Word problems in mathematics often pose a challenge for many students.
These problems involve understanding and interpreting mathematical concepts presented in the form of words.
At Edustuff, we recognize the common struggles students face with word problems, particularly in grasping the underlying structure and effectively manipulating numbers, letters, and figures.
In this tutorial, we aim to eliminate students’ fears by providing simple explanations and examples to build their confidence in tackling word problems.
Understanding Key Terminology:
To solve word problems successfully, it is crucial to comprehend the meaning of specific words and phrases used within them. Here are some essential terminologies explained with illustrative examples:
- Sum: A sum refers to the result obtained when adding two or more numbers together. For instance:
- The sum of 20 and 17 is 37.
- The sum of 5, 10, and 6 is 21.
- If we have a number, let’s say X, then the sum of 3 and that number can be represented as X + 3.
- Difference: Difference represents the result of subtracting one number from another. It can be positive or negative, depending on the arrangement of the numbers. For example:
- The positive difference between 24 and 10 is 14, which implies the bigger number minus the smaller number.
- The negative difference between 2 and 5 means the smaller number minus the bigger number, resulting in -3 (2 – 5).
- Product: The product is the outcome of multiplying two or more numbers together. For instance:
- The product of 2 and 9 is 18.
- If we have an unknown number, represented by a variable like X or A, then the product of 3 and that number can be expressed as 3 * A = 18.
- Consecutive Odd and Even Numbers: Consecutive odd numbers are odd numbers that follow one another sequentially, such as 1, 3, 5, 7, 9, and so on. Similarly, consecutive even numbers are even numbers that appear one after another, like 2, 4, 6, 8, and so on. Notably, the difference between consecutive odd numbers is always 1, while the difference between consecutive even numbers is 2.
Solving Word Problems:
Let’s delve into a few examples to showcase how to approach and solve word problems step by step:
Example 1: “The product of two numbers is 100, with one of the numbers being 5. Find the other number.” Solution: Let’s assume the unknown number as Y. We can then set up the equation: 5 * Y = 100. By dividing both sides of the equation by 5, we find that Y = 20. To validate the answer, we multiply 20 by 5, resulting in 100.
Example 2: “13 was subtracted from the product of a number and 4. The result is the same as adding 5 to the same number. Find the number.” Solution: Let’s represent the unknown number as Y. The problem can be expressed as (Y * 4) – 13 = Y + 5. By simplifying the equation, we get 4Y – 13 = Y + 5. By collecting like terms, we have 4Y – Y = 5 + 13, which simplifies to 3Y = 18. Dividing both sides of the equation by 3 gives us Y = 6. Verifying the solution, we find that (6 * 4) – 13 equals 6 + 5.
Conclusion
Word problems in mathematics can be challenging, especially when dealing with unfamiliar terminologies and complex relationships between numbers.
However, with a clear understanding of key terms and a step-by-step approach to problem-solving, students can overcome their fears and excel in tackling word problems.
At Edustuff, we hope this tutorial has provided you with a solid foundation and boosted your confidence in handling word problems effortlessly.
Remember, practice makes perfect, and with perseverance, you can conquer any mathematical challenge!