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Writing and Evaluating Algebraic Expressions

Introduction

Algebra sounds like a big word, but it is a way of using letters and symbols to represent numbers and quantities in mathematical expressions and equations. This article focuses on how we write and evaluate algebraic expressions. Exciting, right? Let us dive deeper and see how to use algebra in real life.

Grade Appropriateness

This article is tailored for students between the 3rd and 9th grades. 

Math Domain

The domain we are covering falls under Algebra.

Applicable Common Core Standards

6.EE.A.2: Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.B.6: Use variables to represent numbers and write expressions.

Definition of the Topic

Algebraic expressions are math phrases that can have numbers, variables (like x or y), and operation symbols (like +,-,÷, etc.). Unlike algebraic equations, algebraic expressions do not have equal signs. For example, 3x + 4y is an algebraic expression.

Key Concepts

Variable: A symbol, usually a letter, that stands for an unknown number.

Coefficient: The number before a variable. In 5x, 5 is the coefficient.

Constant: A number on its own, without a variable.

Term: A single mathematical expression refers to a variable, a number, or a number and variable multiplied or divided.

Discussion with Illustrative Examples

There are times when the value of a certain number in mathematics may be unknown. A variable is a symbol—typically a letter—denoting an unknown numeric value. A term refers to a variable, a number, or a number and variable multiplied or divided. Algebraic expressions, on the other hand, are made up of a single term or the sum of two or more terms. 

Parts of an Algebraic Expression

A variable is a symbol, typically a letter, representing an unknown number.

A coefficient is a number used to multiply a number.

A constant is a fixed value and does not contain a variable

A term is a single mathematical expression that refers to a variable, a number, or a number and variable multiplied or divided.

Writing Algebraic Expressions

Variables, numbers, addition sign, minus sign, multiplication sign, division sign, and exponents may all be necessary when writing algebraic expressions. In writing algebraic expressions, an equal sign is not necessary.

Let us say you got \$5 as your weekly allowance and did some extra chores, for which you got x dollars. Your total money would be \$5 + x. Here, \$5 + x is an algebraic expression.

The following tables show the commonly used keywords in writing algebraic expressions.

Addition (+)

Subtraction ( – )

Multiplication (×)

Division (÷)

Exponents

Evaluating Algebraic Expressions

In mathematics, evaluating refers to determining the value of an expression, equation, or function.  

Substitute the specified number for the algebraic equation’s variable to evaluate it, and then use the order of operations to simplify the expression. 

For example, if we evaluate 4a+2b-c when a= 3, b= -1, and c = 4, we have,

4(3) + 2(-1) – 4

=12-2-4 

=6

The answer is -6. 

Examples with Solution

Example 1 

Write the following into algebraic expressions using n as the variable.

1. Ten less than six times a number

2.  Seven more than twice a number

3. The difference of 10 and a number

4. Three times the difference between a number and eight

5. Eight is more than the ratio of a number, and six

Solution

1. 6n-10

2. 7+2n

3. 10-n

4. 3(n-8)

5. $\frac{n}{6}$+8

Example 2 

Write an algebraic expression representing an employee’s weekly pay if he earns 12 dollars per hour plus a weekly bonus of twenty dollars.

Solution

Let h be the number of hours the employee works in a week. Hence, his weekly earning may be calculated using the expression 12h+50.

Example 3

Evaluate the following expressions using the given values.

1. 2x-7y+4; x=2 and y=1

2. a(b+2c); a=3, b=2, and c=5

3. m3+n2-4; m=3 and n=6

4. (x+2y)÷z; x=10, y=5, and z=2

Solution

Substitute the given values to the given algebraic expression, perform the indicated operation, and simplify.

1. 2x-7y+4; x=2 and y=1

=2(2)-7(1)+4

=4-7+4

=1

2. a(b+2c); a=3, b=2, and c=5

=3(2+2(5))

=3(12)

=36

3. m3+n2-4; m=3 and n=6

=33+62-4

=27+36-4

=59

4. (x+2y)÷z; x=10, y=5, and z=2

=(10+2(5))÷2

=(10+10)÷2

=20÷2

=10

Real-life Application with Solution

Suppose you are saving money for a toy that costs \$20. You already have \$5. Every week, you save x dollars from your allowance. After three weeks, how much more money do you need?

Expression for savings after three weeks: 3x+5 

Money needed: 20 – (3x+5)

So, if you save \$3 every week (x=3), then: 

Money needed = 20 – (5 + 3(3)) = 20 – 14 = \$6

You will need \$6 more!

Practice Test

1. Write an expression for “10 minus a number t”.

2. The total cost of 5 books if each book costs b dollars.

3. An expression for the total of 8 candies and c candies.

4. Money left after spending d dollars from \$50.

5. Find the total for two pens and three notebooks if a pen costs x dollars and a notebook costs y dollars.

6. The perimeter of a rectangle with length l and width w.

Answers:

1. 10-t

2.  5b

3. 8+c

4. 50-d

5. 2x+3y

6. 2l+2w

Frequently Asked Questions (FAQs)

Why do we use variables in math?

Variables allow us to represent unknown numbers and create formulas for many situations.

Can a word be a variable?

Typically, we use single letters like x or y, but words can also be used if clearly defined.

Is 2x the same as x + x?

Yes! 2x means two times x, which is the same as adding x to itself.

Why is algebra important?

Algebra helps us solve problems when we need to learn all the details. It is used in many areas like science, engineering, and everyday life!

Can there be more than one variable in an expression?

Absolutely! An expression can have multiple variables like 2x + 3y.

This article is just a glimpse into the world of algebraic expressions. You will become an algebra wizard in no time with practice and patience! Keep exploring and keep asking questions.

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