Videotext Algebra Module A

Front 1

Define number symbols.

Back 1

Number symbols are things.

{1, 2, 3, 4/5, .9,...}

Front 2

Define operation symbols.

Back 2

Operation symbols are actions.

{+, -, ×, ÷,...}

Front 3

Define relation symbols.

Back 3

Relation symbols compare something with another.

{=, >, <,...}

Front 4

Define grouping symbols.

Back 4

Grouping symbols associate one thing with another.

{(), [], {},...}

Front 5

Define placeholder symbols.

Back 5

Placeholder symbols 'hold the place' of an unknown number.

{a, b, c, ?, ,...}

Front 6

Define closed phrase.

Back 6

A closed phrase has no relation symbol and no placeholder. Example:

7 + 9

This is a closed phrase because of the lack of relation symbols and placeholders.

Front 7

Define open phrase.

Back 7

An open phrase has no relation symbol but does have a placeholder. Example:

7 + n

This is an open phrase because of the placeholder without a relation symbol.

Front 8

Define closed sentence.

Back 8

A closed sencence has a relation symbol but not a placeholder. Example:

7 + 9 = 17

This is a closed sentence because of the relation symbol and the fact that there is no placeholder.

Extra credit - Is the above statement true or false?
(false)

Front 9

Define open sentence.

Back 9

An open sentence has a relation symbol and has a placeholder. Example:

7 + n = 17

This is an open sentence because of the visible placeholder and relation symbols.

Front 10

Define the following as an open or closed phrase:

a) 8 + 8
b) 4 + n
c) 26 + f
d) 13 + 6

Back 10

Questions (a) and (d) are closed phrases, for the lack of placeholders. Questions (b) and (c) are open phrases, because they have placeholders.

Front 11

Define the following as an open or closed sentence:

a) 5 × n = 350
b) 66 ÷ 11 = 6
c) 23 + y = 55
d) 9 + t = 25

Back 11

Answers (a), (c) and (d) are open sentences, because of the placeholders. (b) is a closed sentence, because the sentence has no room for improvements.

Front 12

Define the following as an open phrase or open sentence:

a) 42 + n
b) 348 - y
c) 64 + t = 78
d) 88 - s = 32

Back 12

Answers (a) and (b) are open phrases, because of the lack of relation symbols. Answers (c) and (d) are open phrases, because of the relation symbols.

Front 13

Define the following as a closed phrase or closed sentence:

a) 56 + 22
b) 39 - 15 = 24
c) 75 - 54 = 21
d) 77 + 42

Back 13

Answers (a) and (d) are closed phrases, because they have no relation symbol. Answers (b) and (c) are closed phrases, because of the relation symbols that are there.

Front 14

Define the following as an open phrase, closed phrase, open sentence or closed sentence:

a) 53 + 60
b) 64 - 20 = a
c) 23 + 59 = 82
d) 34 - 27

Back 14

Answers (a) and (d) are closed phrases, because they do not have placeholders or relation symbols. Answer (b) is an open sentence, because it has a relation symbol and a placeholder. Answer (c) is a closed sentence because of the relation symbol and the lack of a placeholder.

Front 15

Translate these number symbols:

1, 2, 3, ¼, .9

Back 15

one, two, three, one-fourth, point-nine

Front 16

Translate +.

Back 16

add, sum, plus, gain, rise, climb, total, increase, combine,
number more than

Front 17

Translate -.

Back 17

subtract, difference, minus, loss, fall, decrease, take away, deduct,
number less than

Front 18

Translate × or ·.

Back 18

times, multiply, product, of, double, triple, twice

Front 19

Translate ÷.

Back 19

divide, quotient, goes into, fraction

Front 20

Translate these number symbols:

1, 2, 3, ¼, .9

Back 20

one, two, three, one-fourth, point-nine

Front 21

Translate +.

Back 21

add, sum, plus, gain, rise, climb, total, increase, combine,
number more than

Front 22

Translate -.

Back 22

subtract, difference, minus, loss, fall, decrease, take away, deduct,
number less than

Front 23

Translate × or ·.

