Expression, Equation and Variables
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Expression, Equation and Variables: |
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Algebra is a language of symbols. We use different symbols to represent the numbers like + for
addition, - for subtraction, × for multiplication and / for division. An expression a combination of
numbers, variables and atleast one operation. An equation is a mathematical sentence which
subsumes an equal sign. In algebraic expressions, letters represent variables. These letters are
actually numbers in disguise. In this expression, the variables are x and y.
Example1:
Expression:2A+B
Equation:
Example2:
Expression: -3x+4y2z
Equation:
y = mx + c
Properties of Operations:
a. Addition: The order that numbers are added does not change the sum.
x + y = y + x
b. Multiplication: The order that numbers are multiplied does not change the product.
x × y = y × x
2. Associative Property
a. Addition: Grouping of addends does not change the sum.
(x + y) + z = x + (y + z)
b. Multiplication: Grouping of factors does not change the products.
(x × y) × z = x × (y × z)
3. Identity Property
a. Addition: The sum of a number an zero is the number
x + 0 = x
b.Multiplication: The product of a factor and one is the factor.
x × 1 = x
4. Multiplication Property of Zero
a. Addition: The product of a number and zero is zero.
x × 0 = x
5. Distributive Property: For any numbers a,b and c
a (b + c) = ab + ac
Parts of a whole number can be written as fractions, such as 1/2,
or as decimals such as 0.5, read
as "5 tenths".
Examples: 0.04 = 4/100 = 1/25
3.75 = 375/100 = 15/4
Representation of Decimals on Number Line:
parts.
Example: To represent 8.4 on a number line, divide
the segment between 8 and 9 into ten equal
parts.
The arrow is four parts to the right of 8 where it points at
8.4.
Similarly, we can represent 8.456 on a number line by dividing the segment between 8.45 and 8.46 into ten equal parts.
The arrow is six parts to the right of 8.45 where it points at
8.456
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