Page 86 - Calculating Agriculture Cover 20191124 STUDENT - A

6-10 Equations and Formulas CH 6]

COMBINING SIMILAR/LIKE TERMS

Terms are quantities that are added or subtracted:

4n +12 is composed of two terms, namely, 4n and ‘12’.

The term ‘4n’ is composed of two elements, ‘4’ and ‘n’. The ‘4’ and the ‘n’ are called coefficients or
factors because they are multiplied together and hence work together. The ‘4n’ and ‘12’ are separated by
+, and cannot be combined until the ‘n’ value is known. They are dissimilar; that is, not alike.
That which keeps them from being similar is the letter ’n’ (variable) or literal number (4). If you had
8 sheep and 4 cows, you could not call them 12 sheep, nor could you call them 12 cows because they are
not similar.
Similar/Like terms (sheep or cows) can be combined. 4n + 3n can be combined to make 7n because
the numbers (4 and 3) and the letter ‘n’ cause them to be similar in their association. Thus 4n + 3n = 7n.
If the expression 12a - 6a + 3b - 8b is written, those similar terms can be combined:

Example: 12a – 6a + 3b – 8b = Expression
(12a – 6a) + (3b – 8b) =
6a + (–5b) =
Solution: 6a – 5b Combined Expression

Is the answer for combining terms valid? How to prove:

Assign values to the variables such that the value a = 4 and the value b = 2 and insert these values in
both the expression and your solution.

Expression (Example)
12a – 6a + 3b – 8b =

Input values into the variables a = 4 and b = 2
12 (4) – 6(4) + 3(2) – 8(2) =
48 – 24 + 6 – 16 =
24 + 6 – 16 =
30 – 16 = 14

Combined Expression
6a – 5b = Solution When the arithmetic answers are the
Input values into the variables a = 4 and b = 2 same for both the expression and your
solution, then your solution is correct.
6(4) – 5(2) =
24 – 10 = 14

As both answers are 14, therefore, with the same arithmetic solution in each proves the Combined
Expression is correct.

In mathematics, it usually simplifies the equation if you combine similar terms whenever possible.

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