Basics

Question 1

What are the top & bottom of a fraction called?

Answer 1

Numerator & Denominator

Question 2

What is the ‘associative property’?

Answer 2

It means the terms can be associated differently without changing the meaning, e.g. (3 x 4) x 5 is the same as 3 x (4 x 5). Addition and multiplication have the associative property.

Question 3

What the the ‘commutative property’?

Answer 3

The terms can move without changing the result, e.g. 3 x 4 is the same as 4 x 3, but 3 / 4 is not the same as 4 / 3. Addition and multiplication have the commutative property.

Question 4

What is the ‘distributive property’?

Answer 4

a(b + c) = ab + ac

Question 5

Apply the distributive property to: 2x - (3x - 5)

Answer 5

2x - (3x - 5) = 2x - 1(3x - 5) = 2x - 3x +5 = -x + 5

Question 6

Apply the distributive property to: -2x(3x**2 + 5y - 7)

Answer 6

-2x(3x2 + 5y - 7) = (-2x)(3x2) + (-2x)(5y) + (-2x)(-7) = -6x**3 - 10xy + 14x

Question 7

What is a prime number or a composite number? What are the first 10 primes?

Answer 7

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Question 8

What is a factor?

Answer 8

A factor is a number that divides another number and leaves no remainder. e.g. Factors of 12 are 1, 2, 3, 4, and 6.

Question 9

What are the natural numbers?

Answer 9

Positive whole numbers (i.e. no fractional part) such as those used to count, e.g. 1, 2, 3, 4, etc… The double-struck capital N (“ℕ”) is used to represent the infinite set of all natural numbers.

Question 10

What are the whole numbers?

Answer 10

The natural numbers plus 0.

Question 11

What are the integer numbers?

Answer 11

Any number with no decimal or fractional part, including negative numbers, i.e. 5, 0, -7, etc… The double-struck Z (“ℤ”) is used to represent the infinite set of integers.

Question 12

What are rational numbers?

Answer 12

Any number that can be expressed as a ratio of two integers (which includes all decimal fractions), e.g. 2.345, 1/2, 3.33333.., 5/1, etc.. Integers are also rational numbers. The double-struck Q (“ℚ”) is used to represent the infinite set of rational numbers.

Question 13

What are the irrational numbers?

Answer 13

Any number that cannot be expressed as the ratio of 2 integers, e.g. sqrt(2), Math.Pi, Math.e, etc…

Question 14

What are the real numbers?

Answer 14

Real numbers include the rational and irrational numbers, and include any point on an infinite ‘number line’. The double-struck R (“ℝ”) is used to represent the infinite set of real numbers.

Question 15

What are the transcendental numbers?

Answer 15

Irrational numbers that cannot be represented as an algebraic expression, e.g. sqrt(2) is irrational but not transcendental, whereas Math.Pi and Math.e are.

Question 16

What is the absolute value of a number and how do you indicate it?

Answer 16

It is the “amount” or “magnitude” of the value regardless of the sign, represented by put the value in “|” symbols. The result is never negative. e.g: “|-9| = 9”, and “|9| = 9”.

Question 17

What is the opposite of a value?

Answer 17

It’s negative. e.g. the opposite of “-4” = “-(-4)” = “4”.

Question 18

What does ‘quotient’ mean?

Answer 18

From the Latin ‘quotiens’ meaning ‘how many times’, it is the result of division - often just the integer portion. e.g. 11 / 3 has a quotient of 3 and a remainder of 2.

Question 19

What is an “improper fraction”?

Answer 19

When the numerator is greater than the denominator, e.g. 12/5. This can be written as a “mixed number”, with an integer and a “proper fraction”, e.g. 2 2/5

Question 20

What is the “simplified form” of a fraction?

Answer 20

When both parts have no common factors. For example, 24/36 can have both parts factored by 12, giving 2/3

Question 21

What is a GCF?

Answer 21

Greatest Common Factor. It is used to reduce a fraction to its simplified form.

Question 22

What is the LCD? Why might you use it?

Answer 22

Least Common Denominator. You use it to get the denominators of fractions to the same value. For example, the LCD of 1/2, 2/3 & 3/4 is 12, so you can convert to 6/12, 8/12, & 9/12.

Question 23

How do you add or subtract fractions?

Answer 23

Convert all fractions to have a common denominator, then doing basic addition or subtraction on the numerators.

Question 24

How do you multiply fractions?

Answer 24

Simply multiple the numerators to get the numerator of the result, do the same for denominators, then simplify.

Question 25

What is “standard deviation”?

Answer 25

The Standard Deviation is a measure of how spread out numbers are in a “normal distribution” (bell curve). Its symbol is σ (the greek letter sigma). It is the square root of the “Variance” (the average of the squared differences from the Mean).

Question 26

What is the 68-95-99.7 rule?

Answer 26

68% of data/samples fall within 1 std deviation of the mean, 95% within 2, and 99.7% within 3.