# Simplifying Expressions: Combining Like Terms Objective To simplify algebraic expressions by combining like terms.

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3 Date 9 3 Combining Like Terms continued An expression such as 2y 6 4y 8 9y (3) is difficult to work with because it is made up of 6 different terms that are added and subtracted. There are 2 sets of like terms in the expression. The terms 2y, 4y, and 9y are 1 set of like terms. The constant terms 6, 8, and (3) are a second set of like terms. Each set of like terms can be combined into a single term. To simplify an expression that has more than one set of like terms, combine each set into a single term. Example 3: Simplify 2y 6 4y 8 9y (3) by combining like terms. Step 1 Combine the y terms. 2y 4y 9y 6y 9y 3y Step 2 Combine the constant terms. 6 8 (3) 2 (3) 5 Final result: 2y 6 4y 8 9y (3) 3y (5) 3y 5 Check: Substitute 2 for y in the original expression and the simplified expression. 2y 6 4y 8 9y (3) 3y 5 (2 º 2) 6 (4 º 2) 8 (9 º 2) (3) (3 º 2) (3) Simplify each expression by combining like terms. Check each answer by substituting several values for the variable y x 3x n 6 8n 2 3n 14. n π 2n 1 2 π x 9 1.4x d 2a (6a) 3d 15d 7y 24 2x 8 6n 4 3n 1 2, or 3n 2 1.1x 9.6 3d 8a Math Journal 2, p Redo the Math Message problems using the distributive property to combine like terms. To simplify 4y + 7y, think: 4y + 7y = (4 y) + (7 y) = (4 + 7) y = 11 y = 11y So, 4y + 7y = (4 + 7)y = 11y. To simplify 4y - 7y, think: 4y - 7y = (4 y) - (7 y) = (4-7) y = -3 y = -3y So, 4y - 7y = (4-7)y = -3y. To simplify an expression means to write the expression in a simpler form. To support English language learners, explain that even though one expression is in simpler form, the expressions are equivalent. Combining like terms is one way to simplify an expression. Removing parentheses is another way. This method will be the focus of Lesson 9-4. Example 2 shows how to extend the method in Example 1 to combine more than two like terms. The first two terms are combined. The result is then combined with the next term and so on. Adjusting the Activity At the board, demonstrate a factoring procedure for combining like terms. Write the expression 2n - 7n + 3n - 4n. Enclose the expression in parentheses and cross out (or erase) each occurrence of the variable n. Then write the variable n to the right of the parentheses, saying that you have undistributed the variable. Evaluate the numerical expression within parentheses. The simplified expression is -6n. 2n - 7n + 3n - 4n = (2n/ - 7n/ + 3n/ - 4n/ )n = ( )n = -6n A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Provide additional practice by writing several more expressions containing only one kind of term on the board or overhead. Then have students simplify them on their slates. Suggestions: 2b - (-6b) + 4b 12b 4p - 7p - (-4p) 1p or p 1_ 2 m + 3_ 4 m - (- 5_ m) 10_ m, 5_ m, or 21_ w + 9.6w - 7.5w 0.6w Partners complete the problems on journal page 330. When most students have finished, briefly go over the answers. 2 m 800 Unit 9 More about Variables, Formulas, and Graphs

