solving algebraic equations in real life worksheet

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Equation Word Problems Worksheets

This compilation of a meticulously drafted equation word problems worksheets is designed to get students to write and solve a variety of one-step, two-step and multi-step equations that involve integers, fractions, and decimals. These worksheets are best suited for students in grade 6 through high school. Click on the 'Free' icons to sample our handouts.

One Step Equation Word Problem Worksheets

Read and solve this series of word problems that involve one-step equations. Apply basic operations to find the value of unknowns.

(15 Worksheets)

Two-Step Equation Word Problems: Integers

Interpret this set of word problems that require two-step operations to solve the equations. Each printable worksheet has five word problems ideal for 6th grade, 7th grade, and 8th grade students.

Two-Step Equation Word Problems: Fractions and Decimals

Read each word problem and set up the two-step equation. Solve the equation and find the solution. This selection of worksheets includes both fractions and decimals.

MCQ - Two-Step Equation Word Problems

Pick the correct two-step equation that best matches word problems presented here. Evaluate the ability of students to solve two-step equations with this array of MCQ worksheets.

Multi-Step Equation Word Problems: Integers

Read each multi-step word problem in these high school pdf worksheets and set up the equation. Solve and find the value of the unknown. More than two steps are required to solve the problems.

Multi-step equation Word Problems: Fractions and Decimals

Write multi-step equations that involve both fractions and decimals based on the word problems provided here. Validate your responses with our answer keys.

Related Worksheets

» One-step Equation

» Two-step Equation

» Multi-step Equation

» Algebraic Identities

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Linear Equations Project with Real World Relationships

Systems of Equations and Inequalities - Real World Applications

Write Equations Slope-Intercept Form from Real World Situations Guided Notes

Linear Equations Real World Project - Build Your Own Amusement Park

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6th Grade Writing Equations from Real-World Problems PowerPoint

Algebra Project - Real World Linear Equations and Inequalities

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6th Grade Creating Expressions & Equations from Real World Problems 6.EE.B.7

Real World Linear Equations, Tables, and Graphs Power Point 3 Lesson Pack

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Going to the Fair: Equations and Expressions Project | Real World Math Project

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Write and Solve Real World Two Step Equations

Real life exponential equations--Murder Mystery

Real-World Applications of Systems of Equations Algebra 1 Curriculum

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Real Life Equations and Inequalities Quiz (TEKS 7.10C)

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Algebra Worksheets

Welcome to the Algebra worksheets page at Math-Drills.com, where unknowns are common and variables are the norm. On this page, you will find Algebra worksheets mostly for middle school students on algebra topics such as algebraic expressions, equations and graphing functions.

This page starts off with some missing numbers worksheets for younger students. We then get right into algebra by helping students recognize and understand the basic language related to algebra. The rest of the page covers some of the main topics you'll encounter in algebra units. Remember that by teaching students algebra, you are helping to create the future financial whizzes, engineers, and scientists that will solve all of our world's problems.

Algebra is much more interesting when things are more real. Solving linear equations is much more fun with a two pan balance, some mystery bags and a bunch of jelly beans. Algebra tiles are used by many teachers to help students understand a variety of algebra topics. And there is nothing like a set of co-ordinate axes to solve systems of linear equations.

Most Popular Algebra Worksheets this Week

$Combining Like Terms and Solving Simple Linear Equations$

Properties and Laws of Numbers Worksheets

The commutative law.

$solving algebraic equations in real life worksheet$

The commutative law or commutative property states that you can change the order of the numbers in an arithmetic problem and still get the same results. In the context of arithmetic, it only works with addition or multiplication operations , but not mixed addition and multiplication. For example, 3 + 5 = 5 + 3 and 9 × 5 = 5 × 9. A fun activity that you can use in the classroom is to brainstorm non-numerical things from everyday life that are commutative and noncommutative. Putting on socks, for example, is commutative because you can put on the right sock then the left sock or you can put on the left sock then the right sock and you will end up with the same result. Putting on underwear and pants, however, is noncommutative.

