A comprehensive guide to solving basic mathematical equations, focusing on... Show more
Algebra 1
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Updated Mar 2, 2026
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Math Equations: Examples, Formulas, and Solving Tips - Free PDF Included
1 / 10
Mental Math Solutions
This section focuses on solving equations through mental calculation strategies and verification methods.
Example: When solving 4 + b = 10, students learn to test different values (5, 6, 7) to find the correct solution.
Highlight: Mental math strategies involve thinking about what number, when combined with the given operation, yields the desired result.
Example: For m - 5 = 2, students think "what number minus 5 equals 2?" to arrive at 7 as the solution.
Addition Equations and Properties
This section covers solving addition equations using models and the subtraction property of equality.
Definition: Inverse operations are operations that undo each other, like addition and subtraction.
Vocabulary: The subtraction property states that subtracting the same number from both sides of an equation maintains equality.
Example: Solving x + 4 = 5 using both physical models (counters) and algebraic methods.
Word Problem Applications
This section demonstrates practical applications of addition equations through word problems.
Example: A swimming problem where Julie swam 575 meters, which was 150 meters more than Len, is solved using the equation L + 150 = 575.
Highlight: The solution process includes setting up the equation, solving algebraically, and verifying the answer.
Subtraction Equations
Focuses on solving subtraction equations using the addition property of equality.
Definition: The addition property of equality states that adding the same number to both sides of an equation maintains equality.
Example: Solving x - 5 = 10 using both modeling and symbolic methods.
Highlight: Solutions can be verified by substituting the answer back into the original equation.
Financial Applications
This section applies subtraction equations to real-world financial scenarios.
Example: Calculating an initial bank balance after a $50 withdrawal results in $124, using the equation I - 50 = 124.
Highlight: The solution process emphasizes practical application of mathematical concepts.
Multiplication Equations
Covers solving multiplication equations using division and bar diagrams.
Definition: The division property of equality states that dividing both sides by the same non-zero number maintains equality.
Example: Solving 6x = 18 using division and verification methods.
Practical Multiplication Problems
Demonstrates real-world applications of multiplication equations.
Example: A baking problem where 4 cups of flour makes 2 loaves of bread is solved using the equation 2f = 4.
Highlight: Bar diagrams help visualize and solve multiplication problems.
Division Equations
Explores solving division equations using the multiplication property of equality.
Definition: The multiplication property of equality states that multiplying both sides by the same non-zero number maintains equality.
Example: Solving p/7 = 5 using both modeling and symbolic methods.
Applied Division Problems
Concludes with practical applications of division equations.
Example: Finding the total number of sixth-grade students when one-fourth participate in after-school sports.
Highlight: Real-world problems help students understand practical applications of division equations.
Introduction to Equations
This chapter introduces the fundamentals of solving equations and determining equality between expressions. The focus is on developing mental math skills for basic operations.
Definition: An equation is a mathematical sentence showing two expressions are equal, containing an equal sign.
Example: In the equation 5 + y = 21, students learn to identify components and solve for the variable.
Vocabulary: An expression is a combination of numbers and operations which might contain variables .
Highlight: The solution to an equation is the value that makes the equation true when substituted for the variable.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content: Solve
Most popular content in Mathematics
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Math Equations: Examples, Formulas, and Solving Tips - Free PDF Included
A comprehensive guide to solving basic mathematical equations, focusing on mental calculations and fundamental algebraic operations. This guide covers essential equation-solving techniques for addition, subtraction, multiplication, and division operations, with detailed examples and step-by-step solutions.
• The... Show more
Mental Math Solutions
This section focuses on solving equations through mental calculation strategies and verification methods.
Example: When solving 4 + b = 10, students learn to test different values (5, 6, 7) to find the correct solution.
Highlight: Mental math strategies involve thinking about what number, when combined with the given operation, yields the desired result.
Example: For m - 5 = 2, students think "what number minus 5 equals 2?" to arrive at 7 as the solution.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Addition Equations and Properties
This section covers solving addition equations using models and the subtraction property of equality.
Definition: Inverse operations are operations that undo each other, like addition and subtraction.
Vocabulary: The subtraction property states that subtracting the same number from both sides of an equation maintains equality.
Example: Solving x + 4 = 5 using both physical models (counters) and algebraic methods.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Word Problem Applications
This section demonstrates practical applications of addition equations through word problems.
Example: A swimming problem where Julie swam 575 meters, which was 150 meters more than Len, is solved using the equation L + 150 = 575.
Highlight: The solution process includes setting up the equation, solving algebraically, and verifying the answer.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Subtraction Equations
Focuses on solving subtraction equations using the addition property of equality.
Definition: The addition property of equality states that adding the same number to both sides of an equation maintains equality.
Example: Solving x - 5 = 10 using both modeling and symbolic methods.
Highlight: Solutions can be verified by substituting the answer back into the original equation.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Financial Applications
This section applies subtraction equations to real-world financial scenarios.
Example: Calculating an initial bank balance after a $50 withdrawal results in $124, using the equation I - 50 = 124.
Highlight: The solution process emphasizes practical application of mathematical concepts.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Multiplication Equations
Covers solving multiplication equations using division and bar diagrams.
Definition: The division property of equality states that dividing both sides by the same non-zero number maintains equality.
Example: Solving 6x = 18 using division and verification methods.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Practical Multiplication Problems
Demonstrates real-world applications of multiplication equations.
Example: A baking problem where 4 cups of flour makes 2 loaves of bread is solved using the equation 2f = 4.
Highlight: Bar diagrams help visualize and solve multiplication problems.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Division Equations
Explores solving division equations using the multiplication property of equality.
Definition: The multiplication property of equality states that multiplying both sides by the same non-zero number maintains equality.
Example: Solving p/7 = 5 using both modeling and symbolic methods.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Applied Division Problems
Concludes with practical applications of division equations.
Example: Finding the total number of sixth-grade students when one-fourth participate in after-school sports.
Highlight: Real-world problems help students understand practical applications of division equations.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Introduction to Equations
This chapter introduces the fundamentals of solving equations and determining equality between expressions. The focus is on developing mental math skills for basic operations.
Definition: An equation is a mathematical sentence showing two expressions are equal, containing an equal sign.
Example: In the equation 5 + y = 21, students learn to identify components and solve for the variable.
Vocabulary: An expression is a combination of numbers and operations which might contain variables .
Highlight: The solution to an equation is the value that makes the equation true when substituted for the variable.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content: Solve
Most popular content in Mathematics
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user