Saxon Algebra 1 Vocabulary Lesson 4

Front 1

What is a number?

Back 1

A number is an idea.

Hint 1

4.A

Front 2

What is a numeral?

Back 2

A numeral is a single symbol or a collection of symbols that we use to express the idea of a particular number.
ie. 5, 7, 1000, -34, -862
We say "number" when actually referring to a numeral. But the numeral only represents the idea of the number.

Hint 2

4.A

Front 3

What is the value of a numeral?

Back 3

The value of a numeral is the number represented by the numeral, and we see that the words 'value' and 'number' have the same meaning.

Hint 3

4.A

Front 4

Describe the decimal system.

Back 4

The decimal system is the system of numeration that we use to designate numbers.
The Hindus of India invented the decimal system, which passed to their Arab neighbors, and reached Europe around 1200 A.D.
The decimal system uses 10 symbols that we call digits, based on ten fingers or ten toes, called digits from Latin.
The decimal system replaced Roman numerals

Hint 4

4.B

Front 5

What are natural numbers (or counting numbers)?

Back 5

Natural numbers (or counting numbers) are the numbers that we use to count objects or things.
Natural/Counting Numbers = 1, 2, 3, 4, 5...

Hint 5

4.B

Front 6

What is a whole number?

Back 6

The set of natural/counting numbers and zero.
ie {0, 1, 2, 3, 4, 5...}

Hint 6

4.B

Front 7

What is an integer?

Back 7

An member of the set {... -3, -2, -1, 0, 1, 2, 3...}
Integers are positive and negative whole numbers including zero.

Hint 7

4.C

Front 8

What is a positive real number?

Back 8

A positive real number is any number that can be used to describe a physical distance greater than zero.
ie. ⅗, 0,0056, 3⅞, 46, 987.456
The number zero is not a positive number.
We may use a + sign to designate a positive number.
ie. +67 instead of 67
We must remember that a numeral with no sign is always a positive number.

Hint 8

4.C

Front 9

What is zero?

Back 9

Zero is not positive number but can describe a distance or magnitude.
Zero is a real number

Hint 9

4.C

Front 10

What is a negative real number?

Back 10

Negative numbers are real numbers.
Every positive number has a negative counterpart, and we call these numbers negative real numbers.
We must always use a minus sign when we designate a negative number.
ie. -47

Hint 10

4.C

Front 11

What is a real number?

Back 11

A real number is the set of numbers that includes all members of the set of rational numbers and all members of the set of irrational numbers.

Hint 11

4.C

Front 12

What is a rational number?

Back 12

Any number that can be written as a quotient of integers (excluding division by zero)
ie. .25, 46.6, 0, -⅖, -0.125
This means it always divides evenly, ending with a finite quotient.

Hint 12

4.C

Front 13

What is the progression of numbers from simplest to most complex?

Back 13

Natural/Counting Numbers: {1, 2, 3, 4, 5...}
Whole Numbers: 0 + Natural/Counting Numbers
Integers: {...-3, -2, -1, 0, 1, 2, 3...}
Rational Numbers: -⅝, -4.5, -67, 0, ⅕, 82.6, 1022
Irrational Numbers: pi or π, the square root of 2
Real Numbers: all rational + all irrational numbers

Hint 13

4.B
4.C

Front 14

signed number

Back 14

1. When we write a numeral with NO sign we designate a POSITIVE number.
2. Adding NEGATIVE numerals helps eliminate errors caused by subtraction.

Hint 14

4.C

Front 15

What is a number line?

Back 15

A number line is a line divided into units of equal length with one point chosen as the origin, base, or zero point.
The numbers to the right of zero are the positive real numbers, and the numbers to the left of zero are the negative real numbers.
A number line is a graphic aid for working with signed numbers, ie. positive and negative numbers.

Hint 15

4.D

Front 16

What is the origin?

Back 16

The base point of the number line, usually associated with the number zero.

Hint 16

4.D

Front 17

Describe graphing a number.

Back 17

We graph a number when we place a dot on the number line to indicate the location of a number.
The coordinate is the number of the point that we have graphed.

Hint 17

4.D

Front 18

Why do we use a number line?

Back 18

We use the number line to tell if one number is greater than another number by saying that a number is greater than another number if its graph lies to the right of the graph of the other number.

Hint 18

4.D

Front 19

How are fractions multiplied?

Back 19

Fractions are multiplied by mutiplying the numerators to get the new numerator, and by multiplying the denominators to get the new denominator.
1. Multiply numerators making new numerator.
2. Multiply denominators making new denominator.
3. Simplify, if needed. You may simplify by canceling out common factors before multiplying or after.

Hint 19

4.E

Front 20

How do we divide fractions?

