The core of solving word problems lies in accurately translating the given text into a mathematical expression. This process involves identifying keywords, understanding the order of operations, and representing the problem's elements using mathematical symbols. The problem "Multiply 9 and 5 and then subtract two twel...
Identifying Keywords and Operations
The phrase "Multiply 9 and 5" clearly indicates the multiplication operation. The numbers 9 and 5 are the operands. The phrase "subtract two twelves" signifies subtraction. The term "two twelves" means 2 * 12, which simplifies to 24. Therefore, we need to subtract 24 from the result of the multiplication.
Order of Operations (PEMDAS/BODMAS)
The order of operations, often remembered by the acronyms PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), dictates the sequence in which mathematical operations should be performed. In our example, multiplication comes before subtraction. Therefore, we must first multiply 9 and 5, then subtract 24.
Constructing the Mathematical Expression
Based on the identified keywords, operations, and the order of operations, we can construct the mathematical expression: (9 * 5) - 24. The parentheses ensure that the multiplication is performed before the subtraction.
Evaluating the Expression
Evaluating the expression, we first compute 9 * 5 = 45. Then, we subtract 24 from 45: 45 - 24 = 21. Therefore, the solution to the word problem is 21.
Illustrative Examples of Similar Problems
Let's explore similar problems to reinforce understanding. For instance, consider: "Add 7 and 3, then multiply the result by 6." This translates to (7 + 3) * 6 = 60. Another example: "Divide 20 by 4 and then add 8." This becomes 20 / 4 + 8 = 13.
Advanced Techniques for Complex Word Problems
More complex problems might involve multiple operations, variables, and potentially unknowns. Strategies such as defining variables, breaking down the problem into smaller parts, and using diagrams can be helpful. For instance, if a problem involves finding the area of a rectangle with a length expressed as a function of another variable, carefully defining the variables and using the appropriate formula becomes crucial. Advanced techniques might also involve the use of algebraic equations and simultaneous equations to solve multi-step problems with multiple unknowns.
Practical Applications of Mathematical Expression Translation
The ability to translate word problems into mathematical expressions is essential across various fields. In computer programming, algorithms often require translating problem statements into executable code. In finance, calculating interest, profits, and losses involves translating financial word problems into mathematical expressions. Engineers use this skill to translate design specifications into mathematical models. Scientists translate experimental observations into mathematical equations to describe and predict phenomena.
Troubleshooting Common Mistakes
A common mistake is misinterpreting the order of operations. Always adhere to PEMDAS/BODMAS to avoid errors. Another common error is misreading or misinterpreting the word problem itself. Carefully read the problem multiple times to ensure a correct understanding before attempting to translate it. Clearly defining variables in complex problems is also critical for accuracy.
Further Learning Resources
Numerous online resources, textbooks, and educational videos offer further guidance on translating word problems into mathematical expressions. Focusing on practice problems and understanding the underlying concepts are key to mastering this skill. Practice with a variety of problems, gradually increasing in complexity, is crucial for building proficiency.
Conclusion
Successfully translating word problems into mathematical expressions is a fundamental skill in mathematics and its various applications. By understanding keywords, operations, the order of operations, and employing systematic approaches, one can effectively solve a wide range of problems. Consistent practice and a thorough understanding of the underlying concepts are vital to mastering this essential skill.
Example 1: "Add 15 and 7, then divide by 4" translates to (15 + 7) / 4 = 5.5
Example 2: "Subtract 12 from 30, then multiply by 2" translates to (30 - 12) * 2 = 36
Example 3: "Multiply 6 by 8, then add 10 and subtract 5" translates to (6 * 8) + 10 - 5 = 53