✓ Got It?

4. Reasoning Is each statement in parts (a) and (b) true or false? If it is false, give a counterexample. If true, use properties of real numbers to show the expressions are equivalent.
   1. For all real numbers j and k, j · k = ( k + 0 ) · j . j middle dot k equals open k plus 0 close middle dot j .
   2. For all real numbers m and n, m ( n + 1 ) = m n + 1 . m open n plus 1 close equals m n plus 1 .
   3. Is the statement in part (A) of Problem 4 false for every pair of real numbers a and b? Explain.

✓ Lesson Check

Do you know HOW?

Name the property that each statement illustrates.

1. x + 12 = 12 + x x plus 12 equals 12 plus x
2. 5 · ( 12 · x ) = ( 5 · 12 ) · x 5 middle dot open 12 middle dot x close equals open 5 middle dot 12 close middle dot x
3. You buy a sandwich for $2.95, an apple for $.45, and a bottle of juice for $1.05. What is the total cost?
4. Simplify 24 c d c . fraction 24 c d , over c end fraction . .

Do you UNDERSTAND?

5. Vocabulary Tell whether the expressions in each pair are equivalent.
   1. 5 x · 1  and  1 + 5 x 5 x middle dot 1 , and , 1 plus 5 x
   2. 1 + ( 2 t + 1 )  and  2 + 2 t 1 plus open 2 t plus 1 close , and , 2 plus 2 t
6. Justify each step.

   3 · ( 10 · 12 ) = 3 · ( 12 · 10 )   = ( 3 · 12 ) · 10   = 36 · 10   = 360 table with 4 rows and 2 columns , row1 column 1 , 3 middle dot open 10 middle dot 12 close , column 2 equals 3 middle dot open 12 middle dot 10 close , row2 column 1 , , column 2 equals open 3 middle dot 12 close middle dot 10 , row3 column 1 , , column 2 equals 36 middle dot 10 , row4 column 1 , , column 2 equals 360 , end table