Keywords Used In Math Word Problems

Keywords Used in Math Word Problems: A Comprehensive Guide

Math word problems can be tricky, but understanding the keywords they contain is the first step to mastering them. These words act as signposts, guiding you towards the correct mathematical operation to solve the problem. This comprehensive guide delves deep into the keywords frequently used in math word problems, categorized for easier understanding and application. We'll explore keywords related to addition, subtraction, multiplication, division, fractions, decimals, percentages, and more, providing examples to illustrate their use. Mastering these keywords will significantly improve your ability to accurately translate word problems into solvable mathematical equations.

Keywords Indicating Addition

Addition problems involve combining quantities. The keywords used often suggest an increase or a total sum. Here are some common examples:

Common Addition Keywords:

• Total: This is a very common keyword indicating the need to add values together. Example: "Find the total cost of the apples and oranges."
• Sum: Similar to "total," this word asks for the result of adding numbers together. Example: "What is the sum of 15 and 22?"
• In all: This phrase implies a collective amount. Example: "There are 10 red marbles and 15 blue marbles. How many marbles are there in all?"
• Together: This suggests combining quantities. Example: "If you have 5 dollars and your friend has 7 dollars, how much do you have together?"
• Combined: This word indicates merging quantities. Example: "When their scores are combined, what is the total score?"
• Plus: A straightforward indicator of addition. Example: "8 plus 5 equals what?"
• Added to: Indicates one number is being added to another. Example: "5 added to 12 equals what?"
• Increased by: Shows an increase in a quantity. Example: "The temperature increased by 10 degrees."
• More than: Indicates a quantity that is greater. Example: "He has 5 more than his brother."

Advanced Addition Keywords:

• Altogether: This indicates a collective total. Example: "Altogether, how many students are in the class?"
• In total: Similar to "altogether," signifying the final sum. Example: "In total, how many points did the team score?"
• Aggregate: This word suggests a combined total of multiple amounts. Example: "What is the aggregate amount of sales for the year?"

Keywords Indicating Subtraction

Subtraction problems involve finding the difference between two quantities or reducing a quantity. The keywords often suggest a decrease or a remaining amount.

Common Subtraction Keywords:

• Difference: This keyword directly points to subtraction. Example: "Find the difference between 25 and 12."
• Less than: Indicates a smaller quantity. Example: "He has 3 less than his sister."
• Minus: A direct indicator of subtraction. Example: "15 minus 7 equals what?"
• Subtracted from: Indicates one number is being taken away from another. Example: "7 subtracted from 15 equals what?"
• Remainder: The amount left after subtraction. Example: "What is the remainder after subtracting 5 from 15?"
• Left: The quantity remaining after something is removed. Example: "How many apples are left?"
• Decreased by: Shows a decrease in a quantity. Example: "The number of students decreased by 5."
• Reduced by: Similar to "decreased by," indicating a reduction. Example: "The price was reduced by 10%."

Advanced Subtraction Keywords:

• Remaining: Similar to "remainder" and "left," indicating what's left after subtraction. Example: "How many candies are remaining?"
• Net: The final amount after accounting for additions and subtractions. Example: "What is the net profit?"

Keywords Indicating Multiplication

Multiplication problems involve repeated addition or finding the product of two or more quantities.

Common Multiplication Keywords:

• Product: The result of multiplication. Example: "Find the product of 6 and 8."
• Times: A direct indicator of multiplication. Example: "5 times 3 equals what?"
• Multiplied by: Indicates one number is being multiplied by another. Example: "8 multiplied by 4 equals what?"
• Of: Often used with fractions and percentages. Example: "Find one-third of 12."
• Each: Used when multiple groups have the same number of items. Example: "Each box contains 10 apples."

Advanced Multiplication Keywords:

• Total of groups: Suggests multiplying the number of groups by the quantity in each group. Example: "What is the total of 5 groups of 4 pencils?"

Keywords Indicating Division

Division problems involve sharing or splitting a quantity into equal parts.

Common Division Keywords:

• Quotient: The result of division. Example: "Find the quotient of 24 divided by 6."
• Divided by: A direct indicator of division. Example: "24 divided by 6 equals what?"
• Shared equally: Indicates division into equal parts. Example: "The candy is shared equally amongst 5 children."
• Split equally: Similar to "shared equally." Example: "The money was split equally between the two friends."
• Per: Indicates a rate or ratio, often requiring division. Example: "Miles per hour," "cost per item."

Advanced Division Keywords:

• Average: Finding the average involves division. Example: "What is the average score of the students?"
• Rate: Represents a ratio between two quantities, often solved through division. Example: "Calculate the heart rate."
• Ratio: Shows the relationship between two quantities, often requiring division to simplify. Example: "Find the ratio of boys to girls."

Keywords Related to Fractions, Decimals, and Percentages

These keywords often appear in more complex word problems requiring specific mathematical techniques.

Fractions:

• Fraction: Represents a part of a whole. Example: "What fraction of the pizza is left?"
• Part of: Indicates a portion of a larger quantity. Example: "What part of the class is boys?"
• Numerator: The top number of a fraction.
• Denominator: The bottom number of a fraction.

Decimals:

• Decimal: A number with a decimal point.
• Point: Refers to the decimal point.

Percentages:

• Percent: A fraction or ratio expressed as a number out of 100.
• Percentage: The result of a percentage calculation.
• Of: Used in percentage calculations. Example: "What is 20% of 50?"

Keywords Indicating Other Mathematical Concepts

• Area: The size of a surface.
• Perimeter: The distance around a shape.
• Volume: The amount of space a three-dimensional object occupies.
• Speed: Distance covered per unit of time.
• Time: Duration of an event.
• Distance: Length between two points.
• Profit: The positive difference between revenue and cost.
• Loss: The negative difference between revenue and cost.
• Interest: Money earned on savings or paid on loans.

Strategies for Solving Word Problems Using Keywords

1. Identify the Keywords: Carefully read the problem and underline or circle the keywords.

2. Determine the Operation: Based on the keywords, determine whether the problem requires addition, subtraction, multiplication, or division.

3. Translate into an Equation: Translate the words into a mathematical equation using the appropriate symbols.

4. Solve the Equation: Solve the equation using the appropriate mathematical techniques.

5. Check Your Answer: Make sure your answer is reasonable and makes sense in the context of the problem.

Conclusion

Mastering the keywords used in math word problems is crucial for success in mathematics. By understanding these words and their implications, you can effectively translate word problems into solvable mathematical equations. This guide provides a comprehensive overview of commonly used keywords, categorized for clarity and enhanced understanding. Remember to practice regularly and apply these strategies to improve your problem-solving skills. With consistent effort and attention to detail, you'll confidently tackle even the most challenging math word problems. Remember that context is key; sometimes, a word might not directly indicate an operation but contribute to understanding the overall scenario. Practice and experience are invaluable in honing your ability to accurately interpret and solve these problems.