Many students struggle with word problems because they don’t know how to translate words into mathematical expressions. Recognizing clue words in the problem statement helps determine which mathematical operations to use—whether it's addition, subtraction, multiplication, or division. Misinterpreting these keywords can lead to incorrect solutions, so mastering them is essential for accurate and quick problem-solving.
Common Keywords and Their Mathematical Meanings
Multiplication Keywords
"X times greater than" / "X times as much as" / "X times more than"
- These phrases mean multiplication.
- Example:
- “A tree is 3 times taller than another tree that is 5 meters high. How tall is the first tree?”
- Solution: \( 3 \times 5 = 15\) meters
"Product of"
- Indicates multiplication of two or more numbers.
- Example: “Find the product of 7 and 9.”
- Solution: \( 7 \times 9 = 63 \)
Division Keywords
"Divided by" / "Per" / "Each"
- These indicate division.
- Example:
- “A total of 24 apples are divided equally among 6 baskets. How many apples are in each basket?”
- Solution: \( 24 \div 6 = 4 \) apples per basket
"Half of" / "One-third of" / "A fraction of"
- These mean taking a fractional part of a number.
- Example: “What is one-third of 90?”
- Solution: \( 90 \div 3 = 30\)
Addition Keywords
"More than" / "Increased by" / "Sum of"
- These indicate addition.
- Example:
- “A bag contains 15 marbles, and 7 more are added. How many marbles are now in the bag?”
- Solution: \( 15 + 7 = 22 \) marbles
"Total of"
- Means adding all given values.
- Example: “Find the total of 12, 25, and 30.”
- Solution: \(12 + 25 + 30 = 67 \)
Subtraction Keywords
"Lesser than" / "Decreased by" / "Difference between"
- These indicate subtraction.
- Example:
- “A basket had 50 mangoes. If 18 mangoes were sold, how many are left?”
- Solution: \(50 - 18 = 32 \) mangoes
"How many more" / "How much less"
- These are used in comparison problems.
- Example: “John has 12 pencils, while Mark has 8. How many more pencils does John have than Mark?”
- Solution: \( 12 - 8 = 4 \) pencils
Comparison Keywords
"Twice as much" / "Three times as many"
- These indicate multiplication in comparison problems.
- Example:
- “A city’s population is twice that of another city with 40,000 residents. What is the population of the larger city?”
- Solution: \(2 \times 40,000 = 80,000 \)
"Half as much" / "One-third as much"
- These involve fractions.
- Example: “A rope is half as long as a 60-meter rope. How long is it?”
- Solution: \( 60 \div 2 = 30 \) meters
Applying These Keywords to Solve Word Problems
To solve word problems easily:
- Identify the keyword in the problem.
- Determine the correct mathematical operation based on the keyword.
- Translate the word problem into an equation.
- Solve the equation step by step.
Example Problem:
“A box contains 4 times as many pencils as another box that holds 8 pencils. How many pencils are in the larger box?”
- Keyword: “4 times as many” → Multiplication
- Equation: \(4 \times 8 = 32 \)
- Answer: 32 pencils
Conclusion
Word problems become much easier when you recognize key mathematical phrases and know how to translate them into equations. By understanding terms like “times greater,” “lesser than,” “more than,” and “decreased by,” you can quickly identify the correct operations and solve problems efficiently.
For more practice, try mock exams and word problem drills on brevph to sharpen your skills and boost your confidence in solving math problems under exam conditions! 🚀