Support your claims with evidence from your real life
Claim: Absolute value is always positive.
Evidence from real life:
1. Temperature: The absolute value of temperature always represents the magnitude or intensity of heat, regardless of it being positive or negative. For example, if a weather report says the temperature is -5 degrees Celsius, the absolute value would be 5 degrees Celsius.
2. Banking Transactions: When making financial transactions, it is common to have account balances that can be positive or negative. However, when calculating the total balance or determining the overall value of an account, the absolute value is used to indicate the magnitude of the funds, disregarding their polarity.
3. Distance: In everyday life, we often measure distances between two points. Whether it is measuring how far we traveled or estimating the distance between two cities, the absolute value is used to ignore the direction and focus solely on the numerical value. For instance, if the distance between two cities is -200 miles, taking the absolute value leaves us with 200 miles.
These real-life examples show that absolute value is consistently positive, regardless of the initial value being positive or negative, supporting the claim that absolute value is always positive.
Claim: Absolute value is always positive.
Evidence:
1. Definition: The absolute value of a number is defined as the distance of that number from zero on the number line. Distance is always positive, so the absolute value is always positive regardless of the number itself.
2. Algebraic proof: Let's consider a number x. If x is positive, then its absolute value is simply x. If x is negative, the absolute value is -x, which is the negation of x. However, since x is negative, -x will still be positive. Therefore, in both cases, the absolute value is positive.
3. Real-life examples: Consider temperatures. The absolute value of any temperature will always be positive. For instance, if the temperature is -10 degrees Celsius, its absolute value will be 10 degrees Celsius. This holds true for any negative temperature, making it evident that the absolute value is always positive in real-life scenarios.
4. Mathematics applications: In calculus, the concept of absolute value is used to determine the magnitude of rates of change. For example, the absolute value of the velocity of an object represents its speed, which is always positive regardless of the direction of motion.
The combination of these pieces of evidence supports the claim that the absolute value is always positive.