Math 365 Final Exam
What is the additive inverse of 2/3?
-2/3
What is the additive inverse of 3/4?
-3/4
Anything divided by 0 equals what?
0
Is 0/5 undefined, defined, or 0?
0
What is the additive identity element for whole numbers, integers, and rational numbers?
0
What is the additive identity element for whole numbers, integers, rational numbers, and real numbers?
0
What remainder causes a decimal to terminate?
0
With rational numbers, what can't the denominator be?
0
What numbers can always be repeated in a decimal?
0's and 9's
Convert 0.07% to a decimal:
0.0007
Convert 5% to a decimal:
0.05
Convert 0.0008 to a percent:
0.08%
What is the multiplicative identity element for whole numbers, integers, and rational numbers?
1
What is the multiplicative identity element for whole numbers, integers, rational numbers, and real numbers?
1
Convert 137% to a decimal:
1.37
- Convert 9.9 (.9 is repeating) to a fraction:
10
What are examples of powers of 10?
10, 100, 1000, 10000.....
What are examples of multiples of 10?
10, 20, 30, 40, 50....
What is the square root of 144?
12
Convert 1.23 to a percent:
123%
Convert 0.02 to a percent:
2%
What is the multiplicative inverse of 2/3?
3/2
Write 3.74 in a fraction with the denominator as a power of 10:
374/100
Which fraction is undefined: 0/4 or 4/0?
4/0 (because 4 cant be divided by 0)
What is the multiplicative inverse of 3/4?
4/3
What property is this? a+(b+c)=(a+b)+c
Associative property of addition
What property is this? a(bc)=(ab)c
Associative property of multiplication
Why can the subtraction of decimals be accomplished by lining up the decimal points, subtracting them like whole numbers, and then adding the decimal point to the difference?
Because it implements place value when you line up the points
Which property is this? a+b=b+a
Commutative property of addition
What property is this? a(b)=b(a)
Commutative property of multiplication
What is a short cut for getting common denominators and comparing the numerators?
Cross multiplication
True or false: The sum of any 2 irrational numbers is an irrational number.
False √2 + √2 = 2.828....
True or false: The sum of any rational number and any irrational number is a rational number.
False. √2 + 0 = √2
What are two questions that can be made with the equation 8 divided by 2?
How many groups? How many in each group?
What property is this? 0+a=a=a+0
Identity property of addition
What property is this? 1(a)=a=a(1)
Identity property of multiplication
What kind of fraction is it when you have a whole or more if the numerator is greater than or equal to the denominator?
Improper fraction (34/6)
Adding 0's to the end of a whole # changes it's value, but adding 0's to end end of a # to the right of a decimal does what?
It doesn't change the value
If you divide a natural number by a positive rational number that's less than 1, will the answer be greater than or less than the natural number?
It will never be less than the natural number
Will the decimal terminate or repeat if the prime factorization of the denominator has only 2's and 5's as the factors?
It will terminate
Is π equal to 3.14 or 22/7?
Neither; those are approximations not exact
Are any types of numbers closed with respect to division?
No
Can you have more than 100% of something?
No
Does the associative property of division work for any type of numbers?
No
Does the associative property of subtraction hold for any type of numbers?
No
Does the commutative property of division work for any type of number?
No
Does the commutative property of subtraction hold for any type of numbers?
No
Can 0 be divided by anything?
No. Nothing can be divided by 0.
How do you know if a fraction is in it's simplest form?
Only if the denominator is greater than 0 and the greatest common divisor of the numerator and denominator is 1
What sets two ratios equal to each other?
Proportions
Is the square root of a perfect square rational or irrational?
Rational
What are numbers that can always be written as a fraction as long as they are integers and the denominator is not 0?
Rational #'s
What type of numbers have to be integers?
Rational #'s
Why are estimation skills important for dividing decimals?
Several reasons: 1. Many estimation techniques work for whole number division as well as decimal division 2. Long division is more effective with good estimation 3. Estimates are important to tell whether an answer obtained by long division is correct 4. Estimation techniques can be used to place the decimal point in the quotient when decimals are divided
What strategy involves finding the cost for a common number of tickets?
The scaling strategy
What strategy involves finding the cost of one ticket under each plan and then comparing the unit costs?
The unit rate strategy
What is the formula for the constant of proportionality?
Y=kX
Are real numbers closed under addition?
Yes
Can every rational number be written as a repeating decimal?
Yes
Does the associative property of multiplication and addition hold for real numbers?
Yes
Does the commutative property of addition and multiplication hold for real numbers?
Yes
Does the distributive property and multiplication property of equality/inequality still hold for rational numbers?
Yes
Does the distributive property of multiplication and addition hold true for real numbers?
Yes
Does the identity property of addition and multiplication hold for real numbers?
Yes
Does the denseness property hold true for real numbers?
Yes (there are infinitely many numbers between each real number)
Is the sum of two repeating decimals always a repeating decimal?
Yes because every rational number can be written asa repeating decimal
What is a statement that two given ratios are equal?
a proportion
What is a comparison of 2 quantities expressed as the number of times one is greater or less than the other?
a ratio
What do the closure, commutative, associative, and identity properties hold for?
all kinds of numbers
x%= x/100 where x is what?
any non-negative number
Why must the numerator be a non-zero rational # in the Fundamental law of fractions?
because the fraction would be undefined if the numerator was 0. (0/0 is undefined)
What is theorem 6-2: Equality of fractions?
cross multiplying
Wholes must be of what size in order to compare fractions?
equal sizes
How do rational numbers and fractions differ?
fractions don't have to be integers, but rational #'s do
How many irrational numbers are there?
infinitely many
How many numbers can be found between each rational #?
infinitely many
What kind of number is √9 ?
integer, whole number, natural number, rational number, and real number
What kind of number is 1.01001000100001..... ?
irrational number and real number
What kind of number is π ?
irrational number and real number
What are numbers that are not rational called?
irrational numbers
What happens when you create a decimal from a fraction and the remainder is 0?
it terminates
Are irrational numbers closed with respect to multiplication?
no
Are whole numbers closed with respect to subtraction?
no (Ex- 4-7= -3 which is not a whole number)
Are irrational numbers closed with respect to addition?
no (Ex- √2 + √2 does not equal another irrational number)
Are irrational numbers closed with respect to subtraction?
no (Ex- √2 - √2 = 0 which is not an irrational number)
How many answers does x=√17 have?
one answer
What kind of number is 3.14?
rational number and real number,
What kind of number is 3 1/2 ?
real number and rational number
What are the union of rational numbers and irrational numbers?
real numbers
What is the denseness property of rational numbers?
that there are infinitely many numbers between each rational number
What part of the fraction shows the equal size pieces of a whole?
the denominator
What part of a fraction tells how many of the pieces that have been selected?
the numerator
What represents the number of pieces in the whole after it has been cut by fractions?
the numerator
What represents the number of pieces shaded by both fractions?
the numerator
What is the positive number square root?
the principal square root
What is the repeating block of digits?
the repetend
How many answers does x^2=17 have?
two answers: + √17 - √17
Is 0/0 undefined, defined, 0, or can't be simplified?
undefined
Is 5/0 undefined, defined, or 0?
undefined
What kind of number is 0?
whole number, real number, rational number, and integer
