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# Mathematical Expressions

Mathematical expressions are the combination of mathematical symbols or numbers or both. Every expression contains important elements called variables. An Expression generally does not contain equality sign, if it has an equality sign then it represented as an equation.

Example:

x2-2x+5 it is an expression

y=x2-2x+5 is an equation.

Defined and undefined forms:

Defined and undefined forms these are very important things to be noted in expressions. They are generally used to give an expression meaningful value. The meaning of any Mathematical expression depends up on the elements which are present in the expression i.e. symbols, variables, integers etc.

Example:$\frac{0}{1}$, ?, -?, 0/? , (1)×? ,0×0 etc

Properties:

• An expression should have a variables, symbols, and numbers.

• An expression should not have equality symbol.

Students can get Math Expressions online help for understanding the steps involved in solving Math expressions. Students have to first learn about the concepts of variables. It is explained below.

Equations:

The equation is a statement which is used to make two values or expressions equal. These are used to find out the relation between two variables or values. This is used to translate a word problem into mathematical problem.

Example:

Jane has bought 5 apples and 6 oranges for $30, Find the cost of apples if each orange is$2?

5(A) +6(O) =$30 Each apple =$2

So we get 5(2) + 6(O) = $30 10 + 6(0) = 30 6(O) = 30-10 6(O) = 20 ## O =$ \frac{20}{6}$=3.3 There fore each orange is$3.3

In the above problem the question was changed into mathematical format using equations.

## Examples of Math Expressions

The following are Examples of Math Expressions:

1)Find out the roots for the given quadratic expression x2-5x+6.

Soluiton : Given that

Make it into equation x2-5x+6=0

x2-3x-2x+6=0

x(x-3)-2(x-3)=0

(x-3) (x-2)=0

The roots are x= 3,2.

2)Plot the graph for the given expression y=x+3?

In the above graph each point is plotted by the expression y=x+3.

3)Evaluate the expression (1 +p) × 2 + 12 ÷ 3 - p when p= 3?

Solution : Given data,

Expression: (1 +p) × 2 + 12 ÷ 3 – p

p=3

We replace p with the number 3, and simplify using the usual rules: parentheses first, then exponents, multiplication and division, then addition and subtraction.

(1 + p) × 2 + 12 ÷ 3 - p

(1 +3) × 2 + 12 ÷ 3 - 3

4 × 2 + 12 ÷ 3 - 3

8 + 4 - 3

8+1=9.

4)Solve x - 12 + 20 = 37?

Solution : Given,

x-12+20=37

We need to find x values so “x” term should be independent, Hence we will bring constants to other side.

x-12+20=37

Bringing constants to other side

x=37+12-20

x=49-20

x=29.

5) John weighs 70 kilograms, and Mark weighs “s” kilograms. Write an expression for their combined weight?

Given data,

John weighs 70 kilograms

Marks weighs “s” kilograms

Expression for combined weight=?

The combined weight in kilograms of these two people is the sum of their weights, which is "70+s".

By observing the steps, students can solve similar problems on Math Expressions on their own, by following the same methodology.