How to Solve Numerical Expressions: Step-by-Step Guide
Simplifying expressions means rewriting the same algebraic expression with no like terms and in a compact manner. To simplify expressions, we combine all the like terms and solve all the given brackets, if any, and then in the simplified expression, we will be only left with unlike terms that cannot be reduced further.
In this article, we will learn a bunch of things. We will understand what numerical means in Maths and get to know more through numerical expression examples. We will learn the popular BODMAS rule that is used to simplify numerical expressions.
Numerical Expression Examples
A numerical expression consists of only numbers or integers. It includes basic mathematical operations such as addition, subtraction, multiplication, or division. Therefore, a numerical expression can be defined as a combination of numbers or integers and mathematical operators.
Example: k (16 - k) + 8 (16 - k), 9 (15 - k) = 145, etc.
What Does It Mean to Simplify Numerical Expressions?
Simplifying a numerical expression means solving it in the simplest way possible. Simplification refers to reducing complex expressions into simple Maths numerical that can be solved easily with basic arithmetics.
There are a bunch of things that you need to take care of while simplifying an expression such as the BODMAS rule, removing brackets, ordering from left to right, etc. Let us learn all of them, one by one.
Rule of BODMAS
The rule of BODMAS is one of the popular concepts in the field of algebra. The term BODMAS is an acronym. It stands for Brackets, Order, Division, Multiplication, Addition, and Subtraction. The acronym tells you the order in which you need to simplify the expression.
Full Form of BODMAS
Firstly, you need to resolve the brackets. The second preference is for orders or exponents. Then you have to do the division or multiplication in order from left to right, whichever comes first. Similarly, in the end, you must solve addition or subtraction, from left to right, whichever operation comes first.
Example: 5 x 8 - 12 ÷ 6 + 4\[^{2}\]
Ans: First of all we will solve the square of 4. i.e. 16.
= 5 x 8 - 12 ÷ 6 + 16
Now as per the BODMAS rule, first of all, the division will be done, then multiplication. So, the equation will become
= 40 - 2 + 16
Now the addition and subtraction will be done in the next step, which will give the result as:
= 56 - 2
= 54
Types of Brackets Used in Expressions
Generally, three types of brackets are used in a numerical expression and are very important while knowing how to simplify expressions.
The First Bracket is Parentheses, which is denoted by ( ).
The Second Bracket is the Curly Bracket, which is denoted by { }.
The third Bracket is the Square Bracket, which is denoted by $\left[ \right]$.
The rule in the bracket classification is that the operation in the first bracket needs to be performed first. Then the second bracket and finally, the third.
If you are confused with all these rules, you need not worry. We have got some solved examples for you to understand the concepts better.
Solved Examples
Go through these two solved examples to understand how the BODMAS rule is applied while simplifying the numerical expression calculator. Also, notice how the brackets are removed with priority. Below are some examples of numerical expressions with answers:
Example 1: $[8+\{6-(6 \div 2)\}] \times 4$
Ans: First of all-round brackets will be removed
$=[8+\{6-3\}] \times 4$
Then, curly brackets will be removed
$=[8+3] \times 4$
In the end, Square brackets will be removed
$=11 \times 4$ $=44$
Example 2: $12+[16-\{6+(4 \div 2)\}]$
Ans: First of all-round brackets will be removed
$=12+[16-\{6+2\}]$
Then, curly brackets will be removed
$=12+[16-8]$
In the end, Square brackets will be removed
$=12+8$
$=20$
Practice Questions
Simplify numerical expressions given below:
Q1. 15 × 3 - 15 ÷ 3
Ans: 40
Q2. $64-[\{48 \div 6\} \times 4]+8$
Ans: 40
Q3. $(9 \div 3) \times 7-5 \times 4$
Ans: 1
Q4. $22-\{8+(6 \div 2)\}$
Ans: 11
Summary
Firstly, we learned what numerical expressions are, with the help of some examples. The major focus of the article was on the important topic of simplification of numerical expressions for Class 5. We understood the types of brackets used in these expressions.
