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.