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Master Upper and Lower Bounds: Essential Math Concepts

Basic Math: Master Essential Concepts & Skills

Numbers and Relations

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Negative numbers and opposite numbers

Opposite Integers — Up to 10

Understanding Negative Numbers

Upper and lower bound

Upper and Lower Bound

What is an integer?

Understanding the number systems

Place value

Comparing and ordering numbers

Comparing Integers

Comparing Numbers

Comparing Fractions

Rounding numbers

Rounding Decimals

Rounding Integers — Up to 9999

Rational and Irrational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Rational vs. Irrational numbers

Operations of Decimals

Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals 

Dividing Decimals

Order of operations (PEMDAS)

Identify the Order of Operations

Order of Operations — Word Problem

Converting repeating decimals to fractions

Factors and Multiples

Prime factorization

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest Common Factors (GCF)

Greatest Common Factor 2 Numbers

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers – Word Problem

Least Common Multiple (LCM)

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Divisibility rules

Divisibility

Determining Common Factors

Common Factors — Word problem: bouquet

Common Factors — Word problem: party

Common Factors

Factors

Determining common multiples

Common Multiples — Word problem: meals

Common Multiples — Word problem: watches

Multiples

Adding and Subtracting Integers

Introduction to integer addition

Adding 1-digit integers

Adding integers

Adding 2-digit integers

Introduction to integer subtraction

Integer Subtraction — Missing Value

Subtracting 1-digit integers

Subtracting integers

Subtracting 2-digit integers

Application of integer operations

Application of Integer Operations – Word Problem

Application of Integer Operations  – Word Problem

Multiplying and Dividing Integers

Understanding integer multiplication

Multiplying 1-digit Integers

Multiplying 1-digit integers Mixed Sign

Multiplying integers

Multiplying 2-Digit Integers

Multiplying 1 and 2 Digit Integers

Understanding integer division

Dividing by 1-Digit Integers

Dividing by 1-Digit Integers Mixed Sign

Dividing integers

Dividing by 2-Digit Integers

Dividing by 2-Digit Integers Mixed Sign

Applications of integer operations

Multiple Integer Operations

Three Step Integer Operations Combined Multiply Divid

Three Step Integer Operations Divide Add Or Minus Multiply

Three Step Integer Operations Divide Add Or Minus

Three Step Integer Operations Multiply Add Minus Divide

Three Step Integer Operations Multiply Add Or Minus

Fractions

What are fractions?

Comparing and ordering fractions

Ordering Fractions

Multiplying fractions and whole numbers

Multiply a fraction with a whole number

Multiplying Fractions — with whole numbers — 1 digit

Multiplying Fractions — with whole numbers — 2 digits

Application of Multiplying Fractions and Whole Numbers – Word Problems

Dividing fractions with whole numbers

Divide a fraction by a whole number

Divide a Fraction by a Whole Number

Divide a Fraction by a Whole Number Number RHS

Multiplying proper fractions

Multiply Proper Fractions — 1 Digit Fractions

Multiplying improper fractions and mixed numbers

Multiply Mixed Numbers

Dividing fractions and mixed numbers

Divide Fractions and Mixed Numbers – Word Problem

Dividing Mixed numbers

Dividing Mixed Numbers

Applications of fraction operations

Fraction Operations

Using models to add and subtract fractions

Add Fractions With Models

Subtract Fractions With Models

Adding fractions with like denominators

Adding Fractions — with like denominators — 3-digit without simplifying

Adding Fractions — with like denominators — 3-digit

Adding Fractions — Word problem: baking

Add fractions with like denominator

Adding Fractions — with like denominators — 1-digit

Adding Fractions — with like denominators — 2-digit

Adding Fractions — Word problem: beads

Subtracting fractions with like denominators 

Subtract fractions with like denominator

Subtracting Fractions — with like denominators — 2-digit

Subtracting Fractions — with like denominators — Larger 2-digit

Subtracting Fractions — with like denominators — 3 digit

Subtracting fractions — Word problem: competition

Subtracting fractions — Word problem: snack

Adding and subtracting fractions with unlike denominators

Adding and Subtracting Fractions — Find the lowest common denominator (LCD)

Adding and Subtracting Fractions — Find the LCD and evaluate

Add fractions with unlike denominator

Subtract fractions with unlike denominator

Adding and Subtracting Fractions — Word problem: cargo ship

Adding Fractions — with unlike denominators

Subtracting Fractions — with unlike denominators

Adding and subtracting mixed numbers

Adding Mixed Numbers — Word Problem

Subtracting Mixed Numbers — Word Problem

Add mixed fractions with like denominator

Add mixed fractions with unlike denominator

Rates, Ratios, and Proportions

What is ratio?

