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Algebra 186 views·Updated May 27, 2026·3 pagesMaster Operations with Numbers and Simplify Expressions
Cosmic@cosmicfufu
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Operations with Numbers
Absolute value is simple - it's just the distance from zero on a number line. For example, |-4| = 4 and |3.5| = 3.5 because they're both positive distances from zero. And |0| = 0 because zero is zero!
When adding real numbers, remember that combining negative numbers gives you a more negative result. For instance, -12 + (-14) = -26. But when you add a negative and positive number, they can cancel each other out, like -0.3 + 0.7 = 0.4.
Finding the opposite of a number means changing its sign. If x = -6, then -x = 6. If x = 1/2, then -x = -1/2.
Quick Tip: When subtracting numbers, you can rewrite it as addition with an opposite. For example, 6 - 13 becomes 6 + (-13) = -7.
With exponents, pay attention to parentheses! (-6)² means square the negative number (36), while -6² means the negative of the square (-36). Even exponents of negative numbers give positive results, while odd exponents preserve the negative sign.
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More Operations & Properties
Division with real numbers follows a simple pattern: when dividing numbers with different signs, your answer is negative. With same signs, your answer is positive. For example, 20 ÷ (-4) = -5.
Remember PEMDAS when solving complex expressions. Always work from left to right when operations have the same priority!
The commutative property lets you change the order of numbers being added or multiplied without changing the result. For example, 3x + 7 is the same as 7 + 3x (addition), and 3x can be written as x3 (multiplication).
Remember: The commutative property only works for addition and multiplication—not for subtraction or division!
The associative property allows you to regroup numbers being added or multiplied. For example, 7 + = (7 + 3) + x = 10 + x. With multiplication, -6(5x) can be written as (-6 × 5)x = -30x.
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Simplifying Expressions
The distributive property helps you multiply a number by everything inside parentheses. For instance, -2 becomes -6x - 10 because you multiply both terms by -2.
When simplifying expressions, combine like terms by adding their coefficients. In 7x + 12x² + 3x + x², the like terms are 7x and 3x (both have x¹) and 12x² and x² (both have x²). This simplifies to 10x + 13x².
For more complex expressions like 4 - 10x, first use the distributive property to get 28x - 12 - 10x, then combine like terms to get 18x - 12.
Pro Tip: When simplifying expressions with brackets inside brackets, always work from the innermost brackets outward!
Remember that operations with negative numbers follow specific patterns: when adding negatives, your number becomes more negative. When multiplying two negatives, your answer is positive (-16)(-30) = 480.
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Algebra 186 views·Updated May 27, 2026·3 pagesMaster Operations with Numbers and Simplify Expressions
Cosmic@cosmicfufu
Ready to master basic math operations? Let's dive into working with real numbers, absolute values, and simplifying expressions. These skills will help you solve more complex math problems and are essential building blocks for algebra and beyond.
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Operations with Numbers
Absolute value is simple - it's just the distance from zero on a number line. For example, |-4| = 4 and |3.5| = 3.5 because they're both positive distances from zero. And |0| = 0 because zero is zero!
When adding real numbers, remember that combining negative numbers gives you a more negative result. For instance, -12 + (-14) = -26. But when you add a negative and positive number, they can cancel each other out, like -0.3 + 0.7 = 0.4.
Finding the opposite of a number means changing its sign. If x = -6, then -x = 6. If x = 1/2, then -x = -1/2.
Quick Tip: When subtracting numbers, you can rewrite it as addition with an opposite. For example, 6 - 13 becomes 6 + (-13) = -7.
With exponents, pay attention to parentheses! (-6)² means square the negative number (36), while -6² means the negative of the square (-36). Even exponents of negative numbers give positive results, while odd exponents preserve the negative sign.
2
of 3Sign up to see the content. It's free!
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More Operations & Properties
Division with real numbers follows a simple pattern: when dividing numbers with different signs, your answer is negative. With same signs, your answer is positive. For example, 20 ÷ (-4) = -5.
Remember PEMDAS when solving complex expressions. Always work from left to right when operations have the same priority!
The commutative property lets you change the order of numbers being added or multiplied without changing the result. For example, 3x + 7 is the same as 7 + 3x (addition), and 3x can be written as x3 (multiplication).
Remember: The commutative property only works for addition and multiplication—not for subtraction or division!
The associative property allows you to regroup numbers being added or multiplied. For example, 7 + = (7 + 3) + x = 10 + x. With multiplication, -6(5x) can be written as (-6 × 5)x = -30x.
3
of 3Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
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Simplifying Expressions
The distributive property helps you multiply a number by everything inside parentheses. For instance, -2 becomes -6x - 10 because you multiply both terms by -2.
When simplifying expressions, combine like terms by adding their coefficients. In 7x + 12x² + 3x + x², the like terms are 7x and 3x (both have x¹) and 12x² and x² (both have x²). This simplifies to 10x + 13x².
For more complex expressions like 4 - 10x, first use the distributive property to get 28x - 12 - 10x, then combine like terms to get 18x - 12.
Pro Tip: When simplifying expressions with brackets inside brackets, always work from the innermost brackets outward!
Remember that operations with negative numbers follow specific patterns: when adding negatives, your number becomes more negative. When multiplying two negatives, your answer is positive (-16)(-30) = 480.
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 in Algebra 1
9Most popular content
9Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google 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 SiOS 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 KlichAndroid 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.
AnnaiOS user