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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