Simplifying expressions worksheets with answers

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Simplifying expressions worksheets with answers

Grade 8 algebra questions with solutions are presented. Questions on solving equations, simplifying expressions including expressions with fractions are included. NOTE: In what follows, mixed numbers are written in the form a b/c. For example 2 1/3 means the mixed number 2 + 1/3. Simplify the following algebraic expressions. A) -2x + 5 + 10x - 9 B) 3(x + 7) + 2(-x + 4) + 5x Simplify the expressions. A) (2x - 6) / 2 B) (-x - 2) / (x + 2) C) (5x - 5)/10 Solve for x the following equations. A) -x = 6 B) 2x - 8 = -x + 4 C) 2x + 1/2 = 2/3 D) x/3 + 2 = 5 E) -5/x = 2 Evaluate for the given values of x and y. A) x2 - y2 , for x = 4 and y = 5 B) |4x - 2y| , for x = -2 and y = 3 C) 3x3 - 4y4 , for x = -1 and y = -2 Solve the following inequalities. A) x + 6 < 0 B) x + 1 > 5 C) 2(x - 2) < 12 What is the reciprocal of each of the following numbers? A) -1 B) 0 C) 3/4 D) 2 5/7 E) 0.02 Evaluate the following expressions involving mixed numbers. A) 3 3/4 + 6 1/7 B) (1 3/5) ? (3 1/3) - 2 1/2 C) (5 2/3) ? (4 1/5) D) (3 4/7 - 1 1/2) ? (2 3/8 + 2 1/4) Evaluate the folwoing exponential expressions. A) -42 B) (-2)3 C) (-2)4 D) 10000 E) 5661 Convert to fractions and write in simplest form. A) 0.02 B) 12% C) 0.5% D) 1.12 Convert to decimals. A) 1/5 B) 120% C) 0.2% D) 4 8/5 Convert to percent. A) 3/10 B) 1.4 C) 123.45 D) 2 4/5 Which of these numbers is divisible by 3? A) 156312 B) 176314 Which of these numbers is divisible by 4? A) 3432 B) 1257 Which of these numbers is divisible by 6? A) 1233 B) 3432 Which of these numbers is divisible by 9? A) 2538 B) 1451 Evaluate 8x + 7 given that x - 3 = 10. Solutions and Answers to the Above Questions A) -2x + 5 + 10x - 9 : given = (10x - 2x) + (5 - 9) : put like terms together = 8x - 4 : group B) 3(x + 7) + 2(-x + 4) + 5x : given = 3x + 21 - 2x + 8 + 5x : expand = (3x - 2x + 5x) + (21 + 8) : put like terms together = 6x + 29 : group A) (2x - 6) / 2 : given = 2(x - 3) / 2 : factor 2 in numerator = x - 3 : divide numerator and denominator by 2 to simplify B) (-x - 2) / (x + 2) : given = -1(x + 2) / (x + 2) : factor -1 in numerator = -1 : divide numerator and denominator by x + 2 to simplify C) (5x 5)/10 : given = 5(x - 1) / 10 : factor 5 in numerator = (x - 1) / 2 : divide numerator and denominator by 5 to simplify A) -x = 6 : given x = -6 : multiply both sides of the equation by -1 B) 2x - 8 = -x + 4 : given 2x - 8 + 8 = -x + 4 + 8 : add +8 to both sides of the equation 2x = -x + 12 : group like terms 2x + x = -x + 12 + x : add +x to both sides 3x = 12 : group like terms x = 4 : mutliply both sides by 1/3 C) 2x + 1/2 = 2/3 : given 2x + 1/2 - 1/2 = 2/3 - 1/2 : subtract 1/2 from both sides 2x = 1/6 : group like terms x = 1/12 : multiply both sides by 1/2 D) x/3 + 2 = 5 : given x/3 + 2 - 2 = 5 - 2 : subtract 2 from both sides x/3 = 3 : group like terms x = 9 : multiply both sides by 1/2 E) -5/x = 2 : given -5 = 2x : multiply both sides by x and simplify -5/2 = x : : multiply both sides by 1/2 A) x2 - y2 , x = 4 , y = 5 : given 42 - 52 : substitute x and y by the given values =16 - 25 = -9 B) |4x - 2y| , x = -2 , y = 3 : given |4(-2) - 2(3)| : substitute x and y by the given values = |-14| = 14 : evaluate C) 3x3 - 4y4 , x = -1 , y = -2 : given 3(-1)3 - 4(-2)4 : substitute x and y by the given values = -3 - 64 = -67 : evaluate A) x + 6 < 0 : given x + 6 - 6 < -6 : subtract 6 from both sides x < -6 : group like terms B) x + 1 > 5 : given x + 1 - 1 > 5 - 1 : subtract 1 from both sides x > 4 : group like terms C) 2(x - 2) < 12 : given x - 2 < 6 : mutliply both sides by 1/2 x - 2 + 2 < 6 + 2 : add 2 to both sides x < 8 : group like terms A) (-1) a = 1 : definition: a is the reciprocal of -1 a = 1/-1 = -1 : solve for a; -1 is the reciprocal of -1 B) (0) b = 1 : definition: b is the reciprocal of 0 b = undefined : no value of b satisfies the above equation C) (3/4) c = 1 : definition: c is the reciprocal of 3/4 c = 4/3 : solve for c; c = 4/3 is the reciprocal of 3/4 D) (2 5/7) d = 1 : definition: d is the reciprocal of 2 5/7. (19/7) d = 1 : convert the mixed number 2 5/7 into a fraction. d = 7/19 : : solve for d; d = 7/19 is the reciprocal of 2(5/7) E) 0.02 d = 1 : definition: d is the reciprocal of 0.02. d = 1/0.02 : solve for d; d = 50 is the reciprocal of 0.02 A) 3 3/4 + 6 1/7 : given = (3 + 6) + (3/4 + 1/7) : put the whole parts together and the fractional parts together. = 9 + (21/28 + 4/28) : add. = 9 25/28 B) (1 3/5) ? (3 1/3) - 2 1/2 : given = (8/5) ? (10/3) - 2 1/2 : convert mixed numbers to mupliply into fractions. = 80/15 - 2 1/2 = 5 1/3 - 2 1/2 = 4 4/3 - 2 1/2: mupliply and write as mixed number if possible = (4 - 2) + (4/3 - 1/2) : subtract = 2 5/6 C) (5 2/3) ? (4 1/5) : given = (17/3) ? (21/5) : convert mixed numbers to fractions. = 85 / 63 : divide fractions = 1 22/63 : write as mixed number D) (3 4/7 - 1 1/2) ? (2 3/8 + 2 1/4) : given = [(3 - 1) + (4/7 - 1/2)] ? [(2 + 2) + (3/8 + 1/4)]: evaluate numerator and denominator as fractions. = (2 1/14) ? (4 5/8) = (29/14) ? (37/8) = 116/259 A) - 42 = - (4 ? 