 14, so we multiply 3 by 2 to get 6. So we may write

##\frac{1}{2} + \frac{3}{7} = \frac{7}{14} + \frac{6}{14} = \frac{13}{14}##

##\frac{1}{2} + \frac{3}{7} = \frac{1}{2} \cdot \frac{7}{7} + \frac{3}{7} \cdot \frac{2}{2} = \frac{7}{14} + \frac{6}{14} = \frac{13}{14}##

You can always multiply by 1 without changing the underlying value of an expression. Once the denominators are the same, you just add the numerators using that common denominator.

AMenendez said:Which doesn't reduce. So, very roughly speaking,

##\frac{a}{bc} + \frac{d}{ef} = \frac{(aef)+(bcd)}{bcef}##

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