Worksheet 2 Expression Trees An expression tree shows the structure of an expression how the expression s parts fit together An expression tree is made by following these steps 1 Put an operation sign at the top This will be if the expression is a sum if it is a product if it is a difference and so on 2 Draw two line segments that drop to the left and to the right of the operation sign These will connect the operation sign with the things that are being operated upon called operands 3 Put the operands below the operation sign at the ends of the line segments The trick to constructing complicated expression trees is to understand that in step 3 if an operand is an expression you will have to construct another expression tree Example Draw an expression tree for 3 5 2 First rewrite the expression with parentheses 3 5 2 3 5 2 Second write the top operation sign with two branches Third put the things being operated upon at the ends of the branches If an expression is one of the things being operated upon then repeat these steps to write it as an expression tree 2 3 5 Expression Equations P W Thompson Worksheet 2 Page 1 Part I Partial trees Put parentheses where they belong in the expressions Then complete the expression tree for each expression Check yourself by comparing your answer with another student 1 5 10 2 3 4 2 3 4 2 4 2 3 4 4 5 4 6 3 7 2 Expression Equations P W Thompson Worksheet 2 Page 2 Part II 1 For each tree write an expression that will make the tree a b 3 9 7 3 7 6 5 c d 3 a 1 y x 4 x Expression Equations P W Thompson Worksheet 2 Page 3 y x y Part III Draw an expression tree for each expression Check yourself by comparing your answer with another student 1 11 2 9 3 2 6 x 8 2 y 3 u 12 v 8 4 2 z 4 8 5 c d d 4 f 5 6 c d d 4 f 5 Expression Equations P W Thompson Worksheet 2 Page 4
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