4 Read the paragraphs at the top of journal page 331 and go over Example 3, which shows how to combine like terms when there is more than one kind of term. Demonstrate Example 3 on the board as shown below. Remind students that they identified variable terms and constant terms in their work with equations (Lesson 6-11). In the expression 2y y - 8-9y + (-3), the variable terms 2y, 4y, and 9y are one set of like terms. the constant terms 6, 8, and -3 are a second set of like terms. the variable terms are combined into one single term. the constant terms are combined into a second single term. variable terms variable terms constant terms Date 9 3 Estimating and Measuring in Millimeters All measurements are approximations. The pencil shown below measures about 4 inches. A more precise measurement is about inches. An even more precise measurement 6 is about 93 millimeters. The smaller the unit you use to measure an object, the more precise the measurement will be. 1. Explain why 93 millimeters is a more precise measurement than inches for the 16 length of the pencil. Measure each line segment below to the nearest millimeter. 2. A B Length of AB 3. D E Length of DE 4. Measure PQ. Then, in the space provided, draw a line segment that is 5 the length 8 of PQ. Label the segment RS. Length of P œqœ 56 P Q R Length of RœSœ 5. Measure FG. Then, in the space provided, draw a line segment that is 125% the length of FG. Label the segment JK. Length of FG 60 F G J 0 INCHES 1 S 2 0 CM Sample answer: Millimeters are smaller units than sixteenths of an inch. K 3 4 Length of JK constant terms Assign the problems on journal page 331. Go over the answers. Note that an instruction to check answers is included with the problem set. Remind students to check their answers by substituting at least two different values for the variable in each expression. Math Journal 2, p Ongoing Learning & Practice Estimating and Measuring in Millimeters (Math Journal 2, p. 332) PROBLEM SOLVING SMALL-GROUP Date Students measure line segments to the nearest millimeter. Math Boxes 9 3 (Math Journal 2, p. 333) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lessons 9-1 and 9-5. The skills in Problems 4 and 5 preview Unit 10 content. Writing/Reasoning Have students write a response to the following: Explain how the ratio in Problem 3c is related to the ratio of the corresponding sides. Sample answer: The ratio of the perimeters is equivalent to the ratios of the corresponding sides The area of the rectangle is 238 units 2. Write a number sentence to find the value of x. Number sentence Solve for x. 4. I am a regular polygon with all obtuse angles. I have the smallest number of sides of any polygon with obtuse angles. How many sides do I have? 5 Math Boxes x 9 x 238 7(9 x) 25 units 3. Triangles ABC and DEF are similar. a. Length of AB units b. Length of DF units 8 Perimeter of triangle ABC c. 7 Perimeter of triangle DEF units 2. Solve. a w 4 Solution 7 w 8 b. 24 p 8 4 Solution c. 4j 24 6j 120 Solution E 28 D p 20 j Use the diagonals to find the sum of the interior angle measures of the octagon below. C F A B Use your Geometry Template to draw this polygon below. Math Journal 2, p. 333 Sum of the interior angle measures 1, Lesson

6 Teaching Master ENRICHMENT INDEPENDENT Simplifying and Evaluating Expressions (Math Masters, p. 289) 5 15 Min Students extend their knowledge of simplifying expressions by finding missing terms in expressions. They also evaluate simplified expressions. Name Date 9 3 Simplifying and Evaluating Expressions Each expression on the left of the equal sign can be simplified to the expression on the right. Fill in the missing variable or constant terms. 1. 9x = 7x m - 8n = -4m + 32n t - (-2v) + 2w = -4t - 2v + 4w 4. 3c + 2c + 6d - 4d = 2d f - + 4g = -f + g + 10 Simplify each expression below. Then evaluate the expression for x = -2, y = 3, and z = y - 6z + 4x - 2z - 8y - 12x 7. 3x x - 9y + 6x - 4z Sample answers for Problems 3 5: -2x 3-8m 40n 12-2t -4v -2w 5c -8 9f 3g -3-8x - 6y - 8z; 30 5x - 9y - 4z -10; -31 EXTRA PRACTICE PARTNER Generating Equivalent Expressions (Differentiation Handbook, p. 135) 5 15 Min To provide additional practice with finding equivalent expressions, have students complete name-collection boxes for several different expressions. Students exchange papers with a partner and check that their partner s expressions are equivalent by substituting a value for the variable in each of the expressions. Suggestions: 24x 1_ y 34.2d d 3 py g g p _EMCS_B_G6_MM_U09_ indd x + 9-6z + 3y - 6z z - 5x + 9y + x - y + 5z 10. 1_ 2 x - 2_ 3 y + 3_ 4 z - 3_ 2 x Math Masters, p x + 3y - 12z - 6; 47-4x + 8y + 8z; 0 -x + 2_ 3 y + 3_ 4 z; -3 2/26/11 3:11 PM ELL SUPPORT SMALL-GROUP Building a Math Word Bank (Differentiation Handbook, p. 130) 5 15 Min To provide language support for vocabulary terms, have students use the Word Bank template found on Differentiation Handbook, page 130. Ask students to write the phrases combine like terms and simplify an expression and then to represent these phrases using pictures and examples. See the Differentiation Handbook for more information. Lesson

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