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 10^{2} - 10 + 100^{1}

Solution: Step 1: 10^{2} - 10 + 100^{1}

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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