The Associative Law

$solving algebraic equations in real life worksheet$

The associative law or associative property allows you to change the grouping of the operations in an arithmetic problem with two or more steps without changing the result. The order of the numbers stays the same in the associative law. As with the commutative law, it applies to addition-only or multiplication-only problems. It is best thought of in the context of order of operations as it requires that parentheses must be dealt with first. An example of the associative law is: (9 + 5) + 6 = 9 + (5 + 6). In this case, it doesn't matter if you add 9 + 5 first or 5 + 6 first, you will end up with the same result. Students might think of some examples from their experience such as putting items on a tray at lunch. They could put the milk and vegetables on their tray first then the sandwich or they could start with the vegetables and sandwich then put on the milk. If their tray looks the same both times, they will have modeled the associative law. Reading a book could be argued as either associative or nonassociative as one could potentially read the final chapters first and still understand the book as well as someone who read the book the normal way.

Inverse relationships with one blank

$solving algebraic equations in real life worksheet$

Inverse relationships worksheets cover a pre-algebra skill meant to help students understand the relationship between multiplication and division and the relationship between addition and subtraction.

Inverse relationships with two blanks

$solving algebraic equations in real life worksheet$

Missing Numbers or Unknowns in Equations Worksheets

Missing numbers in equations worksheets in three types: blanks for unknowns, symbols for unknowns and variables for unknowns.

Missing Numbers Worksheets with Blanks as Unknowns

$solving algebraic equations in real life worksheet$

In these worksheets, the unknown is limited to the question side of the equation which could be on the left or the right of equal sign.

Missing Numbers Worksheets with Symbols as Unknowns

$solving algebraic equations in real life worksheet$

Equalities with addition on both sides of the equation and symbols as unknowns

$solving algebraic equations in real life worksheet$

Missing numbers worksheets with variables as unknowns

$solving algebraic equations in real life worksheet$

Solving Simple Linear Equations

$solving algebraic equations in real life worksheet$

Algebraic Expressions Worksheets

Using the distributive property.

$solving algebraic equations in real life worksheet$

The distributive property is an important skill to have in algebra. In simple terms, it means that you can split one of the factors in multiplication into addends, multiply each addend separately, add the results, and you will end up with the same answer. It is also useful in mental math, and example of which should help illustrate the definition. Consider the question, 35 × 12. Splitting the 12 into 10 + 2 gives us an opportunity to complete the question mentally using the distributive property. First multiply 35 × 10 to get 350. Second, multiply 35 × 2 to get 70. Lastly, add 350 + 70 to get 420. In algebra, the distributive property becomes useful in cases where one cannot easily add the other factor before multiplying. For example, in the expression, 3(x + 5), x + 5 cannot be added without knowing the value of x. Instead, the distributive property can be used to multiply 3 × x and 3 × 5 to get 3x + 15.

Evaluating algebraic expressions

$solving algebraic equations in real life worksheet$

Exponent Rules and Properties

Practice with basic exponent rules.

$solving algebraic equations in real life worksheet$

As the title says, these worksheets include only basic exponent rules questions. Each question only has two exponents to deal with; complicated mixed up terms and things that a more advanced student might work out are left alone. For example, 4 2 is (2 2 ) 2 = 2 4 , but these worksheets just leave it as 4 2 , so students can focus on learning how to multiply and divide exponents more or less in isolation.

Linear Expressions & Equations

Linear equations worksheets including simplifying, graphing, evaluating and solving systems of linear equations.

Translating algebraic phrases in words to algebraic expressions

$solving algebraic equations in real life worksheet$

Knowing the language of algebra can help to extract meaning from word problems and to situations outside of school. In these worksheets, students are challenged to convert phrases into algebraic expressions.

Simplifying linear expressions (combining like terms)

$solving algebraic equations in real life worksheet$

Combining like terms is something that happens a lot in algebra. Students can be introduced to the topic and practice a bit with these worksheets. The bar is raised with the adding and subtracting versions that introduce parentheses into the expressions. For students who have a good grasp of fractions, simplifying simple algebraic fractions worksheets present a bit of a challenge over the other worksheets in this section.

Rewriting linear equations

$solving algebraic equations in real life worksheet$

Determining linear equations from slopes, y-intercepts, and points

$solving algebraic equations in real life worksheet$

Linear Equation Graphs

$solving algebraic equations in real life worksheet$

Graphing linear equations and reading existing graphs give students a visual representation that is very useful in understanding the concepts of slope and y-intercept.

Solving linear equations with jelly beans is a fun activity to try with students first learning algebraic concepts. Ideally, you will want some opaque bags with no mass, but since that isn't quite possible (the no mass part), there is a bit of a condition here that will actually help students understand equations better. Any bags that you use have to be balanced on the other side of the equation with empty ones.

