"+n/-n" Fraction Shortcut
Posted: Sun Aug 12, 2012 9:12 pmI don't have a good title for the shortcut, and the question on how to do the problems in this form come up often, so I just called it the "+n/-n" trick.
The problem is the subtraction of two fractions of the form [unparseable or potentially dangerous latex formula].
The method to getting the answer is a bit tricky. First, I want to make sure that I have explained how to recognize these problems. Here are some examples:
[unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula] here.
[unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula].
The rules to follow to get the solution follow:
First, check the sign of c in the numerator (assume c is positive. Only look at the [unparseable or potentially dangerous latex formula] sign.) If it's positive, the answer will be negative. It it's negative, the answer will be positive. Minus sign --> positive, plus sign --> negative.
Next, compare the signs of c in the numerator and denominator. If they are the same, find [unparseable or potentially dangerous latex formula]. If they are different, find [unparseable or potentially dangerous latex formula].
Next, find c. Multiply the answer found in the second step by c, and this will be the numerator. The denominator of the answer will be the product of the denominators of the previous two numbers. Make sure to include the sign found in the first step.
Finally, SIMPLIFY IF NECESSARY!
Ok, that might be hard to follow. Make sure you practice this trick! It becomes second nature after a while. Examples follow:
[unparseable or potentially dangerous latex formula]
A numerator has a minus sign, so the answer is positive. Since the signs differ, the numerator will use [unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula], so the numerator is still 5. The denominator is the product of the original denominators, so the final answer is [unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula]
The numerator has a plus sign, so the answer is negative. Since the signs differ, the numerator will use [unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula], so the numerator is still 11. Therefore the final answer is [unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula]
The numerator has a minus sign, so the answer is positive. Since the signs are the same, the numerator will use [unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula], so the numerator is [unparseable or potentially dangerous latex formula]. The denominator is the product of the original denominators. However, the result must be simplified in order to obtain the correct answer. [unparseable or potentially dangerous latex formula].
Hopefully this has been helpful. If all else fails, just cross multiply. The above were easy to cross multiply, but sometimes cross multiplying is very tough to do. This is a shortcut worth memorizing!
The problem is the subtraction of two fractions of the form [unparseable or potentially dangerous latex formula].
The method to getting the answer is a bit tricky. First, I want to make sure that I have explained how to recognize these problems. Here are some examples:
[unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula] here.
[unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula].
The rules to follow to get the solution follow:
First, check the sign of c in the numerator (assume c is positive. Only look at the [unparseable or potentially dangerous latex formula] sign.) If it's positive, the answer will be negative. It it's negative, the answer will be positive. Minus sign --> positive, plus sign --> negative.
Next, compare the signs of c in the numerator and denominator. If they are the same, find [unparseable or potentially dangerous latex formula]. If they are different, find [unparseable or potentially dangerous latex formula].
Next, find c. Multiply the answer found in the second step by c, and this will be the numerator. The denominator of the answer will be the product of the denominators of the previous two numbers. Make sure to include the sign found in the first step.
Finally, SIMPLIFY IF NECESSARY!
Ok, that might be hard to follow. Make sure you practice this trick! It becomes second nature after a while. Examples follow:
[unparseable or potentially dangerous latex formula]
A numerator has a minus sign, so the answer is positive. Since the signs differ, the numerator will use [unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula], so the numerator is still 5. The denominator is the product of the original denominators, so the final answer is [unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula]
The numerator has a plus sign, so the answer is negative. Since the signs differ, the numerator will use [unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula], so the numerator is still 11. Therefore the final answer is [unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula]
The numerator has a minus sign, so the answer is positive. Since the signs are the same, the numerator will use [unparseable or potentially dangerous latex formula]. [unparseable or potentially dangerous latex formula], so the numerator is [unparseable or potentially dangerous latex formula]. The denominator is the product of the original denominators. However, the result must be simplified in order to obtain the correct answer. [unparseable or potentially dangerous latex formula].
Hopefully this has been helpful. If all else fails, just cross multiply. The above were easy to cross multiply, but sometimes cross multiplying is very tough to do. This is a shortcut worth memorizing!