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78 Cards in this Set
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Define number symbols.

Number symbols are things.
{1, 2, 3, 4/5, .9,...} 
Define operation symbols.

Operation symbols are actions.
{+, , ×, ÷,...} 
Define relation symbols.

Relation symbols compare something with another.
{=, >, <,...} 
Define grouping symbols.

Grouping symbols associate one thing with another.
{(), [], {},...} 
Define placeholder symbols.

Placeholder symbols 'hold the place' of an unknown number.
{a, b, c, ?, ,...} 
Define closed phrase.

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. 
Define open phrase.

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. 
Define closed sentence.

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) 
Define open sentence.

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. 
Define the following as an open or closed phrase:
a) 8 + 8 b) 4 + n c) 26 + f d) 13 + 6 
Questions (a) and (d) are closed phrases, for the lack of placeholders. Questions (b) and (c) are open phrases, because they have placeholders.

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 
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.

Define the following as an open phrase or open sentence:
a) 42 + n b) 348  y c) 64 + t = 78 d) 88  s = 32 
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.

Define the following as a closed phrase or closed sentence:
a) 56 + 22 b) 39  15 = 24 c) 75  54 = 21 d) 77 + 42 
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.

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 
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.

Translate these number symbols:
1, 2, 3, ¼, .9 
one, two, three, onefourth, pointnine

Translate +.

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

subtract, difference, minus, loss, fall, decrease, take away, deduct,
number less than 
Translate × or ·.

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

Translate ÷.

divide, quotient, goes into, fraction

Translate these number symbols:
1, 2, 3, ¼, .9 
one, two, three, onefourth, pointnine

Translate +.

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

subtract, difference, minus, loss, fall, decrease, take away, deduct,
number less than 
Translate × or ·.

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

Translate ÷.

divide, quotient, goes into, fraction

Translate these relation symbols:
=, >, < 
= is equal to, is the same as
> is greater than, is more than < is less than, is smaller than 
Translate these grouping symbols:
(), [], {} 
() parentheses
[] brackets {} braces the quantity, "sum", "difference", "product", "quotient" 
Translate these placeholder symbols:
{a, b, c, ... ?, ... ,...} 
a "number", the "unknown", the "age", the "distance", the "weight", ...

Translate the following open sentence:
The sum of a number and 7 is equal to 20. 
n + 7 = 20

Translate the following open sentence:
4 is one less than the quotient of a number and 9. 
4 = n/9  1

Translate the following open sentence:
39 is greater than the result of multiplying the sum of 6 and some number by 3. 
39 > (6 + n) · 3

What are the parts of welldefined operations?

1. Existance
2. Uniqueness 3. Closure 
What is a natural number?

Any number except zero, negative numbers and fractions.
{1, 2, 3,...} 
What is a whole number?

Any number except the negative numbers and fractions.
{0, 1, 2, 3,...} 
What is an integer?

Any number except fractions.
{..., 3, 2, 1, 0, 1, 2, 3,...} 
What is a rational number?

All fractions.
{a/b  a, b are integers} 
What is a real number?

All the rational and irrational numbers combined.
{rationals} + {irrationals} 
What defines all numbers?

Just that  All numbers.
{real} + {complex} 
What does 'fraction' mean?

A part of something.
A Numerator  numeral numerous  enumerate B Denominator  nominate denomination nominal 
Is 37 a prime or composite number?

prime

What does equivalent mean?

Equal value.
Equi Valent Equal Value 
Reduce 24/30.

First, factor the numbers up:
2 · 3 · 2 · 2  2 · 3 · 5 Then cross out the ones. 4  5 
Reduce 12/18.

First, factor the numbers up:
2 · 2 · 3  2 · 3 · 3 Then cross out the ones. 2  3 
What is a terminating answer?

One that comes to a standstill. Example:
38.75 This is a terminating answer. 
What is a repeating answer?

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

Decimal
.35 Percent 35% 
Change the decimal .056 to a fraction and a percent.

Fraction
5.6/100 or 56/1000 Percent 5.6% 
Change the percent 37.5% to a fraction and a decimal.

Fraction
37.5/100 or 375/1000 Decimal .375 
What do the words 'prime numbers' stand for, and what are they derived from?

First, Beginning
primary grades prime time primer coat 
What do the words 'composite numbers' stand for, and what are they derived from?

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

Parts
factory faction 
What are prime numbers?

Numbers that have only two factors  itself and 1.
2, 3, 5, 7 
What are composite numbers?

Numbers that have more than two factors.
9, (1, 3, 9) 10, (1, 2, 5, 10) 
Reduce 5/13.

Trick question  it can't be reduced!

What are the factored forms of 24?

2 · 12
2 · 2 · 6 2 · 2 · 2 · 3 3 · 8 3 · 2 · 4 3 · 2 · 2 · 2 4 · 6 2 · 2 · 2 · 3 
What is the prime factored form of 24?

2 · 2 · 2 · 3

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

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

"moving" numbers
You can only use this property with addition and multiplication. a + b = b + a a · b = b · a 
What is the associative property, and what is it used with?

"grouping" numbers
You can only use this property with addition and multiplication. (a + b) + c = a + (b + c) (a · b) · c = a · (b · c) 
What is the distributive property, and what is it used with?

"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) 
What is the identity property of addition?

any number + 0 is the same number
(0 is the identity element for addition) 
What is the identity property of subtraction?

any number  0 is the same number
(0 is the identity element for subtraction) 
What is the multiplication property of 0?

any number · 0 is 0

What is division by 0?

division by 0 is MEANINGLESS and therefore NOT ALLOWED

What is the additive inverse property?

any number + its additive inverse (opposite) is 0
(0 is the inverse element for addition) 
What is the identity property of multiplication?

any number · 1 is the same number
(1 is the identity element for multiplication) 
What is the multiplicative inverse property?

any number · its multiplicative inverse (reciprocal) is 1
(1 is the inverse element for multiplication) 
What is the identity property of division?

any number ÷ 1 is the same number
(1 is the identity element for division) 
What is the identity property of addition?

any number + 0 is the same number
(0 is the identity element for addition) 
What is the identity property of subtraction?

any number  0 is the same number
(0 is the identity element for subtraction) 
What is the multiplication property of 0?

any number · 0 is 0

What is division by 0?

division by 0 is MEANINGLESS and therefore NOT ALLOWED

What is the additive inverse property?

any number + its additive inverse (opposite) is 0
(0 is the inverse element for addition) 
What is the identity property of multiplication?

any number · 1 is the same number
(1 is the identity element for multiplication) 
What is the multiplicative inverse property?

any number · its multiplicative inverse (reciprocal) is 1
(1 is the inverse element for multiplication) 
What is the identity property of division?

any number ÷ 1 is the same number
(1 is the identity element for division) 
Solve this problem:
3/4 · 8/21 
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 
Solve this problem:
2/7 + 4/7 
If the denominators are the same, then you just add the numerators together.
6  7 
Solve this problem:
1/3 + 1/4 
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 