Back 20

We divide fractions by inverting the divisor [using the reciprocal] and then multiplying.
The reciprocal of a fraction is the the inverted divisor.
ie. 3/4 is the reciprocal of 4/3

Hint 20

4.E

Front 21

Define reciprocal.

Back 21

For any non-zero real number, the number in inverted form.
ie. reciprocal of 5 is ⅕ and the reciprocal of ⅓ is 3.

Hint 21

4,E

Front 22

How do we multiply or divide mixed numbers?

Back 22

We change mixed numbers to improper fractions and then multiply or divide as indicated.

Hint 22

4.E

Front 23

What is an improper fraction?

Back 23

A fraction whose numerator is larger than its denominator, which can also be written as an improper fraction.
ie. 12/5 = 2⅖

Hint 23

4.E

Front 24

What are the signs of equality and inequality?

Back 24

= equal to || ie. 7 = 2+5
≠ not equal to || ie. 6 ≠ 2+5
< less than || ie. 6 < 2+5
> greater than || ie. 9 > 2+5
≤ less than or equal to || ie. 9 ≤ 2+7
≥ greater than or equal to || ie. 9 ≥ 2+5
≈ approximately equal to || ie. π ≈ 3.14

Hint 24

4.F

Front 25

What are the four basic arithmetic operations?

Back 25

addition
subtraction
multiplication
division

Hint 25

4.G

Front 26

What are the four basic algebra operations?

Back 26

Basic algebra operations are the same as basic arithmetic operations:
addition
subtraction
multiplication
division

Front 27

What sign or signs are used for addition?

Back 27

The plus sign is used for addition: 5 + 6

Hint 27

4.G

Front 28

In an addition problem, what are the addends? What is the sum?

Back 28

The addends are the numbers to be added.
The sum is the result of the addition problem.

5 + 6 = 11
addends: 5, 6
sum: 11

Hint 28

4.G

Front 29

What sign or signs are used for subtraction?

Back 29

The minus sign is used for subtraction: 6 - 5

Hint 29

4.G

Front 30

In a subtraction problem, what is the minuend, the subtrahend, and the difference?

Back 30

In a subtraction problem the first number is the minuend,
the second number is the subtrahend,
and the result is the difference.

6 - 5 = 1
minuend: 6
subtrahend: 5
difference: 1

Hint 30

4.G

Front 31

What sign or signs are used for multiplication?

Back 31

Multiplication may be shown in several ways.

5 x -6 using the multiplication sign
5(-6) using parentheses
5 ∙ -6 using a dot
(5) ∙ (-6)
(5) (-6)

Hint 31

4.G

Front 32

What are the parts of a multiplication problem?

Back 32

The numbers to be multiplied are factors.
The result of multiplication is the product.

5(-6) = -30
factors: 5, -6
product: -30

Hint 32

4.G

Front 33

What is the product of a particular real number and the number 1?

Back 33

The product of a particular real number and the number 1 is the particular number itself.

ie. 346.67 ∙ 1 = 346.67

Hint 33

4.G

Front 34

What is the product of any real number and the number zero?

Back 34

The product of any real number and the number zero is the number zero.
ie. -56.3 x 0 = 0

Hint 34

4.G

Front 35

What sign or signs are used for division?

Back 35

Division may be shown in several ways:

division sign: 30 ÷ 6
slash: 30/6
fraction: 30 over 6 [which this will not print]

Hint 35

4.G

Front 36

Explain the parts of a division problem: dividend, divisor and quotient.

Back 36

The dividend is the number or quantity being divided by another number.
The divisor is a number or quantity that divides or is being divided into another number or quantity.
The quotient is the result of dividing one number or quantity by another number or quantity.

30 ÷ 6 = 5
Dividend: 30.
Divisor: 6.
Quotient: 5.

Hint 36

4.G

Front 37

What is the unit multiplier and how does it work?

Back 37

Unit multipliers are fractions with the value of 1.
ie. 4/4 = 1 . . . Because it has all four parts of the fraction, it is a whole.
Unit multipliers are used to used to change the numeral representing the number but not the value since anything multiplied by 1 stays the same.

2/3 x 4/4 [the unit multiplier] = 8/12

3 ft / 1 yd is also a unit multiplier, just as 1 yd / 3 ft also equals one.

Hint 37

4.I

Front 38

What is the table of equivalent measures or unit multipliers for length?

Back 38

1 ft = 12 in
1 yd = 3 ft
1 yd = 36 in
1 mi = 5280 ft
1 mi = 1760 yd

1 in = 2.54 cm

1 m = 100 cm
1 cm = 10 mm
1 km = 1000 m

Hint 38

4.J