When tackling math word problems, it’s essential to break down the problem into manageable parts and solve it systematically. Here’s a structured approach to help you solve these problems effectively:
Two Key Steps
- Translate the Problem into a Numeric Equation:
- Convert the words into mathematical expressions.
- Combine these expressions into a single equation.
- Solve the Equation:
- Follow mathematical rules to find the solution.
Tips for Success
- Read the Problem Thoroughly:
- Start by reading the entire problem to understand the situation.
- Identify Information and Variables:
- List all the known quantities and the variables (unknowns) you need to solve for.
- Assign Units to Variables:
- Attach units of measurement to your variables (e.g., miles, gallons, inches). This helps keep track of what each variable represents.
- Define the Desired Answer:
- Clearly state what you’re trying to find, including its units.
- Work Organically and Methodically:
- Write out your steps clearly. This helps you stay organized and reduces errors.
- Explain each step as you go, which can clarify your thinking and make it easier to track your progress.
- Draw and Label Diagrams if Needed:
- Visual aids like graphs or pictures can be very helpful. Label them clearly.
- Recognize “Key” Words:
- Certain words in the problem indicate specific mathematical operations. Recognizing these can guide you in forming the correct equation.
Key Words and Operations
Different words in a problem suggest different mathematical operations. Here’s a guide:
Addition (+)
- Key Words: increased by, more than, combined together, total of, sum, added to
- Examples:
- What is the sum of 8 and y? → 8+y8 + y8+y
- Express the number of apples (x) increased by two. → x+2x + 2x+2
- What is the total weight of Alphie the dog (x) and Cyrus the cat (y)? → x+yx + yx+y
Subtraction (−)
- Key Words: less than, fewer than, reduced by, decreased by, difference of
- Examples:
- What is four less than y? → y−4y – 4y−4
- What is nine less than a number (y)? → y−9y – 9y−9
- What if the number of pizzas (x) was reduced by 6? → x−6x – 6x−6
- What is the difference between my weight (x) and your weight (y)? → x−yx – yx−y
*Multiplication (× or )
- Key Words: of, times, multiplied by
- Examples:
- What is y multiplied by 13? → 13y13y13y or 13×y13 \times y13×y
- Three runners averaged “y” minutes. What was their total running time? → 3y3y3y
- I drive my car at 55 miles per hour. How far will I go in “x” hours? → 55x55x55x
Division (÷ or /)
- Key Words: per, a, out of, ratio of, quotient of, percent (divide by 100)
- Examples:
- What is the quotient of y and 3? → y/3y/3y/3 or y÷3y ÷ 3y÷3
- Three students rent an apartment for $x per month. What will each pay? → x/3x/3x/3 or x÷3x ÷ 3x÷3
- “y” items cost a total of $25.00. What is their average cost? → 25/y25/y25/y or 25÷y25 ÷ y25÷y
Common Phrases and Their Translations
- “Per” or “a” often means “divided by.”
- Example: “30 miles per gallon” → 30 miles/gallon\text{30 miles}/\text{gallon}30 miles/gallon
- “Less than” can be tricky.
- For example, “1.5 less than x” is x−1.5x – 1.5x−1.5, not 1.5−x1.5 – x1.5−x.
- “Quotient/Ratio of” means division.
- Example: “The ratio of x and y” is x/yx/yx/y.
- “Difference of” means subtraction.
- Example: “The difference of x and y” is x−yx – yx−y.
Practice Examples
- What if the number (x) of children was reduced by six, and then they had to share twenty dollars? How much would each get?
- Solution: 20x−6\frac{20}{x – 6}x−620
- What is 9 more than y?
- Solution: y+9y + 9y+9
- What is the ratio of 9 more than y to y?
- Solution: y+9y\frac{y + 9}{y}yy+9
- What is nine less than the total of a number (y) and two?
- Solution: (y+2)−9(y + 2) – 9(y+2)−9 or y−7y – 7y−7
- The length of a football field is 30 yards more than its width (y). Express the length of the field in terms of its width y.
- Solution: y+30y + 30y+30
By following these steps and recognizing key words, you’ll be better equipped to translate word problems into equations and solve them accurately.