Math Key Words In Word Problems

Decoding Math Word Problems: A Comprehensive Guide to Key Words

Math word problems can be daunting, especially for students who struggle to translate the words into mathematical equations. The key to conquering these problems lies in understanding the underlying language. This comprehensive guide dives deep into the common keywords and phrases used in math word problems, breaking down their meanings and showing you how to identify the correct operation needed to solve them. Mastering these keywords is the first step towards building strong mathematical problem-solving skills.

Understanding the Structure of Word Problems

Before diving into specific keywords, let's look at the general structure of a typical math word problem. Most word problems present a scenario, describe the given information (numbers and quantities), and then pose a question that needs to be answered. The key is to carefully dissect this information, identifying the relevant numbers and the relationships between them. This involves paying close attention to the language used, as this language dictates the mathematical operations required.

Key Words Indicating Addition (+)

Addition word problems typically describe situations where quantities are being combined or increased. Look for these keywords and phrases:

Common Addition Keywords:

• Sum: The sum of 5 and 3 is 8.
• Total: What is the total number of apples and oranges?
• In all: There are 10 red cars and 5 blue cars. How many cars are there in all?
• Combined: How many toys do they have combined?
• Together: If John has 7 marbles and Mary has 8, how many do they have together?
• Plus: What is 12 plus 7?
• Increased by: A number increased by 5 is 15. What is the number?
• Added to: 3 added to 9 is what?
• More than: 7 more than 4 is what?
• Greater than: A number is 5 greater than 12. What is the number?

Advanced Addition Clues:

Sometimes, addition is implied rather than explicitly stated. Look for phrases indicating a cumulative effect or an increase in quantity. For example:

• "Over the course of three days..." This often suggests adding the daily quantities.
• "In addition to..." This clearly indicates an addition.

Key Words Indicating Subtraction (-)

Subtraction problems describe situations where quantities are being reduced, compared, or separated. Look for these keywords and phrases:

Common Subtraction Keywords:

• Difference: What is the difference between 15 and 7?
• Less than: What is 5 less than 12?
• Minus: What is 10 minus 4?
• Decreased by: A number decreased by 3 is 8. What is the number?
• Subtracted from: 5 subtracted from 10 is what?
• Reduced by: The price was reduced by $5.
• Remained: After eating 3 apples, 7 remained. How many apples were there initially?
• Left: How many apples are left?
• Take away: Take away 3 from 9.
• Fewer than: 3 fewer than 10 is what?

Advanced Subtraction Clues:

As with addition, subtraction can be implied. Look out for:

• "How much more..." This usually implies finding the difference between two quantities.
• "How many are left..." This directly indicates a subtraction problem.
• "How much change..." This implies subtracting the cost from the amount paid.

Key Words Indicating Multiplication (×)

Multiplication problems describe situations involving repeated addition or scaling quantities. Look for these keywords:

Common Multiplication Keywords:

• Product: What is the product of 6 and 4?
• Times: What is 8 times 3?
• Multiplied by: What is 5 multiplied by 9?
• Of: What is ½ of 10?
• Each: Each student has 5 pencils.
• Every: Every box contains 12 eggs.

Advanced Multiplication Clues:

Context is crucial in recognizing implied multiplication. Phrases that suggest repetition or scaling often point towards multiplication:

• "For each..." This usually precedes a multiplication problem.
• "Per..." (e.g., "dollars per item," "miles per hour") These denote a rate, requiring multiplication.
• "Twice," "Thrice," etc.: These words represent multiples of a quantity.

Key Words Indicating Division (÷)

Division problems describe situations involving equal sharing or grouping. Look for these keywords:

Common Division Keywords:

• Quotient: What is the quotient of 20 and 5?
• Divided by: What is 18 divided by 6?
• Split equally: The cake was split equally among 4 children.
• Shared equally: The toys were shared equally between two children.
• Each: How many cookies does each person get?
• Per: The speed is 60 miles per hour.
• Average: What is the average score?

Advanced Division Clues:

Pay attention to the context for implicit division:

• "How many times..." This suggests dividing one quantity by another.
• "Grouped into..." This implies division into equal groups.
• "Rate" or "Ratio" problems: These often require division to find the rate or ratio.

Key Words Indicating Other Operations

Beyond the four basic operations, word problems can involve other mathematical concepts:

• Fractions: Keywords like "part of," "portion," "fraction," "half," "third," etc., indicate fractions.
• Decimals: Decimal numbers are often used in word problems involving money, measurements, or percentages.
• Percentages: Look for keywords like "percent," "percentage," "of," "rate," "discount," "increase," "decrease," etc.
• Geometry: Keywords related to shapes (circle, square, triangle, etc.) dimensions (length, width, height, radius, etc.), and geometric concepts (area, perimeter, volume, etc.) suggest geometry problems.
• Algebra: Words like "unknown," "variable," "let x be...", and the use of letters or symbols to represent unknown quantities indicate algebraic problems.

Strategies for Solving Word Problems

Once you've identified the key words and understood the relationships between the quantities, use these steps to solve the problem:

1. Read carefully: Read the problem thoroughly to grasp the context.
2. Identify keywords: Locate the keywords that indicate the mathematical operations.
3. Assign variables: Assign variables to represent the unknown quantities.
4. Write an equation: Translate the word problem into a mathematical equation.
5. Solve the equation: Use appropriate mathematical techniques to solve for the unknown.
6. Check your answer: Verify if the solution makes sense in the context of the problem.

Practicing with Examples

Let's practice with a few examples:

Example 1: John has 15 apples. He gives 5 apples to his friend. How many apples does John have left?

• Keywords: gives, left
• Operation: Subtraction
• Equation: 15 - 5 = 10
• Answer: John has 10 apples left.

Example 2: A baker makes 12 loaves of bread each day. How many loaves does he make in 5 days?

• Keywords: each day, how many
• Operation: Multiplication
• Equation: 12 × 5 = 60
• Answer: The baker makes 60 loaves in 5 days.

Example 3: Sarah has 24 candies. She wants to share them equally among 6 friends. How many candies will each friend receive?

• Keywords: share equally, each friend
• Operation: Division
• Equation: 24 ÷ 6 = 4
• Answer: Each friend will receive 4 candies.

Conclusion

Mastering the vocabulary of math word problems is crucial for developing strong problem-solving skills. By learning to identify the key words and translate them into mathematical equations, you can confidently tackle even the most challenging problems. Remember to read carefully, identify the keywords, and break down the problem into smaller, manageable steps. Consistent practice is key to improving your ability to solve math word problems efficiently and accurately. With dedicated effort and attention to detail, you can transform these seemingly daunting challenges into opportunities for mathematical growth and success.