Grade 7 Integers: Word Problems

Real-world rational number problems

What You'll Learn

Represent real situations with signed numbers
Choose the operation and solve in context

📖Signed numbers in stories

Below zero, below sea level, a loss, a debt or a decrease is negative; above zero, a gain, a deposit or an increase is positive. Write each quantity as a signed number, choose the operation, then solve.

💡Check the sign

Ask whether the answer should be above or below zero. A temperature that drops past zero, or a payment larger than the balance, ends negative.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
A stock's price changed by −$2.74 every day for 6 days in a row. What was the total change in the stock's price, in dollars? Use a negative number for a decrease.
1. Multiply the numbers without their signs: 2.74 × 6 = 16.44.
2. The signs are different, so the answer is negative.
3. (−2.74) × 6 = −16.44
Answer: −16.44
Example 2
Jordan's bank account was overdrawn, with a balance of −$58.68. Then he deposited $18.40. What is his new balance, in dollars?
1. The signs are different: subtract 58.68 − 18.4 = 40.28 and keep the sign of (−58.68), the number farther from zero.
2. (−58.68) + 18.4 = −40.28
Answer: −40.28
Example 3
A scuba diver is 23 meters below sea level, at an elevation of −23 m. She swims up 12.8 meters. What is her new elevation, in meters?
1. The signs are different: subtract 23 − 12.8 = 10.2 and keep the sign of (−23), the number farther from zero.
2. (−23) + 12.8 = −10.2
Answer: −10.2