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Numerical Expression Examples

Numerical Expressions are those expressions which are a mixture of some numbers and some of the four mathematical operations (+, -, *, /) with them.

The solution or result of a numerical expression always represents a certain fixed value.
Solving Numerical Expressions:
To solve a numerical expression, the following rules are performed, which also represents the order of the operations, which should be followed while solving any numerical expression:
Rule 1: Solve any operations which are enclosed in brackets that are one contained inside the other, then start solving the operation from the innermost symbols first.  
Rule 2: Then, solve any exponential expressions.  
Rule 3: Then, solve any indicated division, then multiplication, then addition and in the end, subtraction, in the order the operations occur in the expression from left to right.
Summary: The above rule is also known as PEMDAS.

The following are some examples of numerical expressions.
a.    4 + 20 – 7, (2 + 3) – 7, (6 × 2) ÷ 20, 5 ÷ (20 × 3),
b.    4 + 20 - 7 is the numerical expression which on solving gives a fixed certain value equal to the number 17.

Solved Examples:
Example 1:  Evaluate 102 - 10 + 1001
Solution: Step 1: 102 - 10 + 1001
Step 2: = 10 × 10 - 10 + 100
Step 3: = 100 – 10 + 100
Step 4: = 90 + 100
Step 5: = 190 is the answer.

Example 2: Evaluate: $\frac{21}{3}$ - 3 + 3
Solution: $\frac{21}{3}$ - 3 + 3 = 7 - 3 + 3 = 7

Example 3: Solve 3 + 2 * $\frac{9}{3}$
Solution: 3 + 2 * $\frac{9}{3}$ = 3 + $\frac{18}{3}$ = 3 + 6 = 9

Example 4: Translate the phrase "seven less than twice a number" to an algebraic expression.
Solution: Let "x" be a number.
Twice the number is 2x.
Seven less than twice a number is 2x - 7.

Example 5: Evaluate the expression $\frac{7x}{x-2}$ for the given value x = 4.
Solution: Put x = 4 in the given expression, we get,
$\frac{7(4)}{4-2}$ = $\frac{28}{2}$ = 14

Example 6: Solve $\frac{\frac{14}{3}}{\frac{7}{9}}$
Solution: If there are 2 fractions divided by each other, then we can find the reciprocal of the second fraction and multiply it with the first fraction.
So $\frac{14}{3}$ * $\frac{9}{7}$ = 2 x 3 = 6

Example 7: Solve $\frac{2}{9}$ - $\frac{2}{3}$
Solution: LCD of 3 and 9 is 9
So, $\frac{2}{9}$ - $\frac{2}{3}$ = $\frac{2-6}{9}$ = $\frac{-4}{9}$

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