Basic Operations and Equivalent Expressions - Step-by-Step Lesson
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1 Name Date Basic Operations and Equivalent Expressions StepbyStep Lesson Lesson 1 Simplify the expressions (6x 5) 2. 3 (4 3 7x) Explanation: 1. Step 1) First see what is being asked. We have to simplify the equation using the distributive property. Step 2) Apply the distributive property: multiply a sum by multiplying each addend separately. Multiply 4 with both the numbers because 4 is outside the bracket. 4(6x) 4(5) 24x 20 The answer will be 24x Follow the same pattern. 3 (4 3 ) 3(7x) = x As you may notice, more practice allows the problems to become easier to solve.
2 Name Date Basic Operations and Equivalent Expressions Guided Lesson Complete the following questions: 1) Rewrite the expression: (9a 54 b) 2) Apply the properties of operations to produce an equivalent expression: (x x x) / 3 3) Choose and apply the distributive property to the expression to produce an equivalent expression: 3(5 x) a. 15x 3 b. 15 3x c. 3x 15
3 Name Date Basic Operations and Equivalent Expressions Guided Lesson Explanation Explanation#1 We have to apply the distributive property to the expressions. The expression is: (9a 54 b) Find a common number or variable that you can use. We are looking for an integer that can easily be divided. 9 is a common number (between 9 and 54). When we divide 9 we will get: We will get the answer: 9(a 6b) Explanation#2 We have to apply the properties of operations to produce the equivalent expression: The expression is: (x x x) / 3 Let s rewrite it by adding all the xs together: 3x / 3 Explanation#3 We have to apply the distributive property to the expression to produce the equivalent expression. The expression is: 3(5 x) Now multiply 3 with both the numbers since 3 is outside the bracket. 15 3x The answer will be: b
4 Name Date Basic Operations and Equivalent Expressions Independent Practice Worksheet Write an equivalent expression. 1. (24a 56b) 2. 7(2x 9) 3. (y y y) 4. (12a 60) 5. 9(3 8x) 6. (90x 120) 7. t t t (3 6x) 9. p p (4x 3 2)
5 Name Date Basic Operations and Equivalent Expressions Matching Worksheet Match and solve the expressions. Write the letter of the answer that matches the expression. 1. 4(a b) a. 18x (27a 24b) b. 4a 4b 3. 9(x 2y) c. 5(9 10b) 4. 2(9x 9) d. 9x 18y 5. (45 50b) e. 3(9a 8b)
6 Name: Date Topic : Visual ExpressionsWorksheet 1 Write the numerical expression for the models. Let one green star equal 2 and one blue star equal Use a number line to solve the equation. 15 (10) 8. What integer is represented by 30 positive tiles and 10 negative tiles? 9. Use a number line to solve the equation. 5 (5) 10. What integer is represented by 80 positive tiles and 30 negative tiles?
7 Name: Date Topic : Visual ExpressionsWorksheet 2 Write the numerical expression for the models. Let one black triangle equal 1 and one yellow triangle equal Use a number line to solve the equation. 13 (7) 8. What integer is represented by 40 positive triangles and 25 negative 9. Use a number line to solve the equation. 9 (5) 10. What integer is represented by 60 positive triangles and 20 negative
8 Name: Date Topic : Visual ExpressionsWorksheet 3 Write the numerical expression for the models. Let one red circle equal 2 and one blue circle equal Use a number line to solve the equation. 8 (2) 8. What integer is represented by 85 positive triangles and 35 negative 9. Use a number line to solve the equation. 7 (5) 10. What integer is represented by 55 positive triangles and 25 negative
9 Name: Date Topic : Visual ExpressionsWorksheet 4 Write the numerical expression for the models. Let one green can equal 3 and one purple can equal Use a number line to solve the equation. 5 (2) 8. What integer is represented by 90 positive triangles and 18 negative 9. Use a number line to solve the equation. 10 (1) 10. What integer is represented by 78 positive triangles and 28 negative
10 Name: Date Topic : Visual ExpressionsWorksheet 5 Write the numerical expression for the models. Let one green can equal 2 and one purple can equal Use a number line to solve the equation. 15 (7) 9. Use a number line to solve the equation. 13 (2) 8. What integer is represented by 44 positive triangles and 20 negative 10. What integer is represented by 57 positive triangles and 22 negative
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