+101 Justify the move from Step 1 to Step 2 below.
Step 1: 5m + 3 + 2m
Step 2: 5m + 2m + 3
+23252 The commutative property exchange terms, such as x + 9 becomes 9 + x. (In the same sense that a commuter moves from one place in a city to anothern place.)
The associative property rearranges parentheses, such as x + (3x + 9) becomes (x + 3x) + 9. It changes which terms are associated together; in the first place, the 3x is associated with the 9; in the second case the 3x is associated with the x.
The distributive property either multiplies out or it factors. For example, when 3(x + 7) becomes 3x + 21, you have multiplied out the problem; when 4x + 20 becomes 4(x + 5), you have factored the problem. In both cases, written one way it has parentheses, written the other way, it has no parentheses.
Combining like terms simplifies problems; 3x + 7 + 9 becomes 3x + 16 (the numbers are combined) and 3x + 8x + 12 becomes 11x + 12. The problem becomes shorter, simpler.
In your problem, the 3 + 2m is rewritten as 2m + 3, terms are exchanged.
Now, can you figure out which rule is being used?
+23252 The commutative property exchange terms, such as x + 9 becomes 9 + x. (In the same sense that a commuter moves from one place in a city to anothern place.)
The associative property rearranges parentheses, such as x + (3x + 9) becomes (x + 3x) + 9. It changes which terms are associated together; in the first place, the 3x is associated with the 9; in the second case the 3x is associated with the x.
The distributive property either multiplies out or it factors. For example, when 3(x + 7) becomes 3x + 21, you have multiplied out the problem; when 4x + 20 becomes 4(x + 5), you have factored the problem. In both cases, written one way it has parentheses, written the other way, it has no parentheses.
Combining like terms simplifies problems; 3x + 7 + 9 becomes 3x + 16 (the numbers are combined) and 3x + 8x + 12 becomes 11x + 12. The problem becomes shorter, simpler.
In your problem, the 3 + 2m is rewritten as 2m + 3, terms are exchanged.
Now, can you figure out which rule is being used?
