In general to be able to add or subtract fractions you need to have the same denominator so that you can add the numerators.
The easiest way to find the same denominator is to identify the lowest common denominator (LCD).
You can find the LCD by finding the prime factors of the denominators in question and multiplying them all together. If the denominators share a prime factor, only multiply it once.
Sometimes you can just eyeball the numbers to find the LCD, which might be faster.
For #W we need to find the LCD of 10 and 6, so prime factorize:
10 = 2 x 5 6 = 2 x 3
LCD = 2 x 5 x 3 = 30
The LCD is 30, so we need to change the fraction to reflect that. Remember, what you do to the denominator you need to do to the numerator as well. So:
-9/10 becomes -27/30 (both multiplied by 3) -1/6 becomes -5/30 (both multiples by 5)
Now you can easily add:
-27/30 + (-5/30) = -32/30
In summary: Step #1: find LCD (prime factor or eyeball) Step #2: multiply the numerator of each fraction by the factor needed to obtain the LCD in that denominator Step #3: add the fractions now that they have the LCD
Here’s the solution to #G:
-¾ + (-7/12)
Step #1:
4 = 2 x 2 12 = 2 x 2 x 3
LCD = 2 x 2 x 3 (count each unique prime factor once)
Step #2:
-¾ becomes -9/12 (both multiplied by 3) -7/12 stays the same (it already has the LCD)
Step #3:
-9/12 + (-7/12) = -16/12
Let me know if you have any questions. Try to work though the others!
The explanation for how to solve all of them is shown through the example on the paper. I solved W, the first one, to show you how to solve all of the rest of the problems. Let me know if you have any questions about the work! Hope this helps :)
