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Algebraic expressions are a quick way to represent somewhat complicated situations that might occur in real life. They also help students in a number of ways.
One of these ways is through algebraic equations that contain variables x, y, and mathematical operations like addition, subtraction, multiplication, and division.
Addition
One of the most important algebraic operations is addition. Addition explains how much of something is put together in a collection, and it obeys predictable rules about related operations like subtraction and multiplication.
Adding two numbers is a common operation in elementary arithmetic, and it is often used to calculate sums and differences. It also is an important part of abstract algebra, where it has many generalized generalizations.
Addition is a commutative operation, meaning that the order of the operands does not matter. It is also associative, meaning that the same addition will yield different results if performed on different sets of numbers.
There are several common ways to conduct addition, including breaking numbers according to their place values and using a carry method. Carry is a way to add a number by starting with the most significant digit on the left side and moving to the right side.
Subtraction
There are four basic arithmetic operations in algebra: addition, subtraction, multiplication and division. These can be performed on complex numbers, which are combinations of real and imaginary numbers.
One important rule in math is the order of operations. This means that we perform the arithmetic operations in order to solve expressions.
We follow the rules of the order of operations by breaking down equations into smaller parts using grouping symbols such as parentheses ( ), brackets [ ], braces, and fraction bars.
Once the computation within those groups is done, we can move on to the next set of grouping symbols and work from there. The rule is to perform multiplication first, then add or subtract, then divide.
Another rule is to always use the same sign for two different terms when writing an equation. For example, x+y represents the equations x + y and x – y.
Multiplication
Multiplication is one of the basic arithmetic operations alongside addition, subtraction and division. It is used in a variety of industries, including culinary arts, engineering and retail.
When you multiply two algebraic expressions, the result is called a product. The expressions making up the product are called factors and multiplicands.
During multiplication, you should remember that the product of two components with the same signs is positive and the product of two components with opposite signs is negative.
For example, 3 x 2 equals 6; 8 x 2 equals 48; 2 x 8 equals 15.
You should also be aware that some symbols are grouping symbols and others are multiplication symbols. Be careful not to mix up parentheses ( ) with parentheses, brackets with exponents or fraction bars with fractions.
When you are working with multiplication equations, use a variety of strategies to teach and reinforce your child’s understanding of the concept. Start with concrete strategies such as manipulatives and real-life problems and progress to abstract equations when your child has a firm grasp of the basics.
Division
Division is an operation that breaks down a number into equal groups and then multiplication can be done to get the original number. The operation is denoted by a line symbol, usually a horizontal line with dots each above and below the line.
The quotient is written above the divisor and a non-zero remainder is left below the divisor. This remainder is the fourth part of the division equation.
If you’re not sure what order to conduct operations, the general rule is that multiplication and division should be performed first, working from left to right, and then addition and subtraction.
You can further control the order of these four basic arithmetic operations by using grouping symbols, such as parentheses ( ), brackets [ ], braces and fraction bars. By completing computation within these symbols first, you can make sure that multiplication and division are always performed from left to right.