Probably the best way to illustrate this is through an example. Let's use 3 x + 2 = 14. You may recognize the x as the unknown which is actually the number of jelly beans we put in each opaque bag. The 3 in the 3 x means that we need three bags. It's best to fill the bags with the required number of jelly beans out of view of the students, so they actually have to solve the equation.

On one side of the two-pan balance, place the three bags with x jelly beans in each one and two loose jelly beans to represent the + 2 part of the equation. On the other side of the balance, place 14 jelly beans and three empty bags which you will note are required to "balance" the equation properly. Now comes the fun part... if students remove the two loose jelly beans from one side of the equation, things become unbalanced, so they need to remove two jelly beans from the other side of the balance to keep things even. Eating the jelly beans is optional. The goal is to isolate the bags on one side of the balance without any loose jelly beans while still balancing the equation.

The last step is to divide the loose jelly beans on one side of the equation into the same number of groups as there are bags. This will probably give you a good indication of how many jelly beans there are in each bag. If not, eat some and try again. Now, we realize this won't work for every linear equation as it is hard to have negative jelly beans, but it is another teaching strategy that you can use for algebra.

Solving linear equations

$solving algebraic equations in real life worksheet$

Despite all appearances, equations of the type a/ x are not linear. Instead, they belong to a different kind of equations. They are good for combining them with linear equations, since they introduce the concept of valid and invalid answers for an equation (what will be later called the domain of a function). In this case, the invalid answers for equations in the form a/ x , are those that make the denominator become 0.

Linear Systems

Solving systems of linear equations.

$solving algebraic equations in real life worksheet$

Solving systems of linear equations by graphing

$solving algebraic equations in real life worksheet$

Quadratic Expressions & Equations

Quadratic expressions and equations worksheets including multiplying factors, factoring, and solving quadratic equations.

Simplifying quadratic expressions (combining like terms)

$solving algebraic equations in real life worksheet$

Adding/Subtracting and Simplifying quadratic expressions

$solving algebraic equations in real life worksheet$

Multiplying factors of quadratic expressions

$solving algebraic equations in real life worksheet$

Factoring quadratic expressions

$solving algebraic equations in real life worksheet$

The factoring quadratic expressions worksheets in this section provide many practice questions for students to hone their factoring strategies. If you would rather worksheets with quadratic equations, please see the next section. These worksheets come in a variety of levels with the easier ones are at the beginning. The 'a' coefficients referred to below are the coefficients of the x 2 term as in the general quadratic expression: ax 2 + bx + c. There are also worksheets in this section for calculating sum and product and for determining the operands for sum and product pairs.

Whether you use trial and error, completing the square or the general quadratic formula, these worksheets include a plethora of practice questions with answers. In the first section, the worksheets include questions where the quadratic expressions equal 0. This makes the process similar to factoring quadratic expressions, with the additional step of finding the values for x when the expression is equal to 0. In the second section, the expressions are generally equal to something other than x, so there is an additional step at the beginning to make the quadratic expression equal zero.

Solving Quadratic equations that Equal Zero (e.g. ax² + bx + c = 0)

$solving algebraic equations in real life worksheet$

Solving Quadratic equations that Equal an Integer (e.g. ax² + bx + c = d)

$solving algebraic equations in real life worksheet$

Other Polynomial and Monomial Expressions & Equations

Factoring non-quadratic expressions worksheets with various levels of complexity.

Simplifying polynomials that involve addition and subtraction

$solving algebraic equations in real life worksheet$

Simplifying polynomials that involve multiplication and division

$solving algebraic equations in real life worksheet$

Simplifying polynomials that involve addition, subtraction, multiplication and division

$solving algebraic equations in real life worksheet$

Factoring expressions that do not include a squared variable

$solving algebraic equations in real life worksheet$

Factoring expressions that always include a squared variable

$solving algebraic equations in real life worksheet$

Factoring expressions that sometimes include squared variables

$solving algebraic equations in real life worksheet$

Multiplying polynomials with two factors

$solving algebraic equations in real life worksheet$

Multiplying polynomials with three factors

$solving algebraic equations in real life worksheet$

Inequalities Including Graphs

Inequalities worksheets including writing the inequality that matches a graph and graphing inequalities on a number line.

