How to Solve Simplify Questions with Rules and Solved Examples
Do you feel lost when it comes to Maths problems? If that's the case, simplification questions happen to be your best friend. Join us as we walk you through this problem-solving technique, giving an example of how they work and how they can help simplify Maths examples that are difficult concepts to solve!
Simplification questions can be useful because they help you to solve more complicated problems with ease. Simplification questions are asked in Maths to help the learner simplify a concept. They can be used to help in getting rid of complications. You are simplifying so they can understand the reasoning behind the question.
What are Simplification Questions?
The word simplification refers to any process of making something as easy as possible. Simplification questions are questions that can simplify Maths examples, like the one below:
Example: Simplify $4(10+15\div\,5\times 4-2\times 2)$
Ans: The answer is: $72$
Simplify the Question
The basic idea behind simplifying is that you want to transform your number or expression into its simplest form by reducing the numerical value and getting rid of the signs.
What is the Simplification Formula?
BODMAS: This is an acronym for a set of steps that you should follow when answering a question, which are: Bracket, Order, Division, Multiplication, Addition, and Subtraction. The objective is to reduce the number as much as possible without causing problems with addition or subtraction.
B: Brackets
O: Operation
D: Division
M: Multiplication
A: Addition
S: Subtraction
BODMAS
How Do You Solve Simplification Questions?
To solve simplification problems, you must understand the process behind simplifying.
Step 1: Check for the operations that are equal to each other.
Example: Simplify (a+bc)+(b-d)(a-c)(d+b)-2, using the BODMAS simplification formula.
Step 2: Check for similar operations of the operands. Example: Simplify (ab+cd)(ab-bc)(a-b)+(c-d).
Step 3: If operations are not equal or similar, simplify the one on the right of the equal sign first.
Step 4: Add together (or multiply) all terms using the same or similar operations. Example: Simplify x(x+3)+(x-9)
Step 5: Include any brackets with numbers that have been added together (or multiplied).
How Do You Simplify a Fraction?
You can combine the numerator and the denominator by adding, subtracting, or multiplying them together.
For example, one of the simplification questions with solutions is, $\dfrac{12}{6}$ simplifies to $\dfrac{2}{3}$ by adding 6+12 to get 18 and $\dfrac{18}{3}$=6.
For example, 5x4=20 becomes $\dfrac{20}{10}$= 2 so 5x4 = 20 or 2x5 = 10.
The new number is now divided into 10 parts instead of four parts to get your final answer of two.
How to Simplify Decimals?
If a number is in decimals, you would have to convert it into fractions before simplifying. The simplest form of converting $\dfrac{2}{3}$ into a decimal which is 0.66 or to a fraction with one unit, $\dfrac{6}{1}$=6 becomes the answer.
If it were in fractions, then your number would be easier than doing the multiplication. So try converting them into fractions first, and then simplify while solving simplification problems.
Solved Examples
Q1 Simplify: 37 - [5 + {28 - (19 - 7)}]
Ans: 37 - [5 + {28 - (19 - 7)}]
= 37 - [5 + {28 - 12}] (Removing the innermost bracket ( ))
= 37 - [5 + 16]
= 37 - 21
= 16.
Q2 Simplify: 78 - [24 - {16 (5 - 4 - 1)}]
Ans:-78 - [24 - {16 (5 – 4 - 1)}]
= 78 - [24 - {16(5 - 5)}] (Removing vinculum)
= 78 -[24 - {16 (0)}] (Removing parentheses)
= 78 - [24 – 0] (Removing braces)
= 78 - 24
= 54
Q3. Simplify. $\dfrac{1}{3}+\left[\dfrac{1}{2}-\left\{\dfrac{1}{5}+\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\right\}\right]$
Ans: $\dfrac{1}{3}+\left[\dfrac{1}{2}-\left\{\dfrac{1}{5}+\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\right\}\right]$
$=\dfrac{1}{3}+\dfrac{1}{6}$
$= \dfrac{2+1}{6}$
$=\dfrac{1}{2}$
Practice Questions
Q1. 3 - (5 – 6 ÷ 3)
Ans: 0
Q2. – 25 + 14 ÷ (5 - 3)
Ans: -18
Q3. 25-{5+4-(3+2-1+3)}
Ans: 23
Q4. 27 - [38 - {46 - (15 - 13 - 2)}]
Ans: 35
Q5 36 - [18 - {14 - (15 – 4 ÷ 2 x 2)}]
Ans: 21
Summary
We've covered a lot of different strategies for simplification questions in this article. We've focused on the BODMAS method, which is a helpful way to simplify original equations, and learned to simplify equations by cancelling out factors.
