Number Sense week 2

Question 1

Define expression.

Answer 1

Combination of terms

Question 2

Give an example of a mathematical expression:

Answer 2

5x + 3

Question 3

Define equation.

Answer 3

A mathematical statement that is true

Question 4

Give an example of a mathematical equation:

Answer 4

5x + 3 = 8

Question 5

Define solution.

Answer 5

The value of a variable that makes it true

Question 6

Give an example of a solution:

Answer 6

x = 1

Question 7

How do we isolate a variable?

Answer 7

Move terms over the equal sign by using inverse operations

Question 8

What is an inverse operation?

Answer 8

Opposite operations.

Question 9

List the inverse operations:

Answer 9

+ is the inverse of -
- is the inverse of +
x is the inverse of ÷
÷ is the inverse of x

Question 10

Define variable.

Give an example.

Answer 10

a letter that represents a quantity

x

Question 11

Define constant in algebra.

Give an example.

Answer 11

A number that is by itself, not attached to a variable

7

Question 12

Define coefficient.

Give an example.

Answer 12

A number that is multiplied by a variable

(-5x), where (-5) is the coefficient

Question 13

Define term.

Give an example.

Answer 13

Separated by (+) or (-)
There are two terms in (-5x + 7)

Question 14

What are powers used for?

Answer 14

They can be used to show repeated multiplication of the same number by itself

Question 15

Gives examples of exponential vs. expanded forms of multiplication

Answer 15

Expanded: 2 x 2 x 2 x 2 x 2 x 2 x 2
Exponential: 2^7

Question 16

Do integer rules apply when solving exponents? How?

Answer 16

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.)

Question 17

What does it mean when a number is in a bracket with an exponent attached?

Answer 17

Only the contents of the bracket are being multiplied by the exponent

Question 18

What is the difference between -(3)^5 and (-3)^5

Answer 18

1. In the first question, only the (3) is being multiplied to the power of 5. (negative gets carried over to the solution)
2. In the second question, the (-3) is being multiplied to the power of 5.

Question 19

3^2

What is the base? What is the exponent?

Answer 19

3 is base.

2 is exponent.

Question 20

Product rule of exponents:

Answer 20

When multiplying, we can add powers together when the base is the same throughout.

Question 21

Give an example of the product rule of exponents:

Answer 21

2^3 x 2^2 —> 2x2x2 x 2x2
= 2^5
Add exponents together.

Question 22

Quotient rule of exponents:

Answer 22

When we divide, we can subtract exponents from each other. They cancel each other out when expanded.

Question 23

Give an example of the quotient rule of exponents:

Answer 23

5^5 / 5^2 –> 5x5x5x5x5 / 5x5
= 5x5x5
= 5^3
Subtract numerator quotient from denominator quotient.

Question 24

Power of a power rule:

Answer 24

When a power is raised (attached) to another, we can multiply the exponents together.

Question 25

Give an example of the power of a power rule:

Answer 25

(2^3)^2 –> 2x2x2 x 2x2x2
= 2^6
Multiply exponent by exponent.

Question 26

How do we solve a fraction with an exponent?

Answer 26

(-1/2)^12 –> -1^12 / 2^12

= 1/4096

Question 27

What happens when there is an exponent attached to a base of 1?
Give an example.

Answer 27

No matter how many times one is multiplied by itself, the answer will always be one
1^10 –> 1x1x1x1x1x1x1x1x1x1
= 1

Question 28

What happens when there is a base with an exponent of 1?

Give an example.

Answer 28

The answer is the base.
7^1 –> 7
= 7

Question 29

What happens when there is an exponent attached to a base with a value of 0?
Give an example.

Answer 29

There is nothing to multiply, the answer is 0.
0^99 –> 0
= 0

Question 30

What happens when a base is attached to an exponent with a value of 0?
Give an example.

Answer 30

Power of 0 always equals 1.
7^0 = 1
(times 7)
7^1 = 7
(times 7)
7^2 = 49
(times 7)
7^3 = 343
etc...

Question 31

Solve.

(3^2)^3 x (3^4) / 3^5

Answer 31

(3^2)^3 x (3^4) / 3^5
= 3^6 x 3^4 / 3^5
= 3^10 / 3^5
= 3^5
= 243