Writing the inequality that matches the graph

$solving algebraic equations in real life worksheet$

Graphing inequalities on number lines

$solving algebraic equations in real life worksheet$

Solving linear inequalities

$solving algebraic equations in real life worksheet$

Math Worksheets

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Equations and Word Problems

These free equations and word problems worksheets will help your students practice writing and solving equations that match real-world story problems.

These free algebra worksheets are printable and available in a variety of formats. Of course, answer keys are provided with each free algebra worksheet.

Equations and Word Problems ( Two Step Equations ) Worksheets

Equations and Word Problems (Two Step Equations) Worksheet 1 – This 10 problem worksheet will help you practice writing and solving two step equations that match real world situations. Equations and Word Problems (Two Step Equations) Worksheet 1 RTF Equations and Word Problems (Two Step Equations) Worksheet 1 PDF Preview Equations and Word Problems Worksheet 1 In Your Web Browser View Answers

Equations and Word Problems (Two Step Equations) Worksheet 2 – This 10 problem worksheet will help you practice writing and solving two step equations that match real world situations. Equations and Word Problems (Two Step Equations) Worksheet 2 RTF Equations and Word Problems (Two Step Equations) Worksheet 2 PDF Preview Equations and Word Problems Worksheet 2 In Your Web Browser View Answers

Equations and Word Problems ( Combining Like Terms ) Worksheets

Equations and Word Problems (Combining Like Terms) Worksheet 1 – This 10 problem worksheet will help you practice writing and solving equations that match real world situations. You will have to combine like terms and then solve the equation. Equations and Word Problems (Combining Like Terms) Worksheet 1 RTF Equations and Word Problems (Combining Like Terms) Worksheet 1 PDF Preview Equations and Word Problems Worksheet 1 In Your Web Browser View Answers

Equations and Word Problems (Combining Like Terms) Worksheet 2 – This 10 problem worksheet will help you practice writing and solving equations that match real world situations. You will have to combine like terms and then solve the equation. Equations and Word Problems (Combining Like Terms) Worksheet 2 RTF Equations and Word Problems (Combining Like Terms) Worksheet 2 PDF Preview Equations and Word Problem Worksheet 2 In Your Web Browser View Answers

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Print solving equations worksheets, click the buttons to print each worksheet and associated answer key., moving variables lesson.

Learn how to determine the value of a variable in an equation. Example: x + 1 = 9

Solve for X Worksheet 1

Solve for x for each of these 10 equations. These are two-step problems, mostly. For example these are the basic problem types: 7x + 4 = 494

Worksheet 2

Remember that two negative values form a positive product. Example: 54 = -6x

Solving Equations Review

There is a short lesson at the top to show you how to solve equations with multiple instances of the the same variable. Follow the steps to solve for x: x + 4 = 12. The worksheet also contains 10 problems for you to finish.

Equation Quiz

Solve for x for each of these 10 problems, then check and score your answers below. Example: -64 = x - 76

Do Now Do Now

This is a great class activity to process together. They will have multiple instances of the same variables. So we get into combining like terms. Example: x+ 9 = 2x + 5

3 and 4 Step Lesson

Follow the steps to solve the following equation: x + 2 = 3x + (-16). This will help students become comfortable with 3 and 4 step equation solving.

3 Step Worksheet

You will work on solving the following types of equations: x + 9 = 18 + (-2x). You will work on 3 step problems.

Decimal Equation Worksheet

We get all decimally with these problems. Not all of them, but some have decimals in the equations. Here is an example: 6.2x - 5 = 7.9x + 3.5

Lots of Steps Worksheet

You are going to have to take a few more steps than you are used to here. Example: 6x - 3 = 4x + 7 (2)

Many Moves Worksheet

Your primary goal should be to get your variables and constants together. Example: 2x + 9 = 9x - 271

Equation Warm Up

This will get you fluid with this skill and ready to tackle bigger problems. Example: -14x + 8 = -8x + 248

Basic Skills: Solving Equations Practice

For these 10 problems, solve for each variable. The problems are more 2 and 3 step problems. Example: 2x + 5 = 9

Basic Skills - Independent Practice 2

There are two instances of the variable in most of these problems. You will need to combine like terms. Example: 2x - x=8

Intermediate Skills Practice 1

The parentheses start to complicate things a bit here for you. Example: y - (2y+3) = 3(1 - 2y) - 6

Intermediate Skills Practice 2

These can be solved in just a few quick steps, but you will need to understand the process deeply. Example: 5x - (3x-1) = x-4

Intermediate Skills Practice 3

The last worksheet in the series. This is a bit challenging, but should be very doable for most students. Example: 2(a - 2) + 3(4a - 1) = 0

Solve for the Unknown Lesson

The next 4 worksheets are all for more advanced learners. Students will learn how to solve problems like the following: log 2 b + log 2 49 = 9. Then practice using the problems given below them.

