SOLUTION: Trying to help my daughter solve the following..... 7.5 (a - 3) and it says to use the distributive property (?) and expand like terms when possible. I havent done math in forEVE

Question 341349: Trying to help my daughter solve the following..... 7.5 (a - 3) and it says to use the distributive property (?) and expand like terms when possible. I havent done math in forEVER..'dist.prop' and 'like terms' are mysteries to me!
Found 2 solutions by Theo, nerdybill:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
I believe the problem is 7.5 * (a-3) where * means multiplication, i.e.:
7.5 * (a-3) means 7.5 times (a-3)
the distributive property states that:
a * (b + c) is equal to (a * b) + (a * c).
if c is negative, then it states that:
a * (b - c) is equal to (a * b) - (a * c).
in your problem, that becomes:
7.5 * (a - 3) = 7.5*a - 7.5*3 which becomes 7.5*a - 22.5 which can also be written as 7.5a - 22.5
like terms means the terms are the same.
combining like terms means you add them together.
if you have 5*x + 6*x, then you combine like terms by bringing them together to get 11*x.
you can understand that a lot better if x represents something you can see, like a nickel or a dime.
5 * a nickel + 6 * a nickel equals 5 nickels plus 6 nickels equals 11 nickels.
5 * a dime + 6 * a dime equals 5 dimes plus 6 dimes equals 11 dimes.
in the first equation, if x represents a nickel, then you get 5*x + 6*x = 11*x
in the second equation, if x represents a dime, then you get 5*x + 6*x = 11*x
in the problem you stated, you did not have like terms to bring together.
7.5 * (a - 3) resulted in 7.5*a - 7.5*3 which resulted in 7.5*a - 22.5

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Given:
7.5 (a - 3)
This says "7.5 times the quantity a minus 3".
.
To "distribute" the 7.5, we multiply each term inside the parenthesis by 7.5.
.
The distributive property simply states that given expression is the same as the following:
7.5 (a - 3)
= 7.5(a) - 7.5(3)
= 7.5a - 22.5

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