Back 23

times, multiply, product, of, double, triple, twice

Front 24

Translate ÷.

Back 24

divide, quotient, goes into, fraction

Front 25

Translate these relation symbols:

=, >, <

Back 25

= is equal to, is the same as
> is greater than, is more than
< is less than, is smaller than

Front 26

Translate these grouping symbols:

(), [], {}

Back 26

() parentheses
[] brackets
{} braces

the quantity, "sum", "difference", "product", "quotient"

Front 27

Translate these placeholder symbols:

{a, b, c, ... ?, ... ,...}

Back 27

a "number", the "unknown", the "age", the "distance", the "weight", ...

Front 28

Translate the following open sentence:

The sum of a number and 7 is equal to 20.

Back 28

n + 7 = 20

Front 29

Translate the following open sentence:

4 is one less than the quotient of a number and 9.

Back 29

4 = n/9 - 1

Front 30

Translate the following open sentence:

39 is greater than the result of multiplying the sum of 6 and some number by 3.

Back 30

39 > (6 + n) · 3

Front 31

What are the parts of well-defined operations?

Back 31

1. Existance
2. Uniqueness
3. Closure

Front 32

What is a natural number?

Back 32

Any number except zero, negative numbers and fractions.

{1, 2, 3,...}

Front 33

What is a whole number?

Back 33

Any number except the negative numbers and fractions.

{0, 1, 2, 3,...}

Front 34

What is an integer?

Back 34

Any number except fractions.

{..., -3, -2, -1, 0, 1, 2, 3,...}

Front 35

What is a rational number?

Back 35

All fractions.

{a/b | a, b are integers}

Front 36

What is a real number?

Back 36

All the rational and irrational numbers combined.

{rationals} + {irrationals}

Front 37

What defines all numbers?

Back 37

Just that - All numbers.

{real} + {complex}

Front 38

What does 'fraction' mean?

Back 38

A part of something.

A Numerator - numeral
numerous
- enumerate

B Denominator - nominate
denomination
nominal

Front 39

Is 37 a prime or composite number?

Back 39

prime

Front 40

What does equivalent mean?

Back 40

Equal value.

Equi Valent
Equal Value

Front 41

Reduce 24/30.

Back 41

First, factor the numbers up:

2 · 3 · 2 · 2
-------------
2 · 3 · 5

Then cross out the ones.

4
-
5

Front 42

Reduce 12/18.

Back 42

First, factor the numbers up:

2 · 2 · 3
---------
2 · 3 · 3

Then cross out the ones.

2
-
3

Front 43

What is a terminating answer?

Back 43

One that comes to a standstill. Example:

38.75

This is a terminating answer.

Front 44

What is a repeating answer?

Back 44

One that has its digits repeating themselves. Example:

13.5454545454...

How you represent this is you put a bar over the top of the repeating numbers, like this.

__
13.54

(Even though it doesn't show the bar over the 54, that is where it is supposed to be.)

Front 45

Change the fraction 35/100 to a decimal and a percent.

Back 45

Decimal
.35

Percent
35%

Front 46

Change the decimal .056 to a fraction and a percent.

Back 46

Fraction
5.6/100 or 56/1000

Percent
5.6%

Front 47

Change the percent 37.5% to a fraction and a decimal.

Back 47

Fraction
37.5/100 or 375/1000

Decimal
.375

Front 48

What do the words 'prime numbers' stand for, and what are they derived from?

Back 48

First, Beginning

primary grades
prime time
primer coat

Front 49

What do the words 'composite numbers' stand for, and what are they derived from?

Back 49

Several parts

compose
composition

Front 50

What does the word 'factoring' stand for, and what is it derived from?

Back 50

Parts

factory
faction

Front 51

What are prime numbers?

Back 51

Numbers that have only two factors - itself and 1.

2, 3, 5, 7

Front 52

What are composite numbers?

Back 52

Numbers that have more than two factors.

9, (1, 3, 9)
10, (1, 2, 5, 10)

Front 53

Reduce 5/13.