In our opinion, it is one of the ways to learn maths quickly, because you can use this rule over and over again. At first, you do not understand what it truly means, but as you keep applying it in real-life situations and play games, you begin to grasp the meaning of how many even numbers there are in a set of numbers.
FAQs on Simplify Questions in Algebra and Arithmetic
1. What does it mean to simplify an expression in maths?
To simplify an expression means to rewrite it in its simplest and most compact form without changing its value. This usually involves:
- Combining like terms
- Reducing fractions to lowest terms
- Removing brackets using distributive property
- Applying order of operations (BODMAS/PEMDAS)
For example, 3x + 2x simplifies to 5x because the like terms are combined.
2. How do you simplify algebraic expressions step by step?
To simplify an algebraic expression, follow a clear step-by-step process using order of operations and combining like terms.
- Remove brackets using the distributive property
- Combine like terms
- Simplify constants and coefficients
- Write the final answer in standard form
Example: Simplify 2(x + 3) + 4x → 2x + 6 + 4x → 6x + 6.
3. What are like terms and how do you combine them?
Like terms are terms that have the same variables raised to the same powers. You combine them by adding or subtracting their coefficients.
- 3x and 5x are like terms
- 2a² and -7a² are like terms
- 4x and 4y are not like terms
Example: 7x − 2x = 5x.
4. How do you simplify fractions in maths?
To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF).
- Find the GCF of numerator and denominator
- Divide both by the GCF
- Write the reduced fraction
Example: 12/18 → GCF is 6 → (12 ÷ 6)/(18 ÷ 6) = 2/3.
5. How do you simplify expressions with brackets?
To simplify expressions with brackets, use the distributive property to expand before combining like terms.
- Multiply each term inside the bracket
- Remove the brackets carefully
- Combine like terms
Example: 3(2x − 4) = 6x − 12.
6. What is the order of operations when simplifying?
The order of operations tells you the correct sequence to simplify expressions: Brackets, Orders, Division and Multiplication, Addition and Subtraction (BODMAS).
- Simplify brackets first
- Evaluate powers or roots
- Perform multiplication and division (left to right)
- Perform addition and subtraction (left to right)
Example: 2 + 3 × 4 = 2 + 12 = 14.
7. How do you simplify expressions with exponents?
To simplify expressions with exponents, apply the laws of exponents such as product rule and power rule.
- am × an = am+n
- am ÷ an = am−n
- (am)n = amn
Example: x² × x³ = x⁵.
8. How do you simplify negative numbers in expressions?
To simplify expressions with negative numbers, carefully apply the rules of signs for addition, subtraction, multiplication, and division.
- (−) × (−) = positive
- (+) × (−) = negative
- Subtracting a negative becomes addition
Example: 5 − (−3) = 5 + 3 = 8.
9. Can you give an example of simplifying a complex expression?
A complex expression is simplified by applying order of operations and combining like terms step by step.
- Example: 2(3x + 5) − 4x + 7
- Step 1: Expand → 6x + 10 − 4x + 7
- Step 2: Combine like terms → 2x + 17
The simplified expression is 2x + 17.
10. What are common mistakes when simplifying expressions?
Common mistakes when simplifying expressions include ignoring order of operations and combining unlike terms.
- Adding terms that are not like terms
- Forgetting to distribute negative signs
- Skipping brackets incorrectly
- Not reducing fractions fully
Always check that only like terms are combined and that signs are handled correctly.
