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My son is getting math homework that we don't understand, for instance: Rewrite the expressions by using the distributive property and collecting like terms

3t+2        t-4
_____ + _____       a fraction? Please explain step by step to me so, I can start helping him with these problems.
   7           14
 
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2 Answers

Hi T;
[(3t+2)/7]+[(t-4)/14]
The first priority is to have both denominators, also known as divisors, identical.  One is 7, the other 14.  Let's take the fraction with the former divisor and multiply it by 2/2.
(2/2)[(3t+2)/7]
[2(3t+2)]/14
 
[2(3t+2)]/14+[(t-4)/14]
Let's combine the two numerators, information on top of each fraction.
[2(3t+2)+(t-4)]/14
Now, let's distribute the 2...
(6t+4+t-4)/14
6t+t=6t+1t=7t
4-4=0
7t/14
7/14=1/2
1t/2
t/2
The distributive property is : ab + ac = a(b + c).  In your example:
First, multiply first fraction by 2 using common denominator  14:
2(3t + 2)/14 + (t - 4)/14
The common factor is 1/14: 2(3t + 2)/14 + (t - 4)/14  = 1/14 [2(3t + 2) + (t - 4)] = 1/14 (6t + 4 + t - 4) = 7t/14 = t/2