Unknowns Worksheet 1

Logs rear up on this worksheet. Students should be comfortable with logs to handle these problems. Example: log 6 289 + log 6 a = 3.48

Solve for the Unknown Worksheet 2

For these 10 problems, solve for the unknown. These are slightly more advanced problems. Example: log 2 16 + log(2) 144 = 5

Higher Level Review Worksheet

Not the easiest problems, but not that bad when you plan it out. The types of problems that you will see on here resemble this: log 2 t + log 2 144 = 289

Unknowns Quiz

Complete these 10 problems, then check and score your answers below. Example: log 6 54 + log 6 r = 3.12

Solve Them Do Now

Here is an e xample problem from this worksheet: log 6 125 + log 6 h = 3.01. These are slightly more complex equations to work with.

How to Solve an Algebraic Equation

You must be wondering; what place do letters have in mathematics? Well, letters have had quite a significant role to play in the world of mathematics since algebra was invented. The importance of mathematics is easy to note through the frustration you experience when solving word problems.

Johnny has trees that produce twice as many apples as he currently has. His friend gifts him three apples. Knowing that Johnny now has 17 apples, how many did he initially have?

Now try solving the following equation.

2x + 3 = 17

How easy was that? Imagine a world where people used language to explain an equation that could easily be translated through algebra! What a difficult world that would be.

Now that we have established the importance of numbers in math, let's figure out how to solve an algebraic equation.

What are Algebraic Equations?

Equations are statements in mathematics with two expressions on either side, separated by an equal sign. Algebraic equations contain letters as well as numbers. Letters stand for variables, whereas numbers are constants. Equations can include single and double variables, depending on complexity.

Solving equations is not hard if you look at them as a way to explain complicated situations using numbers. This viewpoint helps give you perspective and view mathematical equations as a challenge rather than an impossible feat.

The most important thing to remember about equations is that they are 'equal,' meaning that whatever you apply to one side to solve the equation needs to be applied to the other. Simplification allows for easy problem-solving. Once the equation is simplified, it is solved.

How to Solve an Algebraic Equation?

There are many different kinds of algebraic equations. However, they can be broadly categorized into two main kinds. We have single-variable and multiple-variable equations (further split into two or more variables).

1. Single Variable Equations

These are relatively easy to solve. The easier the equation, the lesser time it will take you to reach the solution.

The first kind is pretty simple, and the answer lies within the question.

Here, the solution to the algebraic question is hidden in the question. The answer is "x=2."

However, consider the second example below.

2x – 1 = 11

What we need to prioritize here is to bring x to one side. However, we cannot simply take it there.

2x – 1 + 1 = 11

To eliminate 1, we can add 1 to the left side. However, this means we also need to add 1 to the right side.

2x – 1 + 1 = 11 + 1

We are left with the following solution.

To further simplify the expression on the left side, we need to eliminate the multiple of 2. We can do this by dividing the left side by 2.

2x / 2 = 12

However, this means we also need to divide the right side by 2.

2x / 2 = 12 / 2

Much better! Now, all we need to do is calculate the results.

Plugging the six back into the equation leads to 11, confirming our solution! This trick is a great way to test any sum you have solved.

2. Double Variable Equations

These equations can only be solved using simultaneous equations and are slightly more complicated than the regular single-digit equation! In fact, they deserve a guide of their own!

Final Thoughts

How to solve an algebraic equation?

The answer depends on the kind of equation you are supposed to be solving. However, the rules remain the same.

Isolate the x, and remember to apply everything on both sides!

