Chapter 1: Arithmetics

Question 1

Number Line

Answer 1

A visual representation that extends infinitely in both directions, where every number is located, and tick marks indicate integers.

Question 2

Integers

Answer 2

Numbers without a fractional part (… -3, -2, -1, 0, 1, 2, 3, …), represented by the tick marks on the number line.

Question 3

Positive Number

Answer 3

A number to the right of 0 on the number line meaning it is greater than 0.

Question 4

Negative Number

Answer 4

A number to the left of 0 on the number line, meaning it is less than 0.

Question 5

Nonnegative Numbers

Answer 5

Numbers that are not negative, encompassing positive numbers or 0.

Question 6

Nonpositive Numbers

Answer 6

Numbers that are not positive, including 0.

Question 7

Nonzero

Answer 7

A number that is not equal to 0.

Question 8

Variables

Answer 8

Letters, such as ‘a’ or ‘b’, used to represent numbers that can have any value and remain consistent within a single equation.

Question 9

Commutative Addition

Answer 9

The order in which numbers are added doesn’t change their final sum.

Question 9

Whole Numbers

Answer 9

Another name for nonnegative numbers and it starts with 0

Question 10

Natural Numbers

Answer 10

Another name for positive numbers and starts with 1

Question 11

Associative Addition

Answer 11

When you add three numbers, you can change their grouping without affecting the total.

Question 11

Associative Multiplication

Answer 11

You can change how you group numbers in multiplication, and the product will remain the same.

Question 12

Adding Zero

Answer 12

Adding zero to any number won’t change its value.

Question 13

Commutative Multiplication

Answer 13

You can change how you group numbers in multiplication, and the product will remain the same.

Question 14

Multiply by 1

Answer 14

Multiplying any number by 1 leaves the number unchanged.

Question 15

Distributive Property

Answer 15

A property that lets you multiply a number by a sum by first multiplying it by each part of the sum and then adding the results.

Question 16

Expanding

Answer 16

The process of rewriting an expression by using the distributive property to carry out the multiplication and remove the parentheses.

Question 17

Factoring

Answer 17

The opposite of expanding; it’s the process of finding a common factor in an expression and pulling it out of the terms.

Question 18

Multiplying by 0

Answer 18

The result of multiplying any number by 0 is always 0.

Question 19

Negation

Answer 19

The number you add to another number to get a sum of zero.

Question 20

Multiplying by -1

Answer 20

Multiplying a number by -1 is the same as finding its negation.

Question 21

Multiplying by Negation

Answer 21

A positive number multiplied by a negative number always results in a negative number.

Question 22

Negation Times Negation

Answer 22

When you multiply two negative numbers, the result is a positive number.

Question 23

Negation of a Sum

Answer 23

The negation of a sum is equal to the sum of the negations of each number.

Question 24

Adding its Opposite

Answer 24

Subtraction is the same as adding the opposite (or negation) of a number.

Question 25

Subtracting from 0

Answer 25

When you subtract a number from zero, the result is the negation of that number

Question 26

Self-Subtraction

Answer 26

Subtracting a number from itself always gives you zero.

Question 27

Subtraction of Negation

Answer 27

Subtracting a negative number is the same as adding its positive counterpart.

Question 27

Subtracting Zero

Answer 27

Subtracting zero from a number doesn't change the number.

Question 28

Subtraction from Negation

Answer 28

When a positive number is subtracted from a negative number, the result is the negative of the sum of the two numbers.

Question 29

Negation of Subtraction

Answer 29

The negation of a difference is equal to the two numbers subtracted in the opposite order.

Question 30

Not Commutative

Answer 30

Subtraction is not commutative because changing the order of the numbers changes the result.

Question 31

Not Associative

Answer 31

Subtraction is not associative because changing the way numbers are grouped changes the result.

Question 32

Reciprocal

Answer 32

A number that, when multiplied by a given number, gives a product of 1.

Question 33

Reciprocal of 0

Answer 33

The reciprocal of 0 is undefined because you can't multiply 0 by any number to get 1.

Question 34

Reciprocal of Reciprocal

Answer 34

Taking the reciprocal of a reciprocal returns the original number.

Question 35

Reciprocal of Product

Answer 35

The reciprocal of a product is found by multiplying the reciprocals of each number.

Question 36

Reciprocal of Negation

Answer 36

The reciprocal of a negative number is the same as the negative of its reciprocal.

Question 37

Dividing into 0

Answer 37

Dividing 0 by any number (except 0 itself) always gives a result of 0.

Question 38

Self-Division

Answer 38

Any non-zero number divided by itself equals 1.

Question 39

Dividing by 1

Answer 39

Dividing any number by 1 does not change the number's value.

Question 40

Dividing into 1

Answer 40

Dividing 1 by a number results in that number's reciprocal.

Question 41

Dividing by Reciprocal

Answer 41

Dividing by a number is equivalent to multiplying by its reciprocal.

Question 42

Division into Negation

Answer 42

Dividing a negative number by a positive number results in a negative number.

Question 43

Division by Negation

Answer 43

Dividing a positive number by a negative number results in a negative number.

Question 44

Negation Divide by Negation

Answer 44

Dividing a negative number by another negative number results in a positive number.

Question 45

Not Commutative (Division)

Answer 45

Division isn't commutative because changing the order of the numbers changes the result.

Question 46

Not Associative (Division)

Answer 46

Division isn't associative because changing the way you group the numbers will change the result.

Question 47

Cancel Common Factor

Answer 47

To simplify a fraction, divide both the top and bottom numbers by a shared factor greater than 1.