MA120-01 Spring 2017
HW Assignment #1
Name_
Due 1-30-17 before 10AM online
Answer each of the problems showing all work. Final answers with no work shown
will not be given credit. Correct final answer
MA120-01 Spring 2017
HW Assignment #2
Name_
Due 2-8-17 before 5PM online
Answer each of the problems showing all work. Final answers with no work shown will
not be given credit. Correct final answers
we start at zero, take two steps to the right,
and then take three more steps to the right,
which causes us to land on positive 5. -5 -4 -3
-2 -1 0 1 2 3 4 5 Chapter 1: The Numbers of
Arithmetic 9 ADD
is extremely important, and it is impossible to
understand algebra without being thoroughly
familiar with this law. Example: 2(3 + 4)
According to the order of operations rules, we
should evaluate thi
denominator (but not necessarily the Least
Common Denominator). LEAST COMMON
DENOMINATOR (LCD) By Inspection The
smallest number that is evenly divisible by all
the denominators In General The LCD is
the third line was just algebra and the fourth
used the definition of (L1 + L2) again. (h)
Yes. The easiest way to see this is the
identification above of these maps with bitvalued column vectors. In
of that something. In fact, we have one whole
plus one more quarter (if you have 5 quarters
in change, you have a dollar and a quarter).
Chapter 1: The Numbers of Arithmetic 20
MIXED NUMBER NOTATION O
works for the repeating fraction part of a
number. If you have a number like 2.33333.,
you should just work with the decimal part
and rejoin it with the whole part after you
have converted it to a fra
there exists its opposite b, and we can define
subtraction as adding the opposite: a b = a +
(-b) In algebra it usually best to always think
of subtraction as adding the opposite
DISTINCTION BETWEEN S
exponents: (42 ) 3 = (42 )(42 )(42 ) = (4 4) (4 4)
(4 4) = 4 4 4 4 4 4 = 4 6 There are more
rules for combining numbers with exponents,
but this is enough for now. ORDER OF
OPERATIONS When we encounte
minus 2 x 2 difference between the
difference between a number and 8 x 8
from 2 from a number n 2 less a number
less 3 n 3 less than 3 less than a number y
3 fewer than 2 fewer than a number y 2
decr
division. 4. Addition and Subtraction, left to
right The left-to-right order does not matter if
only addition is involved, but it matters for
subtraction. Example: Going back to our
original example,
to add these fractions by finding a common
denominator. In this example, the common
denominator is 1000, and we get 1000 2345
1000 5 1000 40 1000 300 1000 2000 1000 5 100
4 10 3 1 2 2.345 = = + + + =
we can say that 1000x = 345 + x Now solve for
x: 333 115 999 345 999 345 1000 345 1000 345
= = = - = = + x x x x x x CONVERTING FRACTIONS
TO DECIMALS We know the decimal
equivalents for some common fr
would have to add 3/2 Chapter 2: Introduction
to Algebra 51 to both sides of the equation to
isolate the x. It is usually more convenient,
though, to use the addition principle first:
Given: 2x 3 = 5
have zero as an eigenvalue. iii. Since MX = 0
has no non-zero solutions, the matrix M is
invertible. (b) Now we suppose that M is an
invertible matrix. i. Since M is invertible, the
system MX = 0 has
Divide the percentage by 100 (or move the
decimal point two places to the left). Chapter
1: The Numbers of Arithmetic 33 Since 100 % x
x = , the decimal equivalent is just the
percentage divided by 1
REDUCING, AND DIVIDING FRACTIONS
EQUIVALENT FRACTIONS Equivalent fractions
are fractions that have the same value, for
example 8 4 6 3 4 2 2 1 = = = etc. Although all
these fractions are written diffe
MP = P D where D = 0 0 0 0 1 0 0 0 3 .
(e) Yes, the direction given by the eigenvector
1 1 1 because its eigenvalue is zero.
This is probably a bad design for a bridge
because it can be displaced in
reciprocal gives you back what you started
with. This allows us to define division as
multiplication by the reciprocal: a b = a (1/b)
This is usually the most convenient way to
think of division when
are 1. The associative and commutative laws
for addition and multiplication 2. The
existence of the additive and multiplicative
identities (0 and 1) Chapter 1: The Numbers of
Arithmetic 14 3. The exis
the nearest tenth. The digit to the right of the
tenths place is a 6, so we have to round up.
But when we round up the 9 it becomes a
10, forcing the one to be added to the left.
Unfortunately, we fin
3 first, and then add 5 to the result, given the
incorrect answer of 6.3333. To make it perform
the addition first, use parentheses: 4 (3 + 5) =
0.5 In our example problem above, the 2 + 3
in the expo
Numbers of Arithmetic 4 Fractions can be
numbers smaller than 1, like 1/2 or 3/4 (called
proper fractions), or they can be numbers
bigger than 1 (called improper fractions), like
two-and-ahalf, which
number 4 could be factored into 2 2). 2x 3 4 2
- x + 1 Factor SIMPLIFYING ALGEBRAIC
EXPRESSIONS By simplifying an algebraic
expression, we mean writing it in the most
compact or efficient manner, with
problem that way, you should be able to see
what you need to do in order to solve it.
Converting between percents and their
decimal equivalents is so simple that it is
usually best to express all perc
In this last example, the first fraction has a
decimal in it, which is not a proper way to
represent a fraction. To clear the decimal, just
multiply both the numerator and the
denominator by 10 to pro
of them (2x + 4x). The only thing left is the
constants 2 + 7 = 9. Putting this all together we
get x 2 + 2x + 3x 2 + 2 + 4x + 7 = 4x 2 + 6x + 9
PARENTHESES Parentheses must be
multiplied out before c
decimal places: 8.602 7480 1122 2.3 3.74 +
Division You can divide decimal numbers using
the familiar (?) technique of long division. This
can be awkward, though, because it is hard to
guess at produ
we finally have the complete set of real
numbers. Any number that represents an
amount of something, such as a weight, a
volume, or the distance between two points,
will always be a real number. The f