Math 112 Final Exam Study
Addition is Associative
(a+b)+c is the same as a(c+b), ex) (1+2)+3 = 1(2+3)
1 is an identity for multiplication
1 x n = n
Draw a picture to explain 5/(1/3)
15 pies
3900/ 12 using dots and boxes
325
find the 1 to 6 code for the number 25.
41six
use a number line to show: 0/8
Draw a picture!
use a number line to show: 10+5
Draw a picture!
use a number line to show: 3x4
Draw a picture!
ax(bxc)=(axb)xc
associative law
multiplication distributes over addition
ax(b+c) = axb + axc use picture of boxes connected then separated
Multiplication is commutative
axb=bxa use the square picture turned to the side
what makes it true: 35 = 120b
b= base five
Prove that subtraction of whole numbers is not commutative.
3-2=1 but 2-3=-1
use a number line to show: 7-4
Draw a picture!
Is it a mathematical statement? This sentence is false.
No, because it is a paradox meaning that if it is true it makes the sentence false, and if it is false it makes the statement true. It is self contradictory.
Define what it means for addition of whole numbers to be commutative?
a+b=b+a for every number that represents a and b. to prove with a picture use the number line and flip it upside down. If you have a number line that is a+b long and flip it upside down so it is b+a it is the same length
20x (8+5)= 20x8 + 20x5
distributive law
T/F 0 divided by 10 is undefined.
false
T/F any number divided by 0 is 0.
false
(9x3) +0 = 9x3
identity
1x(4x5)= 4x5
identity
conditional statement
if: hypothesis, then: conclusion. If hypothesis is true and conclusion is false then the statement the whole statement is false. If hypothesis is false but conclusion is true the whole statement is true.
zero property of multiplication
n x 0 = 0 and 0 x n = 0 because zero groups of nothing will always be nothing. I hand you zero things and number of times, you having nothing.
Is it a mathematical statement? Is x greater than or equal to 0?
no, because it is asking a question.
Subtraction is Associative
not true
universal statement
something is always true, to prove false find an example, to prove true try every case
Existential statement
sometimes true, to prove false try case to find a good reason why its not true. t prove true find an example
Explain why 5 divided by 0 is undefined.
to solve 0/5 you can change it to 0x ? = 5, but this doesn't work because there is no number times zero that equals 5 because any number times 0 equals 0.
T/F 0 is the identity for multiplication.
true
Draw a picture to explain 4/5, where 5 children share 4 pies.
use pictures to explain.
Is it a mathematical statement? If 3+3=7 then 2+3=8.
yes, it is true because the hypothesis and confusion are both false.
Is it a mathematical statement? 2+2=4 or 5+6=11
yes, true because in an 'or' statement only one part needs to be true, and for this both parts are true.
Is it a mathematical statement? There is some number x such that xsquared = x.
yes, true because the number 1 or x=1 works. 1 squared = 1 which follows what the statement is saying.
multiplication is associative
(axb)xc=ax(bxc) use three dimensional box picture
0 is the identity for addition
0 + n = n, 5 + 0 = 5 you're combining number with nothing so that number stays the same
what number is one more than 555six
1000six
convert 173ten to base five
1143five
453seven + 365seven
1151seven
202five - 134five
13five
Arrange from smallest to largest: 2/7, 3/4, 12/11, 4/8, 1/3, 9/8, 3/7, 5/9, 7/11, 4/4
2/7, 1/3, 3/7,4/8, 5/9, 7/11, 3/4, 4/4, 9/8, 12/11
what number is one less than 210three
202three
4853/23 using dots and boxes method
211
Draw an area model of 3/5 x 2/5
6/25
395ten to base eight
613 eight
convert 2101three to base ten
64 ten
what number has the 1 to 3 code 2122.
71 dots
234/3 using dots and boxes method
78