How to Keep Your Equation Solving Skills Sharp

An equation just tells us that two things are the equivalent of one another. What ever is to the right and left of the equals symbol is equal to the each other. The goal of solving equation is to find a solution that could replace the variable or multiple variables. If there is just a single variable, this is not that difficult. The process is just to get that variable by itself. For instances in the example: 3x - 4 = 2 we would follow two steps to complete this. As long as we do the same time to both sides of the equation, we can counterbalance any operations that are taking place. In this example we can achieve this by added 4 to both sides and this would leave us with: 3x = 6. Using the same principle, we would divide both sides by 2 and be left with x= 2. You will run into problems that have more than one solution. This can be frustrating, but they are doable. In some instances, you may need to guess values in those situations and that is okay until you get more experience with these types of problems. You put our energy into working through algebraic equations by applying basic principles. These sets range in difficulty from basic to intermediate, and may involve exponents, and some logarithms. We are mostly focused on solving for the final unknown variable for each equation. This is one of the key skills in algebra. If you are good at it, it will serve you well in College and even the real world on a daily basis.

Solving equations can be frustrating for students. You need sharp equation-solving skills when working on simple or complex algebraic problems. Many students face problems in evaluating correct answers while solving mathematical problems. Teachers often struggle to teach them the correct methods of solving problems.

If you want to improve your equation-solving skills, we have some tips that can help. The following ways can help you improve your analytical thinking and problem-solving abilities.

Tips to Enhance Equation Solving Skills

Understanding Functions

The most common problem that students face in solving equations is understanding functions. Mathematical equations typically involve multiple functions, including addition, subtraction, multiplication, and division. These functions may be simple to understand alone. However, solving them together in a single problem can be overwhelming.

If you want to sharpen your problem-solving skills, you may need to understand the correct order and method of solving each function in an equation.

Learn New Concepts

One of the essential tips to improve your problem-solving skills is to focus on learning new concepts. Students often stick to the curriculum. They do not spend time learning new mathematical concepts and functions. One of the best ways is to try solving challenging problems without seeking the teacher’s assistance.

If you get stuck, review the concepts and try solving the problem again. You can improve your equation-solving by identifying the problem in your equations.

Always Do Extra

Mathematical functions can be frustrating. You may exhaust yourself by solving a few equations. While this may be correct, covering extra problems can help you perform better. You not only learn to perfect your skills but also improve your speed. To find challenging equations, you can look up Google and search for as many equations as you like.

It is crucial to start with simpler problems. Once you grasp them, you can gradually proceed with complex equations. However, you may not want to try too many new concepts daily. They may be difficult to absorb.

Create Your Own Equations

Creating equations is one of the best ways to improve your equation-solving skills. Students typically rely on the word problems listed in the curriculum books. Although these problems can be sufficient to teach the concepts, altering them with different scenarios can perfect your skills. Changing the values in word problems can also be effective.

You can start with changing the values in an equation. If you successfully evaluate the answer, proceed with changing the conditions in a statement. You can solve the problem under the new conditions and evaluate your answer.

Find Relevance In Daily Life

What many students fail to realize in the earlier stages of their schooling is that mathematics finds its relevance in our daily lives. If you solve word problems, you may be able to understand how we can incorporate mathematics into our daily tasks. When you solve an equation, try to relate it to real-world examples.

By applying your everyday tasks to your problem-solving activities, you can learn to perform better.

Learn Number Tricks

Mathematics is full of surprises. Every number has a significant and unique role in problem-solving. You can find resourceful materials online to learn about the role of numbers in multiplication and division. Using number tricks can save you time and frustration while solving equations.

Most number tricks apply to dividing and multiplying bigger numbers. You do not have to spend too much time simplifying complex numbers.

Wrapping Up

Solving equations may seem a troublesome task. However, you can improve your skills by using the methods mentioned above. If you want to find more tips, you can search online and work on your equation-solving skills.

Algebra in Everyday Life

We use algebra quite frequently in our everyday lives, and without even realizing it! We not only use algebra, we actually need algebra, to solve most of our problems that involves calculations.

Examples of using algebra in everyday life

Here are some simple examples that demonstrate the relevance of algebra in the real world.

Going shopping

`(text(10 items))/(text (3 items/bag))` = `3.33` bags ≈ `4 bags `, explanation :.

The figure below illustrates the problem: The different shapes inside the bags denote different items purchased. The number depicts the item number.

We use simple algebraic formula `x/y` to calculate the number of bags.

x = Number of items purchased = 10

y = Capacity of 1 bag = 3

`10/3` = `3.33` bags ≈ `4` bags

So,we need 4 shopping bags to put 10 items.

Calculating grocery expense

The figure below shows the three items in different shapes and colors.

This will help your mind to calculate faster.