4) = -16 : expand and calculate B) (-2)3 = (-2)?(-2)?(-2) = -8 : expand and calculate C) 10000 = 1 : definition: any nonzero number to the power zero gives 1 D) 5661 = 566 A) 0.02 = 1/50 B) 12% = 3/25 C) 0.5% = 1/200 D) 1.12 = 28/25 A) 1/5 = 0.2 B) 120% = 1.2 C) 0.2% = 0.002 D) 4 8/5 = 5.6 A) 3/10 = 30% B) 1.4 = 140% C) 123.45 = 12345% D) 2 4/5 = 280% A) 156312 , is divisible by 3 B) 176314 , is not divisible by 3 A) 3432 , is divisible by 4 B) 1257 , is not divisible by 4 A) 1233 , is not divisible by 6 B) 3432 , is divisible by 6 A) 2538 , is divisible by 9 B) 1451 , is not divisible by 9 Evaluate 8x + 7 given that x - 3 = 10. x - 3 = 10: given equation x = 10 + 3 = 13: solve the given equation. 8(13) + 7 = 111 substitute x by 3 in the given expression and evaluate. Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers This page contains 95+ exclusive printable worksheets on simplifying algebraic expressions covering the topics like algebra/simplifying-expressionss like simplifying linear, polynomial and rational expressions, simplify the expressions containing positive and negative exponents, express the area and perimeter of rectangles in algebraic expressions, factorize the expressions and then simplify and much more. Recommended for students of 6th grade, 7th grade, 8th grade, and high school students. Access our free simplifying algebraic expressions worksheets with just a single click! Missing Terms Determine the missing term in the first section. Find the value of the missing variable in the next section. Area and Perimeter of a Rectangle The dimensions of the rectangles are expressed in algebraic expressions. Use relevant formulae to determine the area and perimeter of the rectangles. Simplifying Rational Expressions ? Practice Problems Move your mouse over the "Answer" to reveal the answer or click on the "Complete Solution" link to reveal all of the steps required for simplifying rational expressions. Related Pages Solving Linear Equations Algebraic Expressions More Algebra Lessons Combining Like Terms An algebraic expression consisting of two or more like terms can be simplified by combining like terms. Like terms are terms that have the same variable part i.e. they only differ in their coefficients. The following diagram shows some examples of like terms. Scroll down the page for more examples and solutions on simplifying expressions by combining like terms. Like terms can be added or subtracted from one another. Example: Simplify the expressions: a) 14x + 5x b) 5y ? 13y c) p ? 3p Solution: a) 14x + 5x = (14 + 5)x = 19x b) 5y ? 13y = (5 ?13)y = ?8y c) p ? 3p = (1 ? 3)p = ? 2p To simplify an algebraic expression that consists of both like and unlike terms, it might be helpful to first move the like terms together. (When moving the terms, we must remember to move the + or ? attached in front of them). Example: Simplify 3x + 2y ? 2x + 6 Solution: 3x + 2y ? 2x + 6 = 3x? 2x + 2y + 6 = (3 ? 2)x + 2y + 6 = x + 2y + 6 Example: Simplify 3x + 2a ? 4x Solution: 3x + 2a ? 4x = 3x ? 4x + 2a = (3 ? 4)x + 2a = ?x + 2a The following videos show some examples of simplifying expressions by combining like terms. Example: Simplify -7ab + 6b - 3ab - 4b - 3ab Show Video Lesson Example: Simplify 7xy + 9yz - 3xy - 3yz + 7xy - 2yz Show Video Lesson Simplify Algebraic Expressions - Combine Like Terms Examples: 4x3 - 2x2 + 5x3 + 2x - 4x2 - 6x 4y - 2x + 5 - 6y + 7x - 9 Show Video Lesson Simplify an Algebraic Expression by Combining Like Terms. This video shows how to simplify a couple of algebraic expressions by combining like terms by adding, subtracting, and using distribution. Example: Simplify a) 4x3 + x2 - 2x3 + 5 b) 10x5 + 3(2x5 - 4b2) Show Video Lesson Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

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