Podcast
Questions and Answers
Which integer represents 8°C below 0°C?
Which integer represents 8°C below 0°C?
- -8 (correct)
- |8|
- 8
- -|8|
What is the value of | -9|?
What is the value of | -9|?
- -9
- 18
- 0
- 9 (correct)
What is Luisa's new location after climbing 14 feet from 43 feet underground?
What is Luisa's new location after climbing 14 feet from 43 feet underground?
- -48 feet
- -57 feet
- -29 feet (correct)
- -14 feet
What is the result of 3 - 14?
What is the result of 3 - 14?
If Marisa has $26 and spends $5 for lunch, which expression correctly represents her remaining amount?
If Marisa has $26 and spends $5 for lunch, which expression correctly represents her remaining amount?
What is the absolute difference in elevation between the highest and lowest points in California?
What is the absolute difference in elevation between the highest and lowest points in California?
Which integers represent the values of S and T for the position on the number line?
Which integers represent the values of S and T for the position on the number line?
What is the value of |3|?
What is the value of |3|?
If Aaron's air conditioning caused a temperature change of 6 degrees, what integer represents this change?
If Aaron's air conditioning caused a temperature change of 6 degrees, what integer represents this change?
What is the outcome of the expression 3 - 14?
What is the outcome of the expression 3 - 14?
How much further below sea level is Death Valley compared to Mount Whitney?
How much further below sea level is Death Valley compared to Mount Whitney?
Which option correctly reflects the expression for Marisa’s remaining money after buying lunch?
Which option correctly reflects the expression for Marisa’s remaining money after buying lunch?
If Luisa climbs 14 feet up from 43 feet underground, what would be her new location?
If Luisa climbs 14 feet up from 43 feet underground, what would be her new location?
What is the absolute value of -9?
What is the absolute value of -9?
Which integers represent S and T as positioned on a number line as described?
Which integers represent S and T as positioned on a number line as described?
What is the result of the expression $16 imes (-8)$?
What is the result of the expression $16 imes (-8)$?
What integer is represented by 8 degrees lower than 0 degrees?
What integer is represented by 8 degrees lower than 0 degrees?
If Luisa is currently at -43 feet and climbs up 14 feet, what expression represents her new depth?
If Luisa is currently at -43 feet and climbs up 14 feet, what expression represents her new depth?
What integer represents a decrease of 6 degrees in temperature?
What integer represents a decrease of 6 degrees in temperature?
What is the absolute difference in elevations between Mount Whitney (14,494 feet) and Death Valley (282 feet below sea level)?
What is the absolute difference in elevations between Mount Whitney (14,494 feet) and Death Valley (282 feet below sea level)?
What does the expression $26 + (-5)$ represent in Marisa's situation?
What does the expression $26 + (-5)$ represent in Marisa's situation?
What will be the value of the expression $3 + (-14)$?
What will be the value of the expression $3 + (-14)$?
How does one express climbing from -2 to 4 on a number line?
How does one express climbing from -2 to 4 on a number line?
What is the absolute value of |-9|?
What is the absolute value of |-9|?
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Study Notes
Integers and Absolute Value
- Absolute Value: The absolute value of a number is its distance from zero on the number line. It is always represented as a positive value.
- Symbol for Absolute Value: The absolute value of a number is denoted by vertical bars "|" on either side of the number. For example, |-5| = 5.
Operations with Integers
- Adding and Subtracting Integers:
- When adding integers with the same sign, add their absolute values and keep the same sign.
- When adding integers with different signs, subtract their absolute values and keep the sign of the larger absolute value.
- Subtracting an integer is the same as adding its opposite.
- Multiplying and Dividing Integers:
- If the signs of the two numbers are the same, the product or quotient is positive.
- If the signs of the two numbers are different, the product or quotient is negative.
Number Line Understanding
- Number Line: A number line is a visual representation of numbers, where positive numbers are to the right of zero and negative numbers are to the left.
Real World Applications
- Temperature Changes: Negative integers represent temperatures below zero.
- Elevation: Negative integers can represent distances below sea level.
- Financial Transactions: Negative integers can represent money spent or lost.
Absolute Value
- The absolute value of a number is its distance from zero.
- The symbol for absolute value is two vertical bars: | |
- |3| = 3, because 3 is 3 units away from zero.
- |-9| = 9, because -9 is 9 units away from zero.
Integers and Number Line
- Integers are whole numbers, including negative numbers.
- A number line helps visualize positive and negative numbers.
- Numbers to the right of zero are positive.
- Numbers to the left of zero are negative.
Adding and Subtracting Integers
- Adding a positive number moves to the right on the number line.
- Adding a negative number moves to the left on the number line.
- Subtracting a positive number is the same as adding a negative number.
- Subtracting a negative number is the same as adding a positive number.
Word Problems and Integers
- Word problems can be represented using integers and operations.
- "Below zero" or "decrease" indicates a negative number or subtraction.
- "Above zero" or "increase" indicates a positive number or addition.
Integers and Absolute Value
- The absolute value of a number is its distance from zero on the number line.
- The absolute value of a number is always positive.
- The symbols || are used to represent absolute value.
- Example: |-9| = 9
Addition and Subtraction of Integers
- Adding a positive number to another positive number results in a positive sum.
- Adding a negative number to another negative number results in a negative sum.
- Subtracting a positive number from another number is the same as adding the negative of that number.
- Example: 3 - 14 = 3 + (-14) = -11
Word Problems Involving Integers
- Temperature changes can be represented by integers. A decrease in temperature is represented by a negative integer, while an increase in temperature is represented by a positive integer.
- Elevations can be represented by integers. An elevation above sea level is represented by a positive integer, while an elevation below sea level is represented by a negative integer.
- Financial transactions can be represented by integers. A deposit is represented by a positive integer, while a withdrawal is represented by a negative integer.
Integers and Absolute Value
- Absolute Value is the distance of a number from zero on the number line. It is always a positive number.
- The symbol for absolute value is two vertical bars:
| |. |3| = 3because 3 is 3 units from zero.|-9| = 9because -9 is 9 units from zero.
Adding and Subtracting Integers
- Adding a positive number moves to the right on the number line.
- Adding a negative number moves to the left on the number line.
- Subtracting a positive number is the same as adding a negative number.
- Subtracting a negative number is the same as adding a positive number.
Real-World Applications of Integers
- Temperature changes: Decreases in temperature are represented by negative numbers.
- Elevation changes: Going down in elevation is represented by a negative number.
- Financial transactions: Spending money is represented by a negative number, earning money is represented by a positive number.
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