Of course. Here is a complete, in-depth article on the keywords used to solve math word problems.
Cracking the Code: The Essential Keywords to Master Math Word Problems
Math word problems can feel like a secret language, full of clues hidden in plain sight. That said, for many students, the frustration isn't in the math itself, but in knowing where to begin. The key to unlocking these problems lies in recognizing specific keywords that signal the mathematical operation required. This article serves as your decoder ring, translating the language of word problems into clear, actionable steps. By learning to identify these crucial words, you will transform from feeling confused to feeling confident, able to tackle a wide range of problems with ease.
People argue about this. Here's where I land on it.
The core of solving any word problem is a four-step process: Read, Understand, Solve, and Check. Keywords are most vital during the "Understand" phase, where you translate the narrative into a mathematical equation. Let's break down the most common keywords, categorized by operation.
Addition Keywords: Words that Signal Combining or Increasing
Addition problems involve finding a total or combining separate quantities. Look for words that imply a sum or an increase Simple, but easy to overlook..
- Sum: This is the most direct keyword. If a problem asks for the "sum of" two numbers, it is explicitly telling you to add.
- Example: What is the sum of 15 and 27? (15 + 27)
- Total: This word indicates the final amount after combining things. It's often the goal of the problem.
- Example: If Sarah has 8 apples and Tom has 12, what is the total number of apples? (8 + 12)
- In all: This phrase is similar to "total" and is commonly used in younger-grade problems.
- Example: There are 4 red balls and 5 blue balls. How many balls are there in all? (4 + 5)
- Combined: This means put together.
- Example: Mary read 30 pages on Monday and 45 pages on Tuesday. How many pages did she read combined? (30 + 45)
- More than: This can be tricky. "5 more than 10" means 10 + 5. It's essential to identify the starting number first.
- Example: Tom has 7 marbles. He has 3 more than Steve. How many does Steve have? (This requires understanding that Tom's amount is Steve's amount plus 3: Steve's marbles + 3 = 7, so Steve has 4).
- Increased by: This signals a growth or addition to an original amount.
- Example: The temperature was 20°C and then increased by 5°C. What is the new temperature? (20 + 5)
Subtraction Keywords: Words that Signal Taking Away or Finding the Difference
Subtraction problems involve finding what is left, comparing two quantities, or determining a decrease.
- Difference: This is the most straightforward subtraction keyword. It asks "how much bigger or smaller?"
- Example: What is the difference between 50 and 32? (50 - 32)
- Fewer / Less than: These words indicate a smaller quantity. "7 is 3 less than 10" (10 - 3 = 7).
- Example: Jane has 10 stickers. Mark has 4 fewer stickers than Jane. How many does Mark have? (10 - 4)
- Left / Remaining: This is used when something is taken away from a group.
- Example: There were 25 cookies in the jar. After the party, there were 8 left. How many were eaten? (25 - 8)
- Decreased by: The opposite of "increased by," this signals a reduction.
- Example: The price of a shirt was $40, but it was decreased by $10. What is the new price? (40 - 10)
- Take away: A very concrete term for subtraction.
- Example: Billy had 15 marbles. He took away 6. How many does he have now? (15 - 6)
Multiplication Keywords: Words that Signal Equal Groups or Repeated Addition
Multiplication is about finding the total when you have several equal groups or when something is repeated a certain number of times.
- Product: The direct term for the result of multiplication.
- Example: Find the product of 6 and 7. (6 × 7)
- Times: The most common keyword, indicating multiplication.
- Example: What is 8 times 9? (8 × 9)
- Of: This word often appears in fraction and percentage problems but can also signal multiplication. "Half of 20" means ½ × 20.
- Example: What is 25% of 80? (0.25 × 80)
- Each / Per: These words indicate a rate or a cost for a single item, which is then multiplied by the number of items.
- Example: If apples cost $2 each, how much do 5 apples cost? ($2 × 5)
- Example: The car travels 60 miles per hour. How far does it travel in 4 hours? (60 × 4)
- Groups / Sets: These words explicitly describe the equal groups being multiplied.
- Example: There are 6 groups of students, with 5 students in each group. How many students are there in total? (6 × 5)
Division Keywords: Words that Signal Sharing or Grouping
Division is the inverse of multiplication. It's used to find how many equal parts or groups can be made from a total.
- Quotient: The direct term for the result of division.
- Example: Find the quotient of 45 divided by 9. (45 ÷ 9)
- Divided by: The standard operation keyword.
- Example: 56 divided by 7 equals what? (56 ÷ 7)
- Shared equally / Split equally: These phrases describe the act of dividing a total into equal parts.
- Example: 20 candies are shared equally among 4 children. How many does each child get? (20 ÷ 4)
- Per / Each: While used in multiplication, "per" can also signal division when you are finding the rate for one item.
- Example: If 3 pounds of apples cost $6, what is the cost per pound? ($6 ÷ 3)
- Ratio: This word often implies a comparison that can be solved using division.
- Example:
