Number Sense week 2 Flashcards
Define expression.
Combination of terms
Give an example of a mathematical expression:
5x + 3
Define equation.
A mathematical statement that is true
Give an example of a mathematical equation:
5x + 3 = 8
Define solution.
The value of a variable that makes it true
Give an example of a solution:
x = 1
How do we isolate a variable?
Move terms over the equal sign by using inverse operations
What is an inverse operation?
Opposite operations.
List the inverse operations:
+ is the inverse of -
- is the inverse of +
x is the inverse of ÷
÷ is the inverse of x
Define variable.
Give an example.
a letter that represents a quantity
x
Define constant in algebra.
Give an example.
A number that is by itself, not attached to a variable
7
Define coefficient.
Give an example.
A number that is multiplied by a variable
(-5x), where (-5) is the coefficient
Define term.
Give an example.
Separated by (+) or (-) There are two terms in (-5x + 7)
What are powers used for?
They can be used to show repeated multiplication of the same number by itself
Gives examples of exponential vs. expanded forms of multiplication
Expanded: 2 x 2 x 2 x 2 x 2 x 2 x 2
Exponential: 2^7
Do integer rules apply when solving exponents? How?
Yes.
- When a base is negative but the exponent is odd, the final answer will always be negative (1 neg. and 1 pos.)
- When a base is negative but the exponent is even, the final answer will always be positive (2 neg. = pos.)
What does it mean when a number is in a bracket with an exponent attached?
Only the contents of the bracket are being multiplied by the exponent
What is the difference between -(3)^5 and (-3)^5
- In the first question, only the (3) is being multiplied to the power of 5. (negative gets carried over to the solution)
- In the second question, the (-3) is being multiplied to the power of 5.
3^2
What is the base? What is the exponent?
3 is base.
2 is exponent.
Product rule of exponents:
When multiplying, we can add powers together when the base is the same throughout.
Give an example of the product rule of exponents:
2^3 x 2^2 —> 2x2x2 x 2x2
= 2^5
Add exponents together.
Quotient rule of exponents:
When we divide, we can subtract exponents from each other. They cancel each other out when expanded.
Give an example of the quotient rule of exponents:
5^5 / 5^2 –> 5x5x5x5x5 / 5x5
= 5x5x5
= 5^3
Subtract numerator quotient from denominator quotient.
Power of a power rule:
When a power is raised (attached) to another, we can multiply the exponents together.
