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