Algebra in Daily Life Exmaple with shopping

We will use algebra to solve the problem easily and quickly.

The prices are

a = Price of two dozen eggs = $10

b = Price of one bread = $5

c = Price of one bottle of juice= $8

=> Money needed = a + 3b + 5c

=> Money needed = $10 + 3($5) + 5($8) = $10 + $15 + $40 = $65

Filling up the gas tank

`5 ` gallons.

In the below diagram, each block represents $1, and each row is a bundle of $3, which is used to buy 1 gallon of gas.

Algebra in Daily Life example gas refill

We use simple algebraic formula,`x/y` to calculate the total gallons that can be bought.

x = Money in your pocket= $15

y = Price of 1 gallon of gas= $3

`($15)/($3)` = 5 gallon

So, with $15 we can buy 5 gallons of gas.

Word problems

Life's many problems are disguised in the form of math equations, and if we know the math, it's fairly simple to solve those problems.

Find three consecutive numbers whose sum is 216.

71, 72 and 73.

1. Understand the problem

The task is to find three consecutive numbers whose total is 216.

2. Write the variable

Let "`x`" represent the first number

So, `x` = first number

`x+1` = second number

`x+2`= third number

3. Write the equation

When you add up all the numbers, you are supposed to get 216

`x + (x + 1) + (x + 2 )`= 216

`3x + 3 `= 216

4. Solve the equation

Subtract 3 from both sides

`3x + 3 - 3 `= 216 - 3

`3x ` = 213

Divide each side by 3

`(3x) / 3 `= 213 ÷ 3

5. Check your answer

First number + Second number + Third number = 216

`x + (x + 1 )+ (x + 2)`

71 + (71 + 1) + (71 + 2)

71 + 72 + 73 = 216

So the three numbers whose sum is 216 are 71, 72 and 73

A group of 5 boys goes to the theatre for an evening show. The total cost of ticket is $55 and popcorn is $25. What is the cost per person?

A group of 5 boys goes to the theatre. The cost of ticket and popcorn is $55 and $25 respectively. What is cost per person?

Let’s say, `x` = cost of ticket/person and `y` = cost of popcorn/person

If 5 tickets cost $55, then cost of one ticket is,

`x ` = `55 / 5`

If 5 bags of popcorn cost $25, then the cost of each bag is,

`y ` = `25 / 5`

Total cost of the movie (ticket + popcorn) per person = `x + y `

Cost of ticket/person

`x` = `55 / 5`

Cost of popcorn/person

Cost of ticket/person + Cost of popcorn/person = Total cost

11 + 5 = 16

If we add up 16 five times (since there are 5 boys), the result is,

16 + 16 + 16 + 16 + 16 = 80

$80 is the total cost.

The area of a rectangle is 72`cm^2`, in which the width is twice its length. What is the dimension of the rectangle?

the length is 6 cm and the width is 12 cm.

The area of a rectangle is 72 cm. The width is twice its length. What is the length and width of the rectangle?

Let "`x`" be the length and "`2x`" be the width

Length `×` Width = Area

`x ` x `(2x)` = `2x^2 `= Area

So, the length is 6 cm

The width is twice its length

`2x` = 2 x 6 = 12

So, the width is 12 cm

The length is 6 cm and width is 12 cm

The perimeter i.e. the distance around the edges is the sum of lengths and widths. Since rectangle has two lengths and two breadths hence the equation is,

2 x (length + width)

2 x (6 + 12) = 2 x 18 = 36 cm

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Key to Algebra Workbooks

Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

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Algebra Word Problems Worksheets

In algebra word problems worksheets, we will talk about algebra, which is a branch of mathematics dealing with symbols and the rules for manipulating these symbols. They represent quantities without fixed values, known as variables. Solving algebraic word problems requires us to combine our ability to create and solve equations. Translating verbal descriptions into algebraic expressions is an essential initial step in solving word problems.

Benefits of Algebra Word Problems Worksheets

We use algebra in our everyday life without even realising it. Solving algebraic word problems worksheets help kids relate and understand the relevance of algebra in the real world. Algebra finds its way while cooking, measuring ingredients, sports, finance, professional advancement etc. They help in logical thinking and help students to break down a problem and then find its solution.

Download Algebra Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

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This Solving Algebraic Equations Activity is a Great Activity for any Algebra Class
Algebra 1: Chapter 3

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Solving Equations
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