# Introduction to Algebra

## Mathematics, Grade 5

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Algebraic Expressions Translating word phrases into algebraic expressions Evaluating algebraic expressions An algebraic expression is a mathematical phrase consisting of variables, numbers, and operations. Solving Equations An equation is a mathematical sentence which shows that two expressions or values are equal. Think of an equation as a balance scale. To evaluate an algebraic expression, replace the variable with a number Replace m with 4 in the expression The letter m is a variable which represents an unknown number. 3 x 2m is an algebraic expression evaluate m + 5 for m = 4 m + 5 4 + 5 = 9 Operation Word Phase Algebraic Expression Addition m + 9 Subtraction m 9 Multiplication 2m + 9 2 x m 2 m 2m Division A number plus 9 The sum of m and 9 9 more than a number A number increased by 9 The difference between a number and 9 A number minus 9 9 less than a number A number decreased by 9 9 more than twice a number 2 x a number A number multiplied by 2 The product of 2 and a number A number divided by 9 9 divided by a number The quotient of a number and 9 m 9 9 m m 9 28 = m + 16 equal sign What number plus 16 equals 28? Solve 16 + m = 28 Solution m = 12 12 + 16 = 28 28 = 28 Solve the equation to find the value of the variable that makes the equation true. The value of the variable is called the solution. Examples of Algebraic Expressions Addition Subtraction Multiplication Division 6 + d, or d + 6 c - 6 6 x b, or 6b a ÷ 6, or a 6 expression expression 28 16 m © Copyright NewPath Learning. All Rights Reserved. 93-4507 www.newpathlearning.com Introduction to Algebra
Algebraic Expressions Translating word phrases into algebraic expressions Evaluating algebraic expressions An algebraic expression is a mathematical phrase consisting of variables, numbers, and operations. Solving Equations An equation is a mathematical sentence which shows that two expressions or values are equal. Think of an equation as a balance scale. To evaluate an algebraic expression, replace the variable with a number Replace m with in the expression The letter m is a which represents an unknown number. 3 x 2m is an evaluate m + 5 for m = 4 m + 5 4 + 5 = 10 Operation Word Phase Algebraic Expression Addition Subtraction Multiplication Division A number plus 9 The sum of m and 9 9 more than a number A number increased by 9 The difference between a number and 9 A number minus 9 9 less than a number A number decreased by 9 9 more than twice a number 2 x a number A number multiplied by 2 The product of 2 and a number A number divided by 9 9 divided by a number The quotient of a number and 9 What number plus 16 equals 28? Solve 16 + m = 28 Solution m = 12 + 16 = 28 = 28 Solve the equation to find the value of the variable that makes the equation true. The value of the variable is called the solution. Examples of Algebraic Expressions Addition Subtraction Multiplication Division 28 = m + 16 equal sign expression expression 28 16 m Key Vocabulary Terms algebra algebraic expression difference equation increase more plus product quotient solution sum variable © Copyright NewPath Learning. All Rights Reserved. 93-4507 www.newpathlearning.com Introduction to Algebra \|xiBAHBDy01648pzY