Math Key Words For Word Problems

Math Keywords for Word Problems: A Comprehensive Guide

Solving math word problems can be challenging, but mastering the language of these problems is the first step towards success. This comprehensive guide delves into the crucial role of keywords in understanding and solving mathematical word problems. We'll explore various categories of keywords, providing examples and strategies to help you decipher the meaning behind the numbers and unlock the solutions.

Understanding the Importance of Keywords

Keywords are the signposts in word problems. They act as clues, directing you towards the correct operation (addition, subtraction, multiplication, or division) to solve the problem. Identifying these keywords accurately is crucial for setting up the problem correctly and avoiding common mistakes. Ignoring these subtle cues can lead to incorrect calculations and frustratingly wrong answers. This guide will equip you with the knowledge to confidently tackle even the most complex word problems.

Categories of Keywords and Their Corresponding Operations

Math word problems use specific keywords to indicate the mathematical operation required. Let's break down the most common categories:

Addition Keywords

Addition problems involve combining quantities. Keywords associated with addition often indicate a process of combining, increasing, or totaling. Here are some examples:

• Sum: "Find the sum of 5 and 12." This directly indicates addition.
• Total: "What is the total number of apples if you have 10 red apples and 7 green apples?" This asks for the combined quantity.
• In all: "There are 8 birds in one tree and 5 birds in another. How many birds are there in all?"
• Plus: "15 plus 7 equals...?" This is a direct indicator of addition.
• Added to: "6 added to 9 gives...?" This means 9 + 6.
• Increased by: "A number increased by 3 is 11. What is the number?" This implies adding 3 to an unknown number.
• Combined: "When two numbers are combined, they equal 25." This necessitates addition.
• Together: "How many cookies are there together if there are 12 chocolate chip and 8 oatmeal cookies?" This signals a combining of quantities.
• More than: "John has 5 more than Mary. Mary has 3 apples. How many does John have?"

Subtraction Keywords

Subtraction involves finding the difference between two quantities or reducing a quantity. Look for keywords that suggest difference, reduction, or remaining.

• Difference: "Find the difference between 20 and 15." This clearly points to subtraction.
• Subtract: "12 subtract 5 equals...?" A direct instruction to perform subtraction.
• Minus: "25 minus 10 is...?" Another clear indication of subtraction.
• Less than: "John has 3 apples less than Mary, who has 8. How many does John have?" This implies subtracting 3 from 8.
• Reduced by: "The price was reduced by $5. The original price was $20. What is the new price?" This signifies subtracting $5 from $20.
• Decreased by: "The temperature decreased by 10 degrees. The original temperature was 30 degrees. What is the new temperature?" This denotes subtraction.
• Left: "After eating 5 cookies, there were 7 left. How many cookies were there initially?" Finding what remained implies subtraction.
• Remaining: "How many apples are remaining if you started with 10 and ate 3?"
• Fewer than: "Sarah has 2 fewer than Tom. Tom has 7 toys. How many does Sarah have?" This necessitates subtracting 2 from 7.

Multiplication Keywords

Multiplication problems involve repeated addition or finding the product of two or more quantities. Watch for words that indicate repeated groups, product, or times.

• Product: "Find the product of 6 and 4." This is a direct instruction for multiplication.
• Times: "8 times 5 equals...?" This explicitly signals multiplication.
• Multiplied by: "7 multiplied by 3 is...?" Another way of expressing multiplication.
• Of: "Find 1/2 of 10." "Of" often indicates multiplication, especially when dealing with fractions or percentages.
• Each: "Each box contains 6 apples. You have 3 boxes. How many apples do you have?" This indicates multiplication of 6 apples per box by 3 boxes.
• Per: "The speed is 60 miles per hour. How many miles will be traveled in 2 hours?" "Per" signifies a rate, indicating multiplication.
• Total: While also used for addition, "total" can also indicate multiplication if the context involves repeated quantities. For example, "What is the total cost of 5 items at $3 each?"

Division Keywords

Division involves splitting a quantity into equal groups or finding how many times one number goes into another. Keywords related to division often suggest sharing, equal groups, or dividing.

• Divide: "15 divided by 3 equals...?" A direct instruction to perform division.
• Quotient: "Find the quotient of 24 and 6." Refers to the result of division.
• Split: "If you split 20 candies equally among 4 friends, how many does each friend get?" This signals division.
• Shared equally: "12 cookies are shared equally among 3 people. How many cookies does each person get?" This involves division.
• Each: While also used in multiplication, "each" can indicate division when determining the size of each group. For example, "If 20 apples are distributed equally among 4 baskets, how many apples are in each basket?"
• Per: Similar to multiplication, "per" can be a division keyword if it asks for a rate. For example, "What is the cost per item if 10 items cost $20?"
• Rate: The term rate often implies division. For example: "What is the average speed (rate) if you travel 150 miles in 3 hours?"

Advanced Keywords and Contextual Clues

Beyond these basic categories, some words require careful consideration of the context to determine the appropriate operation. These can often be trickier:

• Average: Finding the average usually involves addition (summing values) followed by division (dividing by the number of values).
• Twice: This means multiplying by 2.
• Triple: This means multiplying by 3.
• Half: This means dividing by 2 or multiplying by 1/2.
• Percent: Percentage problems involve multiplication and division, often using the formula: (Percentage/100) * Whole number.
• Ratio: Ratio problems often involve division, focusing on comparing relative sizes of two or more quantities.
• Proportion: Similar to ratios, proportion problems involve equal ratios, often using cross-multiplication to solve.

Strategies for Deciphering Keywords

1. Read carefully: Thoroughly read the problem multiple times, paying close attention to the wording and context.
2. Identify the unknown: Determine exactly what the problem is asking you to find.
3. Underline keywords: Highlight the keywords that indicate the mathematical operations required.
4. Draw diagrams or pictures: Visual representations can help clarify the problem and its relationships.
5. Check your work: After calculating your answer, review your steps to ensure accuracy. Does the answer make sense in the context of the problem?
6. Practice regularly: Consistent practice is key to mastering the interpretation of keywords in math word problems. The more you practice, the better you'll become at recognizing patterns and applying the correct operations.

Examples of Word Problems and Keyword Identification

Let's look at a few examples to illustrate how to identify keywords:

Example 1:

• Problem: Sarah has 15 apples. She gives 5 to John. How many apples does Sarah have left?

• Keywords: "left" (subtraction), "gives" (subtraction)

• Solution: 15 - 5 = 10 apples

Example 2:

• Problem: A bakery sells 12 muffins per hour. How many muffins are sold in 3 hours?

• Keywords: "per" (multiplication)

• Solution: 12 muffins/hour * 3 hours = 36 muffins

Example 3:

• Problem: Four friends share 20 cookies equally. How many cookies does each friend receive?

• Keywords: "share," "equally" (division)

• Solution: 20 cookies / 4 friends = 5 cookies per friend

Example 4:

• Problem: What is the total cost of 3 books at $10 each?

• Keywords: "total" (multiplication, in this context)

• Solution: 3 books * $10/book = $30

Conclusion

Mastering math word problems hinges on effectively identifying and understanding keywords. By diligently practicing and employing the strategies outlined in this guide, you can significantly improve your problem-solving skills. Remember to read carefully, underline keywords, and visualize the problem to enhance comprehension. With consistent effort, deciphering the language of math word problems will become second nature, leading you to confident and accurate solutions. Continue to practice and hone your skills to confidently tackle increasingly challenging problems and unlock the world of mathematical problem-solving.