Algebra homework help. Can you explain how to work it and then the answer

1.) 1/4 - 12
2.) -18 + (-12)
3.) x + 29 for x = -15
4.) -3/4 - (-1/4)

1.) 1/4 - 12
We need the fractions to have a common denominator, so we convert 12/1 to 48/4
That leaves us with 1/4 - 48/4
1/4 -48/4 = -47/4

2) (-18) + (-12)
I usually approach these problems by factoring out -1 ( -18 + -12 ) = -1(18+12), but you may not be required to show much work here.
-1(18+12) = -30

3) x + 29 for x=-15
Here we just substitute -15 for x
x + 29 = -15 + 29 = 14

4) -3/4 - (-1/4)
Subtracting a negative is the same as adding a positive, so -3/4 - (-1/4) = -3/4 + 1/4 = -1/2
You could also solve this by factoring out the -1, such that -3/4 - (-1/4) = -1(3/4 - 1/4) = -1(1/2) = -1/2

for 1.) in order to combine fractions they need to have the same denominator (bottom number) the denominator of (1/4) is 4, and the bottom number of (12) is 1, so what you do is you multiply 4/4 times 12/1. 12 times 4 is 48, and 4 times 1 is 4. So now you have (1/4) - (48/4)

2.) -18 +(-12): so that is negative 18 plus negative 12. when you are 'adding' negatives, the minus always wins, so in actuality the problem is -18 minus 12, or you can think of it as 'adding' the two, where 18 plus 12 is 30, -18 -12 is going to be -30.

3.) x + 29 for x = -15 : x is just a variable, something that we know or don't know. In this instance x is given as -15. so just rewrite the equation as:

-15 + 29 which is the same as 29 - 15... easy peasy.

4.) (-3/4) -(-1/4) : here's something that is going to help you later..., when you see a minus sign in front of brackets, mentally put a negative one in front of it. so it would be like -(-1/4) is actually -1(-1/4)

and of course we know that when we multiply two negatives it becomes a positive, so the problem is actually:

-3/4 + 1/4, so then add a 1 to that -3 (= -2) and then you get your answer. (don't forget to plop a /4 under that -2!)