How to Evaluate a Numerical Expression Step by Step with Examples
In this topic, we will learn the definition of a numerical expression, what is the meaning of numerical and learn how to write a number in numerical form. We will discuss here the simplification of numerical expressions. Students will be provided with plenty of examples to clearly illustrate this important mathematical concept. When we look at a problem with numbers, we are most likely looking at a numerical expression. In this article, we will explain how to simplify numerical expressions with the help of various numerical expression examples.
What is the Meaning of Numerical?
Numerical Definition-The term numerical means involving numbers.
The term numerical expression consists of two words, numerical meaning numbers and expression meaning phrase. Thus, it is a phrase involving numbers. A numerical expression in mathematics is a combination of numbers integers combined using mathematical operators such as addition, subtraction, multiplication, or division.
There are different forms in which the number can be expressed,, such as word form and numerical form.
A numerical expression is a mathematical statement that involves only numbers along with one or more operation symbols. Examples of operation symbols are addition, subtraction, multiplication and division. It can also be expressed in the radical symbol (the square root symbol) or the absolute value symbol.
Numerical Expression Example
A numerical expression is formed by the combination of numbers, including various mathematical operators. There is no limit to the number of operators that a numerical expression may contain. Some numerical expressions use only one operator between two numbers, whereas some may contain more than one.
The only requirements for a numerical expression are that it only contains numbers and operation symbols. Some numerical expressions have only one operation symbol. Others have two or more.
Here are Some Examples of Numerical Expressions
4 + 5
134 - 75
56 * 4 + 6
60/5*7-2+1
Examples of Non-Numerical Expressions:
As we know, numerical expressions can only contain numbers; expressions containing variables (such as x or y) cannot be considered numerical expressions. They are actually called algebraic expressions instead. Given below are two examples of algebraic expressions:
2x + 5
250 - y
How to Write Numerical Expression?
Any mathematical word problem is solved by first converting it into a numerical expression.
Below we have provided one example to understand it.
Question: Nancy has 10 chocolate bars. She gives 3 chocolates to her sister, 1 to her friend and eats 2. Later she visits her grandmother, and she (grandmother) offers Nancy 12 more chocolate bars. How many chocolate bars does Nancy have now?
Solution: Here first look at the numbers involved in the above problem. Nancy has 10 chocolate bars. She gives away 4 (3 to her sister and 1 to her friend), eats 2 and then again gets 12 chocolate more from her grandmother. So, it can be represented in numerical expression as 10 - 3 - 1 - 2 + 12
= 7 - 1 - 2 + 12
= 6 - 2 + 12
= 4 + 12
= 16
Hence, Nancy has now 16 chocolate bars.
Did you know?
Power can also be expressed as a numerical expression. It has two parts: an exponent and a base.
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2⁴ can be written as 2.2.2.2
An expression can also be a combination of variables and constants that are combined using mathematical operations. Such expression is known as an algebraic expression.
Simplification of Numerical Expressions
To simplify a numerical expression that has two or more operations, we perform the BODMAS rule. In this rule, we have to solve operations like Brackets, order of powers or roots, Division first, followed by Multiplication, Addition and then Subtraction. A standard result called BODMAS is followed for simplification of these operations.
The word BODMAS stands for:
B → Brackets
O → Order of powers or roots
D → Division
M → Multiplication
A → Addition
S → Subtraction
If the brackets are present in the problem, first, we have to simplify the brackets. There are four kinds of brackets.
( ) → This symbol is simple brackets or round brackets or parenthesis.
{ } → Braces or Curly brackets.
[ ]→ Square brackets.
______ → This symbol is a line called bar or vinculum. It is used when two or more types of brackets are involved in the problem. Brackets are removed in this order ‘_________’, ( ), { }, [ ]
Simplify the Following Numerical Expressions
(i) Solve
10+7−(8÷2) × 3
First, we will solve the round bracket
=10+7−4 × 3
=17-12
=5
Hence the final value is 5
(ii) Find the Value of 15 +20−8+(6÷2)
First, remove the round bracket
= 15 +20−8+3
=35-8+3
=38-8
=30
Hence the final value is 30
(iii) Evaluate the Numerical Expression 10² - 10 + 100
Fist evaluate the square value
= 10 x 10 - 10 + 100
=100-10+100
=90+100
=190
Hence the final value is 190.
FAQs on Numerical Expression in Mathematics
1. What is a numerical expression in Maths?
A numerical expression is a mathematical phrase that contains only numbers and operation symbols, without any variables. It can include addition, subtraction, multiplication, division, and brackets.
- Example: 5 + 3 × 2
- This expression has numbers and operations only.
- When simplified, it gives a single numerical value.
2. How do you evaluate a numerical expression?
To evaluate a numerical expression, follow the order of operations (BODMAS/PEMDAS) to get the correct value.
- B – Brackets
- O – Orders (powers, roots)
- D/M – Division and Multiplication (left to right)
- A/S – Addition and Subtraction (left to right)
- Multiply first: 2 × 3 = 6
- Add: 6 + 6 = 12
3. What is the order of operations in numerical expressions?
The order of operations is a rule that tells you the correct sequence to solve a numerical expression. It is commonly remembered as BODMAS or PEMDAS.
- Brackets/Parentheses
- Orders (powers and roots)
- Division and Multiplication (left to right)
- Addition and Subtraction (left to right)
4. Can you give an example of solving a numerical expression step by step?
Yes, solving a numerical expression step by step means applying the order of operations carefully. Example: Evaluate 8 + (4 × 2) − 3.
- Step 1: Brackets → 4 × 2 = 8
- Step 2: Expression becomes 8 + 8 − 3
- Step 3: Add → 8 + 8 = 16
- Step 4: Subtract → 16 − 3 = 13
5. What is the difference between a numerical expression and an algebraic expression?
The main difference is that a numerical expression contains only numbers, while an algebraic expression includes variables.
- Numerical example: 7 + 5 × 2
- Algebraic example: 7 + 5x
- Numerical expressions give a fixed value when evaluated.
- Algebraic expressions depend on the value of the variable.
6. Why are brackets important in numerical expressions?
Brackets are important because they change the order in which operations are performed in a numerical expression.
- Example 1: 10 − 2 × 3 = 10 − 6 = 4
- Example 2: (10 − 2) × 3 = 8 × 3 = 24
7. How do you simplify a numerical expression with exponents?
To simplify a numerical expression with exponents, calculate the powers before multiplication or addition according to BODMAS.
- Example: 2 + 3² × 2
- Step 1: Exponent → 3² = 9
- Step 2: Multiply → 9 × 2 = 18
- Step 3: Add → 2 + 18 = 20
8. What are common mistakes when evaluating numerical expressions?
The most common mistake is ignoring the order of operations when solving a numerical expression.
- Solving from left to right without following BODMAS
- Forgetting to solve brackets first
- Ignoring exponents
- Making sign errors in subtraction
9. How do you write a word problem as a numerical expression?
To write a word problem as a numerical expression, translate key words into mathematical operations.
- “Sum” means addition (+)
- “Difference” means subtraction (−)
- “Product” means multiplication (×)
- “Quotient” means division (÷)
10. Can a numerical expression have more than one answer?
A numerical expression has only one correct value when evaluated properly using the order of operations.
- Example: 6 + 4 ÷ 2
- Divide first: 4 ÷ 2 = 2
- Add: 6 + 2 = 8
