Math Problem Statement

The temperature of a freezer changed from 16.1°C to 14.7°C. a) i) By how much did the temperature change? ii) Is this an increase or a decrease in temperature? Explain how you know. b) By how much does the temperature need to change again before it is at 3.8°C?

Solution

Solution:

a) i) By how much did the temperature change?

The change in temperature is calculated by finding the difference between the two temperatures:

Temperature change=16.1C14.7C\text{Temperature change} = 16.1^\circ\text{C} - 14.7^\circ\text{C}

Temperature change=1.4C\text{Temperature change} = 1.4^\circ\text{C}

a) ii) Is this an increase or a decrease in temperature?

This is a decrease in temperature because the final temperature 14.7C14.7^\circ\text{C} is less than the initial temperature 16.1C16.1^\circ\text{C}. A decrease occurs when the value becomes smaller.

b) By how much does the temperature need to change again before it is at 3.8C3.8^\circ\text{C}?

To find the required change, calculate the difference between the current temperature (14.7C14.7^\circ\text{C}) and the target temperature (3.8C3.8^\circ\text{C}):

Required change=14.7C3.8C\text{Required change} = 14.7^\circ\text{C} - 3.8^\circ\text{C}

Required change=10.9C\text{Required change} = 10.9^\circ\text{C}

Thus, the temperature needs to decrease by 10.9C10.9^\circ\text{C} to reach 3.8C3.8^\circ\text{C}.


Summary:

  • a i) The temperature changed by 1.4C1.4^\circ\text{C}.
  • a ii) It is a decrease because the final temperature is lower than the initial temperature.
  • b) The temperature needs to decrease by 10.9C10.9^\circ\text{C} to reach 3.8C3.8^\circ\text{C}.

Would you like more details or have any questions? Here are five related questions to explore further:

  1. How do you calculate percentage changes in temperature?
  2. What tools can help track temperature changes over time?
  3. How do you represent temperature changes graphically?
  4. How does temperature change relate to the physical states of matter?
  5. What is the significance of temperature in weather forecasting?

Tip: Always pay attention to the signs of changes (increase or decrease) to avoid errors in interpretation.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Temperature Change

Formulas

Temperature change = Initial temperature - Final temperature
Required change = Current temperature - Target temperature

Theorems

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Suitable Grade Level

Grades 5-7