How to Solve Simplification Questions Quickly
In Mathematics, sometimes you get complicated sums and long calculations, which is very common in fraction questions. Some students find it more difficult and take a long time to solve. But don’t worry, this article on simplification in Maths has a resolution for you. It will help you to simplify the fractions in easy ways. In this article, you'll learn what simplification is, how to simplify fractions, and the steps involved in simplifying fractions. You'll also find out how to do it step by step.
What is Simplification?
As you know, simplification of mathematical problems helps increase scores in exams and is also used in daily life like in malls you get 35% discount, flat discount or 20% discount up to Rs 100. You only need to use fundamental simplification rules to solve equations in this part.
Thus, simplifying an expression implies employing different procedures to reduce it to a simpler version. The operations required to simplify things are done in a set order called BODMAS.
Where,
B = Bracket
0 = of
D = Division
M = Multiplication
A = Addition
S = Subtraction
Introduction to Simplification
To simplify a fraction, reduce it to its most basic form. If a fraction's numerator and denominator only share the number one, it is said to be in its simplest form. The process of simplifying difficulties as we work to tackle fractional problems is essential. The value of the fraction won't change even after we simplify them. This indicates that the true fraction and the simplified fraction are two equivalent fractions. We shall discover a few simple methods for simplifying fractions in this article.
Simplifying Fractions
How to Simplify Fractions?
Simplify Fractions
Reducing a fraction to its simplest form is the definition of simplifying a fraction. If a fraction's numerator and denominator are coprime or share only the number one as a common factor, it is said to be in its simplest form. The given fraction is equal to the given fraction in its simplest form. For instance, the fraction $\dfrac{3}{4}$ is in its most basic form since the only element that 3 and 4 have in common is 1.
Let's attempt to gradually simplify the fraction $\dfrac{8}{24}$.
How to Simplify Fractions Step by Step?
How to Simplify Fractions Stepwise
Following is the process of how to simplify fractions step by step -
Step 1: Write the denominator and numerator's factors in step one.
The ratio between 8 and 24 is 1 through 8 factors: 2; 4; and 8
1, 2, 3, 4, 6, 8, 12, and 24 are the 24 factors.
Step 2: Verify the shared factors between the denominator and the numerator. 1, 2, 4, and 8 are the common factors of the numbers 8 and 24.
Step 3: Subtract the common components from the numerator and denominator until there is only one remaining.
The fraction that is so obtained is in its most basic form. Starting with a division of 2, $\dfrac{8}{24}$ becomes $\dfrac{\dfrac{8}{2}}{\dfrac{24}{2}}=\dfrac{4}{12}$.
Up until the point where we can no longer divide by 2, we will keep doing so. Thus, $\dfrac{\dfrac{4}{2}}{\dfrac{12}{2}}=\dfrac{2}{6}$, which is equal to $\dfrac{\dfrac{2}{2}}{\dfrac{6}{2}}=\dfrac{1}{3}$.
The fraction $\dfrac{8}{24}$ is thus represented by its simplest form, $\dfrac{1}{3}$.
Let's return to the original issue of how to make the fraction $\dfrac{8}{24}$ simpler. Between 8 and 24, 8 is their largest common factor. The simplest form of the fraction, which is $\dfrac{1}{3}$, can be obtained by immediately dividing the numerator, 8, by the denominator, 24, and vice versa.
How to Simplify Numbers
How to Simplify Numbers
Following is the way how to simplify numbers-
Round it Off.
Produce zeros. 200, therefore, becomes 199.
Round to an Order of Magnitude.
To the nearest "power of 10," round a lot. The result is that 218 becomes 100 and 2,180 becomes 1,000.
Slide the Decimal Point.
Rounding zeros are compacted by sliding the decimal point.
This makes 200,000,000 into 2 x 108. (exponential notation).
Replace it with a Number You Can Recall.
Find a nearby number that you can remember rather than rounding.
Thus, 218 can be easily converted to 222, 210, 200, or any number.