We also got to know about the BODMAS rule and learned how to use it to simplify complex expressions by going through some solved examples. If an expression is simplified without using the BODMAS rule, you might still get an answer but it will be incorrect. Therefore, it is necessary to follow the BODMAS rule carefully.
FAQs on Simplification of Numerical Expressions Explained
1. What is a numerical expression and what does it contain?
A numerical expression is a mathematical phrase that combines numbers with one or more operational symbols. These symbols can include addition (+), subtraction (-), multiplication (×), and division (÷). For example, 10 + 5 or (3 × 4) - 2 are numerical expressions. Unlike an equation, a numerical expression does not contain an equals sign (=).
2. What is the main purpose of simplifying a numerical expression?
The main purpose of simplifying a numerical expression is to reduce it to its simplest form, which is a single numerical value. This process, often called 'evaluating' the expression, involves performing all the indicated mathematical operations in a specific order until no more calculations can be done. For instance, simplifying 8 + (5 × 2) results in the single value 18.
3. What is the BODMAS rule and how is it used to simplify expressions?
The BODMAS rule is an acronym that dictates the correct sequence of operations for simplifying a numerical expression. It ensures that everyone arrives at the same answer for the same problem. The order is as follows:
- B - Brackets (Parentheses)
- O - Orders (Powers and Square Roots)
- D - Division
- M - Multiplication
- A - Addition
- S - Subtraction
You must first solve the operations inside the brackets, then evaluate any powers, followed by division and multiplication, and finally, addition and subtraction.
4. What is the key difference between simplifying an expression and solving an equation?
The key difference lies in the objective and the presence of an equals sign. Simplifying an expression means reducing a mathematical phrase to a single value (e.g., 7 + 3 becomes 10). Solving an equation involves finding the value of an unknown variable that makes a statement true (e.g., in x + 3 = 10, you solve for x to find that x = 7). An expression does not have an equals sign, while an equation does.
5. Can you provide some examples of how to translate word problems into numerical expressions?
Yes, real-world problems are often translated into numerical expressions to be solved. For example:
- Word Problem: "Riya bought 4 notebooks for ₹20 each and a pen for ₹15. What was the total cost?"
Numerical Expression: (4 × 20) + 15 - Word Problem: "A pizza with 8 slices is shared equally among 4 friends. If one friend eats one of their slices, how many do they have left?"
Numerical Expression: (8 ÷ 4) - 1
6. Why is the order in BODMAS so important? What happens if we don't follow it?
The order in BODMAS is crucial because it provides a universal standard for calculation. Without a fixed order, the same expression could yield multiple different answers, leading to confusion. For example, consider the expression 5 + 2 × 3.
- Following BODMAS: You multiply first (2 × 3 = 6), then add (5 + 6 = 11). This is the correct answer.
- Ignoring BODMAS: If you add first (5 + 2 = 7), then multiply (7 × 3 = 21), you get an incorrect answer.
Following the rule ensures consistency and accuracy in mathematics.
7. In the BODMAS rule, do we always have to perform division before multiplication?
This is a common misconception. Division (D) and Multiplication (M) have equal priority. You do not always perform division before multiplication. Instead, you work from left to right and perform whichever of the two operations appears first in the expression. The same principle applies to Addition (A) and Subtraction (S), which also have equal priority and are solved from left to right.
8. How do brackets or parentheses affect the simplification of a numerical expression?
Brackets (or parentheses) have the highest priority in the BODMAS rule. They act as a grouping symbol, forcing you to perform the operations inside them first, regardless of the other operations in the expression. For instance, in 10 × (4 + 2), you must first calculate the value inside the brackets (4 + 2 = 6) and then multiply by 10, giving a final answer of 60. Without the brackets, the expression 10 × 4 + 2 would be simplified to 40 + 2 = 42.