Converting among ratios, fractions and decimals

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

math

<h2>What is Math?</h2>
Math is the program of study that looks at things like <a href="https://en.wikipedia.org/wiki/Quantity">quantities</a> (numbers), <a href="https://en.wikipedia.org/wiki/Shape">shapes</a>, (geometry), and <a href="https://en.wikipedia.org/wiki/Calculus">continuous change</a> (calculus). It can be used to build video games, calculate tips at restaurants, and even <a href="https://www.studypug.com/blog/how-basic-math-can-lead-to-the-perfect-nights-sleep/">evaluate the perfect night&apos;s sleep</a>!
Math is a compulsory course of study that is taught at grade 1 through to grade 12, and students can continue to study math at college and university. Starting with elementary school math, young students are introduced to basic arithmetic problems (adding, subtracting, dividing and multiplication). As the students move on from simple math, they will explore topics like fractions, decimals, rounding numbers, and percentages. They will then move on to more complex elements like <a href="[[region_textbook.html|{"textbook_key":"basic-algebra"}]]">algebra</a>, <a href="[[region_textbook.html|{"textbook_key":"trigonometry"}]]">trigonometry</a>, and <a href="[[region_textbook.html|{"textbook_key":"calculus"}]]">calculus</a>.
The great thing about math is that it never changes, and its presence can be found in practically everything around us, from music and architecture, to video games and cooking. With that in mind, it's easy to see why learning math is so important.

<h2>What is Arithmetic?</h2>
Arithmetic is the area of math that deals with the properties and manipulation of numbers via "operations". These operations combine numbers (+), remove numbers (-), repeat additions (x), and separate numbers into equal groups (&divide;).
The operations are known by the following words:
<ul type="disc">
<li>Addition</li>
<li>Subtraction</li>
<li>Multiply</li>
<li>Divide</li>
</ul>
In arithmetic the equals sign (=) is used to highlight the answer of an operation.
For example: 2 + 2 = 4
The operation is addition and the equals sign points to the answer of the operation. Each operation has a different name for the answer and these are as follows:
<ul type="disc">
<li>The answer to an addition operation is known as the <q>sum</q></li>
<li>The answer to a subtraction operation is known as the <q>difference</q></li>
<li>The answer to a multiplication operation is known as the <q>product</q></li>
<li>The answer to a division operation is known as the <q>quotient</q></li>
</ul>
So if someone were to say "what's the sum of 6 and 4?" you&apos;ll know that they want you to add the two numbers together.

<h2>How Can I Learn Math?</h2>
The best way to learn math is to pay attention in class. Listening to your teacher will make math problems easier to follow and to solve. To help you learn in class, you should try your best to avoid distractions. It can be tempting to sit next to your friends or play on your phone, but avoid the temptations, focus on the lesson, take notes, and listen to your teacher.
Another way to learn math is to ask questions. Your teacher will be a useful resource in learning math, not only will they teach you what you need to know, but unlike a textbook, they can respond to any questions you may have. If you have any math questions, raise you hand and ask for help. There&apos;s a good chance that other students in the class have the same questions as you, but don&apos;t wait for them to ask the questions for you. Take ownership of your learning and don&apos;t be afraid to ask for assistance, it will help you in the long run.
If you need further help with math, and you want a convenient way to learn math fast, browse our collection of <a href="[[canon_textbook.html|{"textbook_key":"basic-math-help"}]]">online tutorials</a> and search for the topics that are causing you issues. You may find that our easy to follow math videos do a better job of conveying the information to you. We cover all the content found in modern textbooks and we have step-by-step examples for everything you&apos;d be expected to know ahead of your upcoming exams.
Additionally, you should also make every effort to complete the homework assignments given to you by your teachers. Your teacher gives you homework to allow you to practice what you&apos;ve been taught, and as we&apos;ll explore below, practice makes perfect.

<h2>How to Get Better at math?</h2>
Whether it's elementary math, basic math, or complex math, the best way to learn is with repetition. Much like learning a language or playing a sport, the more you practice, the better you get, so if you want to learn and improve your math skills, take the time to practice outside of your scheduled lessons.
During your independent study sessions, go over your class notes (if you&apos;re not taking notes, you should be) and review your past quiz/test results to identify your strengths and weaknesses. Based off of that information, you can focus your efforts on building your weaker areas of math and in turn, become a more rounded mathematician. Watch our basic math tutoring videos to further strengthen your understanding of the curriculum content and then attempt to complete a basic math test. Doing so, will allow you to assess your progress in your weaker areas and will help to reinforce your stronger areas too (remember, practice makes perfect!).
When taking a basic math test, try to replicate exam conditions, which means no phones or any other potential distractions. Stick to the time limited of the paper and have someone else mark it for you. Getting into the habit of sitting these tests regularly will strengthen your knowledge in math, help you track your improvements, and boost your confidence ahead of your actual exams.
Whatever your skill level, and regardless of the topics you&apos;re struggling with, we&apos;ll have the revision aides to make math easier to understand. As a subscriber to our service, you&apos;ll have access to every video on our site, allowing you to select the lessons that are relevant to you, and providing you with a tailored study plan that addresses your needs.
Furthermore, as your online math tutor, our basic math lessons can be accessed 24/7 and can be paused, rewound, and fast-forwarded, meaning that you can learn when it's convenient for you, at your own pace, and without being left behind.
For easy practice tools and 24/7 help, <a href="[[signup.html]]">sign-up to StudyPug today</a>. Alternatively, take advantage of our free math help with complimentary lessons across a variety of math topics.

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