Solved Examples
Example 1: Simplify: $660 \div 22 \times(2+1)$
Ans: $660 \div 22 \times(2+1)$ (Solve parentheses first)
$=(660 \div 22) \times 3 \text { (From left to right, division appears first) }$
$=30 \times 3=90$
Example 2: Simplify: 37 − [28 + (19 − 7)]
Ans: $37-[28+(19-7)]$ First solve ( )
$=37-[28+12]$ Next, solve []
$=37-40$
$=77$
Practice Time
Q1. Simplify the expression: $4+(3 \times 4) \div 2$
Ans: 10
Q2. Simplify fractions: (i) $\dfrac{124}{136}$
(ii) $\dfrac{182}{192}$
Ans: (i) $\dfrac{31}{34}$
(ii) $\dfrac{91}96{}$
Conclusion
Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner. Making something simpler is making it less complex. When you describe a complex mathematical idea to a child in words they can easily understand, you are simplifying.
FAQs on Simplification in Maths: Complete Guide
1. What is the basic concept of simplification in Maths?
Simplification in Maths is the process of reducing a complex mathematical expression into its simplest and most compact form. The goal is to make the expression easier to understand and solve without changing its original value. This involves performing operations like addition, subtraction, multiplication, and division in a specific order, combining like terms, and reducing fractions.
2. What is the BODMAS rule and why is it crucial for simplification?
The BODMAS rule dictates the correct order of operations to simplify any mathematical expression. It is an acronym that stands for:
- B - Brackets
- O - Orders (powers and square roots)
- D - Division
- M - Multiplication
- A - Addition
- S - Subtraction
This rule is crucial because it ensures that everyone arrives at the same, single correct answer when simplifying the same problem. Without a standard order, an expression could have multiple different answers, leading to confusion and errors.
3. What is the main difference between 'simplifying' an expression and 'solving' an equation?
The key difference lies in the objective. Simplifying involves rewriting an expression in a more concise form, like reducing 2x + 3x to 5x. There is no equal sign to begin with. Solving, on the other hand, applies to an equation (which has an equal sign) and involves finding the specific value of a variable that makes the equation true, for example, finding x in the equation 2x = 10, where x=5.
4. How do you simplify an algebraic expression with like and unlike terms?
To simplify an algebraic expression, you first identify and group the 'like terms'. Like terms are those that have the same variable raised to the same power (e.g., 5x and -2x). You can then combine them by adding or subtracting their coefficients. 'Unlike terms' (e.g., 3x and 4y) cannot be combined. For example, in the expression 7a + 3b + 2a - b, you would combine 7a and 2a to get 9a, and 3b and -b to get 2b. The simplified form is 9a + 2b.
5. What are the steps to simplify a fraction to its lowest terms?
Simplifying a fraction involves making the numerator and denominator as small as possible without changing the fraction's value. The steps are:
- Find the Highest Common Factor (HCF) of the numerator and the denominator.
- Divide both the numerator and the denominator by their HCF.
- The resulting fraction is in its simplest or lowest form. For example, to simplify 12/18, the HCF of 12 and 18 is 6. Dividing both by 6 gives 2/3.
6. Why is simplification considered a foundational skill for higher-level mathematics?
Simplification is a foundational skill because complex problems in algebra, calculus, and trigonometry are built upon simpler expressions. By mastering simplification, students can break down intimidating, multi-step problems into manageable parts. This not only makes the problem easier to solve but also helps in identifying patterns and relationships between variables, which is a key aspect of advanced mathematical thinking as per the CBSE 2025-26 syllabus.
7. What is a common mistake to avoid when simplifying expressions involving brackets?
A very common mistake is incorrectly distributing a negative sign across terms inside a bracket. For example, in the expression 10 - (x + 5), students often incorrectly write it as 10 - x + 5. The correct approach is to distribute the negative sign to every term inside the bracket, resulting in 10 - x - 5. Forgetting to change the sign of the second and subsequent terms is a frequent source of errors.
8. How does the process of simplification help in checking the correctness of a solution?
Simplification is a powerful tool for verification. After solving a complex equation, you can substitute your answer back into the original, un-simplified equation. If both sides of the equation are equal after performing the operations, it confirms your solution is correct. Furthermore, simplifying both sides of a complex identity or proof independently can show that they are equivalent, thus proving the relationship is true.
