6th Grade Math Textbook, Progress

Addition and Subtraction

Expressions with Fractions

7-8

Mark mixed a solution of 1
^34 
L of colored

water, 2
^13 
L of salt water, and some liters

of lemon juice. What algebraic expression

represents the amount of mixed solution?

Let jrepresent the liters of lemon juice.

colored salt lemon

water water juice

1 
^34 
  2 
^13 
  j

If Mark mixed 
^14 
L of lemon juice, how

many liters of solution did he make?

To determine how many liters of solution

Mark made, evaluate the expression:

1 
^34 
 2 
^13 
j, when j
^14 
.

1 
^34 
 2 
^13 

^14 
 Replacejwith
^14 
.

( 1 
^34 

^14 
)  2 
^13 
 Use the Commutative and Associative Properties.

2  2 
^13 
 Simplify using the order of operations.

4 
^13 

Mark made 4
^13 
L of solution.

Study this example.

Evaluate: f 4 
^45 
g 6 
^13 
, when f 5 
^23 
and g 2 
^25 
.

5 
^23 
 4 
^45 
 2 
^25 
 6 
^13 
 Replacefwith 5 
^23 
andgwith 2 
^25 
.

(5
^23 
 6 
^13 
)( 4 
^45 
 2 
^25 
) Use the Commutative and Associative Properties.

12  7 
^15 
 Simplify using the order of operations.

19 
^15 

Commutative means “order.”

Associative means “grouping.”

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