Pre-algebra Basics

Question 1

numerator

Answer 1

the number of parts are present

Question 2

denominator

Answer 2

the bottom of a fraction; tells how many parts the whole is divided into

Question 3

percentage

Answer 3

parts per 100

Question 4

average (mean)

Answer 4

the sum divided by the count

If three values then sum them and divide by 3 to get the mean or average of the set.

2 + 4 + 6 = 12

12 / 3 = 4

the mean average of 2, 4, 6 …. is 4

Question 5

absolute values

Answer 5

distance from zero

• means only positive since 6 is 6 away from zero and -6 is also 6 away from zero.

marked by bars:
| 6 | = 6
| -6 | = 6

Sometimes absolute value is also written as “abs()”, so abs(−1) = 1 is the same as |−1| = 1

Question 6

Complex numbers definition

Answer 6

Combination of a real and an imaginary number in the form a + bi

where a and b are real numbers and i is the imaginary constant ✔️(-1) (Square root of (negative one)

Question 7

complex number types

Answer 7

The values a and b can be zero.

These are all complex numbers:
1 + i
2 − 6i
−5.2i (an imaginary number is a complex number with a=0)
4 (a real number is a complex number with b=0)

Question 8

3 types of fractions

Answer 8

1 - proper fractions
2 - improper fractions
3 - mixed fractions

Question 9

Proper fractions

Answer 9

Have a smaller numerator than the denominator.

1/2 or 3/4 for example

Question 10

Improper fractions

Answer 10

have a larger or greater numerator than the denominator

8/5 or 51/24 for example

Question 11

Mixed fractions

Answer 11

have a whole number and a proper fraction written together

4 3/4 for example or 7 5/8

Question 12

Mixed fractions are converted to

Answer 12

Improper fractions by multiplying the denominator times the whole number and then adding that to the numerator and putting the new sum over the original denominator to get the improper fraction.

1 2/3 for example = 5/3

Denominator 3 times whole number 1 = 3
Add that to the numerator 2 so 3 + 2 = 5
Put that sum of 5 over the original denominator 3 which then gives you your improper fraction and the answer as 5/3

Question 13

Division term names

Answer 13

Dividend / Divisor = Quotient

10 / 2 = 5

10 dividend

2 divisor

5 quotient

Question 14

equation

Answer 14

this expression of numbers is equal to that expression of numbers

any number sentences with = between them

a formula is an equation but not all equations are formulas

Question 15

formula

Answer 15

an equation of two or more variables that states a rule or fact of how things are related to each other.

volume = length x width x height (or depth)

v = lwh

(v = lwd)

Formulas are equations but not all equations are formulas. An equation with only one variable such 2x + 1 = 5 is NOT a formula.

But x = 2y - 7 is a formula

Question 16

equivalent fraction

Answer 16

Fractions that have the same value even though written with different numbers.

Question 17

ratio

Answer 17

one finite number related to another finite number …. can be written as a simple fraction - also called a rational number

Question 18

irrational number

Answer 18

a number that cannot be written a fraction because its decimal point goes on forever (such as pie)

Question 19

Four famous irrational numbers

Answer 19

pie 3.14….

Euler’s number 2.718…

The Golden Ratio (a terrible name since it cant be a ratio as an irrational number) 1.618….

Many square and cube roots etc are also irrational numbers - square root of 3 is 1.73….