Key Words Used In Math Word Problems

Key Words Used in Math Word Problems: A Comprehensive Guide

Math word problems can be tricky, but understanding the language used is half the battle. This comprehensive guide will equip you with a strong understanding of the key words and phrases commonly found in math word problems, categorized by the mathematical operation they typically indicate. Mastering these keywords will significantly improve your ability to translate word problems into solvable equations, boosting your problem-solving skills and confidence.

Understanding the Language of Math Problems

Before diving into specific keywords, let's establish a foundational understanding of how word problems are structured. They generally present a scenario, describing a situation involving numbers and relationships between them. Your job is to extract the relevant information, identify the required operation, and solve the problem. This involves carefully identifying the keywords that hint at the mathematical operations needed.

The Importance of Context

While keywords provide strong clues, it's crucial to remember that context is king. Sometimes, a word might suggest one operation, but the overall context of the problem points to a different one. Always read the entire problem carefully before attempting to solve it.

Keywords and Phrases Indicating Addition

Addition problems often involve combining quantities, increasing amounts, or finding totals. Here are some key words and phrases that suggest addition:

Common Addition Keywords:

• Sum: The sum of 5 and 3 is 8.
• Total: The total number of apples is 12.
• Plus: 7 plus 4 equals 11.
• Added to: 5 added to 2 is 7.
• Increased by: The number increased by 6 is 15.
• More than: 10 more than 5 is 15.
• Combined: The combined weight is 20 pounds.
• Together: The numbers together equal 25.
• In all: There are 15 students in all.
• Altogether: There are 10 cookies altogether.

Advanced Addition Phrases:

• The aggregate of: Find the aggregate of 2, 4, and 6.
• In addition to: In addition to the 5 apples, she bought 3 oranges.

Keywords and Phrases Indicating Subtraction

Subtraction problems deal with finding differences, reducing quantities, or comparing amounts. Look for these keywords:

Common Subtraction Keywords:

• Difference: The difference between 10 and 4 is 6.
• Minus: 8 minus 3 is 5.
• Subtracted from: 7 subtracted from 12 is 5.
• Less than: 5 less than 10 is 5.
• Decreased by: The amount decreased by 3 is 8.
• Reduced by: The price reduced by $5 is $10.
• Left: After spending $5, she had $10 left.
• Remaining: The remaining amount is $20.

Advanced Subtraction Phrases:

• How much more: How much more is 15 than 10?
• How much less: How much less is 7 than 12?
• Exceeds: The first number exceeds the second by 5.

Keywords and Phrases Indicating Multiplication

Multiplication problems involve repeated addition, finding the total of equal groups, or calculating areas and volumes. These words are helpful indicators:

Common Multiplication Keywords:

• Product: The product of 6 and 4 is 24.
• Times: 5 times 3 is 15.
• Multiplied by: 9 multiplied by 2 is 18.
• Of: Find ½ of 10.
• Each: Each person has 3 apples.
• Twice: Twice 7 is 14.
• Triple: Triple the amount is 15.
• Area: Calculate the area of the rectangle.

Advanced Multiplication Phrases:

• Per: The speed is 60 miles per hour.
• Rate: What is the rate of growth?
• Doubled: The quantity doubled in size.

Keywords and Phrases Indicating Division

Division problems focus on sharing, splitting, or finding equal parts. The following keywords usually signal division:

Common Division Keywords:

• Quotient: The quotient of 12 and 4 is 3.
• Divided by: 20 divided by 5 is 4.
• Shared equally: The candy was shared equally amongst 5 children.
• Split: The money was split equally between two people.
• Average: Find the average of the numbers.

Advanced Division Phrases:

• Ratio: What is the ratio of boys to girls?
• Proportion: Solve the proportion.
• Unit rate: Find the unit rate.

Keywords Indicating Other Mathematical Operations

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

Percentage Keywords:

• Percent: What is 20 percent of 50?
• Percentage: Calculate the percentage increase.
• Rate: What is the interest rate?

Fraction Keywords:

• Fraction: What fraction of the pizza is left?
• Part: What part of the whole is shaded?

Geometry Keywords:

• Perimeter: Calculate the perimeter of the triangle.
• Area: Find the area of the circle.
• Volume: Calculate the volume of the cube.

Practice Makes Perfect

The best way to master these keywords is through consistent practice. Solve a wide variety of word problems, paying close attention to the language used. Over time, you’ll develop a natural intuition for recognizing the mathematical operation implied by the words and phrases in the problem.

Advanced Strategies for Tackling Word Problems

Beyond keyword recognition, here are some advanced strategies that can help you tackle even the most challenging word problems:

• Read Carefully and Repeatedly: Don't rush through the problem. Read it several times to fully grasp the scenario and the relationships between the numbers.
• Identify the Unknown: What is the question asking you to find? Clearly identify the variable you need to solve for.
• Draw Diagrams or Pictures: Visual aids can be extremely helpful, especially for geometry problems or problems involving multiple steps. A diagram can make complex relationships easier to understand.
• Break Down Complex Problems: Divide complex problems into smaller, more manageable parts. Solve each part individually, then combine the results to get the final answer.
• Check Your Answer: Once you've arrived at an answer, take a moment to check if it makes sense in the context of the problem. Does it seem reasonable? If not, review your calculations.
• Practice Regularly: Consistent practice is key to improving your problem-solving skills. The more problems you solve, the better you'll become at identifying keywords and translating word problems into equations.

Conclusion

Math word problems don't have to be intimidating. By mastering the key words and phrases associated with each mathematical operation, and by employing effective problem-solving strategies, you can significantly improve your ability to translate word problems into solvable equations and confidently arrive at the correct answer. Remember that consistent practice is the key to success. Keep practicing, and you'll find yourself tackling even the most complex word problems with ease and confidence. Good luck!