GCSE Maths Practice: integers-and-directed-numbers
This question links division of signed numbers to a real-world context — the rate of temperature drop in a science experiment.
Divide the total negative change by time. A negative rate means a steady decrease.
Using Negative Division in Science
Dividing positive and negative numbers helps explain rates of change in scientific contexts. For example, a drop in temperature or a fall in pressure can be represented by a negative rate. This question links number operations with real-life scientific thinking.
Scenario
A laboratory freezer cools from 0°C to −14°C evenly over 14 minutes. To find the average change per minute, we divide the total temperature change (−14°C) by the time (14 minutes):
(−14) ÷ 14 = −1°C per minute.
The result is negative because the temperature is decreasing — each minute, the temperature drops by 1°C.
Step-by-Step Method
- Find the total change: final − initial = −14 − 0 = −14.
- Divide by time: −14 ÷ 14 = −1.
- Interpret the result: the negative sign means the temperature is going down.
Understanding the Rule
When dividing numbers with different signs, the result is negative. If both numbers had the same sign (e.g., −14 ÷ −14), the result would be positive because two negatives make a positive.
Worked Examples
- (−20) ÷ 4 = −5 → a fall of 5 units per step.
- 12 ÷ (−3) = −4 → opposite direction or loss rate.
- (−14) ÷ 14 = −1 → temperature drops 1°C per minute.
Common Misunderstandings
- Ignoring the direction the sign represents (thinking −1 means smaller, not downward rate).
- Forgetting to apply the negative when only one value is below zero.
- Reversing the order of change (subtracting wrongly).
Real-Life Applications
This type of calculation appears in climate studies, chemistry, and physics. Scientists often describe changes using negative rates — such as cooling per minute or decrease in pressure per second. Understanding these helps interpret graphs, trends, and formulas accurately.
FAQs
- Q: Why does the answer have a negative sign?
A: Because the change (−14) and the time (14) have opposite signs — different signs give a negative quotient. - Q: What if both values were negative?
A: Then the result would be positive, since two negatives cancel out. - Q: Does the size of the negative number matter?
A: Only its sign affects direction; the magnitude tells you how fast it changes.
Study Tip
In word problems, always identify what each negative means — direction, drop, or loss. Dividing negative by positive simply indicates the rate of decrease per unit, not that the quantity is “less.”