Solved Examples: Translating Subtraction Word Problems into Equations

📚 Quick Study Guide

• ➖Identifying Subtraction Keywords: Look for words like 'less than,' 'decreased by,' 'difference,' 'fewer,' 'take away,' and 'subtract.'
• ✍️Translating Keywords into Symbols: 'Less than' and 'subtracted from' often require reversing the order of the numbers. For example, '5 less than $x$' becomes $x - 5$.
• 🧮Setting up the Equation: Carefully read the problem to identify what is being subtracted from what. Ensure you place the numbers in the correct order based on the keywords.
• ✅Solving the Equation: Once you have the equation, use basic arithmetic to find the unknown variable.
• 💡Checking Your Answer: Substitute your solution back into the original word problem to ensure it makes sense.

Practice Quiz

1. What equation represents: "A number decreased by 12 is 25"?
   1. $x + 12 = 25$
   2. $12 - x = 25$
   3. $x - 12 = 25$
   4. $12 + x = 25$
2. Translate into an equation: "15 less than a number is 8"?
   1. $15 - x = 8$
   2. $x - 15 = 8$
   3. $15 + x = 8$
   4. $x + 15 = 8$
3. Which equation represents: "The difference between a number and 7 is 3"?
   1. $x + 7 = 3$
   2. $7 - x = 3$
   3. $x - 7 = 3$
   4. $x * 7 = 3$
4. What equation matches: "A number subtracted from 20 is 11"?
   1. $x - 20 = 11$
   2. $20 - x = 11$
   3. $20 + x = 11$
   4. $x + 20 = 11$
5. Translate: "9 fewer than a number is 4"?
   1. $9 - x = 4$
   2. $x + 9 = 4$
   3. $x - 9 = 4$
   4. $9 + x = 4$
6. Which equation shows: "6 less than twice a number is 10"?
   1. $6 - 2x = 10$
   2. $2x - 6 = 10$
   3. $2(x - 6) = 10$
   4. $6 + 2x = 10$
7. What equation represents: "A number decreased by 3, then subtracted from 15, is 2"?
   1. $x - 3 - 15 = 2$
   2. $15 - x - 3 = 2$
   3. $15 - (x - 3) = 2$
   4. $15 - (x + 3) = 2$