Back 53

Trick question - it can't be reduced!

Front 54

What are the factored forms of 24?

Back 54

2 · 12
2 · 2 · 6
2 · 2 · 2 · 3

3 · 8
3 · 2 · 4
3 · 2 · 2 · 2

4 · 6
2 · 2 · 2 · 3

Front 55

What is the prime factored form of 24?

Back 55

2 · 2 · 2 · 3

Front 56

What is the difference between a factor and a multiple of a number?

Back 56

The factors are what numbers go into the bigger number. 2 is a factor of 8.

A multiple is what numbers the first number goes into. 8 and 16 are multiples of 8.

Front 57

What is the communative property, and what is it used with?

Back 57

"moving" numbers

You can only use this property with addition and multiplication.

a + b = b + a
a · b = b · a

Front 58

What is the associative property, and what is it used with?

Back 58

"grouping" numbers

You can only use this property with addition and multiplication.

(a + b) + c = a + (b + c)
(a · b) · c = a · (b · c)

Front 59

What is the distributive property, and what is it used with?

Back 59

"handing out" numbers

You can only use this property to convert multiplication to addition or subtraction.

to addition
a · (b + c) = (a · b) + a · c)

to subtraction
a · (b - c) = (a · b) - (a · c)

Front 60

What is the identity property of addition?

Back 60

any number + 0 is the same number

(0 is the identity element for addition)

Front 61

What is the identity property of subtraction?

Back 61

any number - 0 is the same number

(0 is the identity element for subtraction)

Front 62

What is the multiplication property of 0?

Back 62

any number · 0 is 0

Front 63

What is division by 0?

Back 63

division by 0 is MEANINGLESS and therefore NOT ALLOWED

Front 64

What is the additive inverse property?

Back 64

any number + its additive inverse (opposite) is 0

(0 is the inverse element for addition)

Front 65

What is the identity property of multiplication?

Back 65

any number · 1 is the same number

(1 is the identity element for multiplication)

Front 66

What is the multiplicative inverse property?

Back 66

any number · its multiplicative inverse (reciprocal) is 1

(1 is the inverse element for multiplication)

Front 67

What is the identity property of division?

Back 67

any number ÷ 1 is the same number

(1 is the identity element for division)

Front 68

What is the identity property of addition?

Back 68

any number + 0 is the same number

(0 is the identity element for addition)

Front 69

What is the identity property of subtraction?

Back 69

any number - 0 is the same number

(0 is the identity element for subtraction)

Front 70

What is the multiplication property of 0?

Back 70

any number · 0 is 0

Front 71

What is division by 0?

Back 71

division by 0 is MEANINGLESS and therefore NOT ALLOWED

Front 72

What is the additive inverse property?

Back 72

any number + its additive inverse (opposite) is 0

(0 is the inverse element for addition)

Front 73

What is the identity property of multiplication?

Back 73

any number · 1 is the same number

(1 is the identity element for multiplication)

Front 74

What is the multiplicative inverse property?

Back 74

any number · its multiplicative inverse (reciprocal) is 1

(1 is the inverse element for multiplication)

Front 75

What is the identity property of division?

Back 75

any number ÷ 1 is the same number

(1 is the identity element for division)

Front 76

Solve this problem:

3/4 · 8/21

Back 76

There are two ways we could go, but this (I think) is the more simple way.

3/4 · 8/21
3 · 8
------
4 · 21

Factor them out.

3 · 2 · 2 · 2
-------------
2 · 2 · 2 · 7

Cross out the ones.

2
-
7

Front 77

Solve this problem:

2/7 + 4/7

Back 77

If the denominators are the same, then you just add the numerators together.

6
-
7

Front 78

Solve this problem:

1/3 + 1/4

Back 78

In this type of problem, you first have to find the least common multiple of the denominator.

(3) (4)
3 · 2 · 2
12

Multiply 1/3 by 4/4 and 1/4 by 3/3...

4/12 + 3/12

...and solve.

7
--
12