Hi Connor! Your post title and your question suggests a couple different questions, so I tried to help the best I could. :) I hope this helps you!
The easiest way to remember the distributive property is that you distribute the number that is outside the parenthesis to each number inside the parenthesis. For example: Say you have a question like a(b+c) you will distribute a to each number inside the parenthesis. Therefore, you will have a(b+c)=ab+ac
For fractions, you must first find the common denominator. All this means is that you have to find two or more fractions that share the same denominator. Sometimes you may need to simplify them if they are not the same and find the least common denominator or multiply both parts of the fraction by the other.
Say you have 1/6+2/7
If we multiply 6 and 7, we will find that 42 is the common denominator for the fractions.
Now multiply both parts of each fraction by the denominator of the other. The easiest way to remember is to draw an X between the two fractions.
Then you will have (1×7)/(6×7)+(2×6)/(7×6)=7/42+12/42
Now the denominators are the same and we can add the numerators.
7+12=19 and now we have our final fraction 19/42
Equivalent fractions are just fractions that have the same overall value. For example: 1/2=1/4+1/4 The easiest way to check if the fractions are equivalent is to multiply the numerator of the first fraction by the denominator of the second fraction and the denominator of the first fraction by the numerator of the second fraction. Example: ½ and 6/12
1x12=12 2x6=12 Therefore, 12=12 and ½=6/12
Now what about 2/3 and 3/8? 2x8=16 3x2=6 16≠6 Therefore, 2/3≠3/8