Study guide: Reason with Signed Changes
Combine, multiply, divide, and solve for signed changes in supplied situations.
Ideas to explain in your own words
- Represent increases and decreases with signed numbers.
- Apply multiplication signs and interpret repeated changes.
- Find a signed per-interval change and check by multiplication.
- Use inverse operations to solve a signed two-step equation.
Watch your reasoning
- −6 + 9 = 3, then 3 − 4 = −1 °C. The total change is +5 °C; adding that change to −6 also gives −1.
- Both factors are negative, so the product is positive. Their magnitudes multiply to 5 × 3 = 15.
- The two signs match, so the quotient is positive: 24 ÷ 6 = 4. Checking (−6) × 4 = −24 verifies it.
- Add seven to get 4x = 16, then divide by four: x = 4. The check is −7 + 4 × 4 = 9.
A worked review example
Follow a temperature change: −4 + 7 = 3 °C; then 3 − 5 = −2 °C. The total change is +2 °C even though the final temperature remains below zero. Multiply Signed Changes: 4 × (−3) = −12 and (−4) × (−3) = +12. Their sum is 0, agreeing with [4 + (−4)] × (−3) = 0. Divide a Signed Total: −18 ÷ 3 = −6 units per interval. Multiplication checks this because 3 × (−6) = −18. Algebraically, (−18) ÷ (−3) = +6 because (−3) × 6 = −18. Solve for an Unknown Number of Changes: −8 + 3x = 7 leads to 3x = 15 and x = 5. Checking −8 + 3 × 5 = −8 + 15 = 7 confirms five intervals.
Make a practice plan
- Try the supplied lesson problems without looking at the answers.
- Compare your method with the worked examples and explain any correction.
- Use the new review cases, then complete the transfer task on paper or in your own document.