Part a), simplify six 𝑎𝑏 over 𝑎. Part b, simplify eight minus two 𝑐 minus 20 plus nine 𝑐.
If we start with part a), we have six 𝑎𝑏 over 𝑎. Since there is an 𝑎 in the numerator and in the denominator, they cancel each other out. This is because it’s the same thing as saying six 𝑏 over one times 𝑎 over 𝑎. And anything over itself equals one; 𝑎 over 𝑎 equals one. If we multiply six 𝑏 times 𝑎 over 𝑎, that’s the same thing as six 𝑏 times one, which equals six 𝑏. The simplified form of this fraction is six 𝑏.
If we look at part b), we realize that we’re dealing with addition and subtraction. And that means we need to group like terms. We have the number eight and the number negative 20 or minus 20. To group those together, we say eight minus 20. And then we have two terms that have a variable of 𝑐, negative two 𝑐 and positive nine 𝑐. We want to combine negative two 𝑐 and nine 𝑐. Eight minus 20 equals negative 12. Negative two 𝑐 plus nine 𝑐 equals seven 𝑐. We could call this negative 12 plus seven 𝑐 or seven 𝑐 minus 12, as long as your simplified form includes positive seven 𝑐 and negative 12.