### Collecting like terms - Solving linear equations - IntoMath

An equation is an equality of two quantities and it always contains an equal sign. To solve an equation means to determine the value of the unknown(s) that makes the equation true, so that when the unknown is being substituted with the value in the equation, the left side is equal the right side.
An expression does not have an equal sign, but it may contain variables that represent a certain quantity or relationship. To simplify an expression means to complete operations within the expression that would bring it to its simplest form. In order to do that collecting like terms ins required. Like terms are terms that have different coefficients but identical variables with the same exponent.
You are going to learn how to solve a linear equation by completing the reverse BEDMAS and performing opposite operations. For example, an equation 2x + 3 = 9 could be solved by first subtracting 3 from both sides of the equation and then dividing both sides of the equation by 2. Thus, x = 3. It is important to make sure that the same operation is done to both sides of the equation to keep the equation balanced.
Collecting like terms is often necessary on one or both sides of the equation.
Doing the “left side, right side check” is an important component of solving equations, as it would help you determine whether the solution is correct. This lesson will teach you how to do it.
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### Multiplying and Dividing Integers - IntoMath

In this lesson you will learn about multiplying and dividing integers (positive and negative).
You will learn the general rules that apply to every problem.
For example, when multiplying or dividing two negative integers, the product or a quotient is positive.
When one of the integers is negative and the other one is positive, the result is always negative.
The absolute value of each number does not affect the sign of the answer like it does with addition and subtraction of positive and negative integers.
You will discover how to multiply a negative number by 0 and what happens when you try to divide by 0.
You will see how understanding operations with integers can be helpful in real life.
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### Adding and Subtracting Integers - Absolute Value - IntoMath

In this lesson you will learn about adding and subtracting integers. Integers are positive and negative whole numbers and when first learning about integers it is useful to visualize how one integer is related to the other.
This is when we use a number line. A number line is a line that has the origin, 0, to the right of which there are positive numbers and to the left of which there are negative numbers. We can move along the number line and determine the position of any integer. We have previously used it to compare integers.
You will discover the concept of the absolute value and why it is important when performing operations with integers. It is also useful when solving certain types of equations and later, when analyzing absolute value functions and their graphs.
On a number line, the distance between the two numbers is given as an absolute value.
For example, the distance from -10 to +10 is 20. However, if we add -10 and +10 the answer is 0 – they are the exact opposites. If we were to subtract +10 from -10, it would be recorded as -10 – (+10) and would equal -20 ( because on a number line a positive direction has changed to a negative direction).
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### Multiplying and Dividing Fractions - IntoMath

Multiplying and dividing fractions is not difficult.
Knowing how to multiply and divide fractions will help you succeed when other, more complex mathematical concepts, such as simplifying algebraic expressions, solving equations and so on.
In order to multiply and divide fractions it is not required to find the GCF, unlike when adding and subtracting them.
Most students find the process of multiplying fractions the easiest of all operations with fractions. All you have to do is multiply numerators and denominators respectively (the product of the numerators over the product of the denominators), recording the final answer as a reduced simplest fraction. In order to reduce a fraction, divide both the numerator and the denominator by their GCF (greatest common factor).
The process of dividing the two fractions is a bit more complex. But as long as you understand why things are done a certain way everything is really simple.
In order to divide one fraction by another fraction, find the reciprocal of the second fraction and then change the operation to multiplication. To get the reciprocal of a fraction, just turn it upside down. Switch the numerator and denominator.
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### Adding and Subtracting Fractions - Unlike Denominators - IntoMath

Adding and subtracting fractions involves representing them as a part of the same whole. Thus, their denominators must be the same. In order to bring them to the same denominator, we need to change all of the existing denominators while at the same time changing the numerator such that the fractions remain equivalent to the original ones.
If two fractions with different denominators are being added or subtracted, first bring them to the Lowest Common Denominator by determining their Least Common Multiple.
For example, for denominators 2 and 5, the Lowest Common Denominator is 10 – the lowest number divisible by both given denominators.
For mixed numbers, first convert the mixed numbers into improper fractions and then follow the steps above.
In order to convert a mixed number to an improper fraction multiply the whole portion of the mixed number by the denominator of the fractional portion and then add the numerator – the result becomes the new numerator over the unchanged denominator. The numerator will end up being a greater number than the denominator.
In general, becoming proficient in adding and subtracting fractions will help you with many other more complex concepts, such as solving equations with fractions, simplifying algebraic expressions and solving rational equations.
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### What are integers - Number Line - IntoMath

In order to display positive and negative numbers we often use a number line.
A number line is a line that contains all negative and positive integers, including zero (the origin). One of the real life examples of a number line is a thermometer. A thermometer has a scale that usually goes from -50 to +50 degrees Celsius. 0 degrees is the middle between the coldest and the hottest temperatures.
When we add and subtract positive and negative integers, we can always use a number line to calculate the absolute distance between the two digits – in mathematics this distance is called “absolute value”.
A number line is an excellent tool that helps understand operations with integers visually.
For example, what is -8 + 9?
We would locate the -8 on the number line and move 9 digits in the positive direction (from left to right). We would land on 1, which would be the answer to the problem.
A number line can also be used to compare positive and negative integers.
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### Area and Perimeter - Rectangle and Square - IntoMath

We are often required to calculate the area and perimeter of objects or spaces in 2 dimensions (flat surface like a piece of paper or a field).
In real life, this skill is helpful when designing living spaces or calculating the amount of fencing required to enclose a certain piece of land, etc.
Perimeter is the length and width around the object – the sum of all outer sides.
Area – the 2 dimensional space surrounded by the sides of the shape.
The two shapes we are looking at in this lesson are rectangle and square.
A square is also a rectangle, but a regular rectangle. “Regular” means all sides and angles are equal.
We develop formulas for both area and perimeter and analyze different situations where those formulas can be applied. It is important to not only memorize the formulas or substitute numbers into them. It is important to understand where the formulas are coming from, how they were derived. Making connections and understanding relationships is one of the key components of being successful in math.
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