Do you love math? Do you like solving puzzles? If so, then you'll love learning about the top 6 logical math techniques! In this article, we will explore six powerful math techniques that will revolutionize the way you approach math problems.
In this section, we will delve into the technique of breaking problems down into manageable parts. By breaking complex problems into smaller, more approachable components, we can simplify the problem-solving process and gradually build our way towards a solution.
The Break the Problems technique involves the following steps:
John has 24 apples. He wants to distribute them equally among his 3 friends. How many apples will each friend get?
Problem:
A,P,R,X,S, and Z are sitting in a row.
S and Z are in the centre.
A and P are at the end.
R is sitting to the left of A.
Who is to the right of P.
Solution:
To solve this problem using the "break the problem" method, let's break down the given information:
P _ _ _ _ _ A
Next, we consider the third point: R is sitting to the left of A. Since A is at the end, R must be sitting to the immediate left of A. Therefore, the seating arrangement becomes:
P _ _ _ _ R A
Now, let's address the final question: Who is to the right of P? Based on our arrangement, S is the only remaining person who can be to the right of P. Therefore, the final seating arrangement is:
P S _ _ _ R A
In conclusion, S is the person who is sitting to the right of P in the given seating arrangement.
The Trial & Error method involves systematically trying different possible solutions until the correct one is found. It is particularly useful when the problem does not have a straightforward solution path.
Example: Substituting different values of the variable and checking the equality of LHS and RHS is the trial and error method. Let us solve the equation 3x + 4 = 16. We start to substitute different values of x. The value for which both the sides are balanced is the required solution.
LHS | RHS | |
x=1 | 3x1 + 4 = 7 | 16 |
x=2 | 3x2 + 4 = 10 | 16 |
x=3 | 3x3 + 4 = 13 | 16 |
x=4 | 3x4 + 4 = 16 | 16 |
Hence, x = 4.
The Elimination Technique involves systematically eliminating incorrect options or possibilities through a series of logical deductions. This technique is commonly used in multiple-choice questions or scenarios where we need to narrow down the choices to identify the correct solution.
Example: Problem: Tim, Tom and Jim are triplets(three brothers born on the same day). Their brother is exactly 3 years older. Which of the following numbers can be the sum of the ages of the four brothers?
Step 1: From question, we understand that there is a triplet(3 brothers) and an elder brother who is 3 years older. Step 2: With above info, we can say the sum of their ages should be a number divisible by 4 + 3.
Step 3: Using elimination from answers, we can eliminate 61, 25 and 30. Then, we can find only 27 is 24(divisible by 4) + 3. Hence, that’s the answer.
Backward solving involved working from the result backwards to find the initial unknown value. Backward operations for different arithmetic operations are given below:
Original Operation | Backward Operation |
Addition + | Subtraction - |
Subtraction - | Addition + |
Multiplication x | Division ÷ |
Division ÷ | Multiplication x |
Square | Square root |
Square root | Square |
Example:
Problem: Find a number such that when multiplied by 5 and added to 8, the result is 28. Step 1: We need to work backwards here. Result is 28. Step 2: 28 is got when u added 8, so working backward, we need to subtract 8 from 28. So, 20 Step 3: When a number was multiplies by5, we got 20. Now working backwards, we need to divide 20 by 5. So its 4.
The Solving from Answers technique involves plugging the answer choices into the problem and checking which choice satisfies the given conditions. It can save time and effort by eliminating incorrect options and pinpointing the correct solution.
Example: Problem: Find the value of x that satisfies the equation 2x - 5 = 7.
Step 1: Start with the given equation: 2x - 5 = 7. Step 2: Plug the answer choices into the equation and check:
The Plugging in Numbers technique involves substituting specific values into the problem to simplify the calculations and arrive at the solution. This technique is useful when dealing with complex formulas or variables.
Example: Problem: Find the value of y in the equation 3y - 4 = 2y + 8.
Step 1: Start with the given equation: 3y - 4 = 2y + 8. Step 2: Choose a value for y to simplify the equation:
By incorporating the above techniques, you can now confidently tackle even the most challenging math problems.
But remember, practice makes perfect. Keep honing your problem-solving skills by applying these techniques to a variety of math problems. With practice and a solid understanding of these techniques, you'll become a math-solving champion in no time.
This article on Logical Math Techniques explores six powerful math techniques that can revolutionize the way you approach math problems. From breaking down complex problems into smaller parts to using trial and error, elimination, backward substitution, solving from answers, and plugging in numbers, these math techniques can help you solve math problems more efficiently. Whether you are studying 7th-grade math formulas or looking for new tricks to improve your problem-solving skills, these math new tricks can be applied to various levels of math and can help you save time and eliminate incorrect choices. So, keep practicing and honing your problem-solving skills with these logical math techniques.
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