Good day students and welcome to part 1 of the compass practice test for numerical skills
and pre-algebra.
These are sample test questions i'm going to go over to help you get ready for your
compass test.
I hope this helps and i hope you do well on your exam.
Alright let's go ahead and take a look at question number 1 we're working on the numerical
skills component what is the value of 54 minus 6 divided by 2 plus 6?
This is assessing our master of the order of operations.
Please Excuse My Dear Aunt Sally, we can group multiplication and division and addition and
subtraction.
so all this means is you do parenthesis first, exponents, multiply and divide you can do
together from left to right which ever comes first.
And then addition and subtraction in the same group you can do from left to right which
ever one comes first.
So first, second, these two third and then these last, fourth.
So let's do that here, if you look at this, let me rewrite the expression, we have 54
minus 6 divided by 2 plus 6.
So division is the highest one here, so we have to divide first, so we're going to divide
6 and 2 so 6 divided by 2 is, actually negative 6 divided by negative 2 is negative 3, we
always have to keep the sign, plus 6 ok?
Addition and subtraction are in the same category but moving from left to right which ever comes
first we work on first, ok? so since minus comes first, going from left to right we're
going to do the subtracting here first, so 54 minus 3 is 51 plus 6, 51 plus 6 is 57 so
the answer to question one is E. Alright moving along to number 2 it says, the lowest temperature
on a winter morning was negative 8 degrees Fahrenheit.
Later the same day the temperature reach a high of 24 degrees Fahrenheit.
By how many degrees Fahrenheit did the temperature increase?.
So there are two ways we can do this, we can just give ourselves, use a visual approach
to solve this, uh to solve this problem, so we have zero degrees, it was negative 8 below
first, and then this was the low and then the high later was 24, so how many degrees
is it going to take to go from negative 8 under all the way up to 24?
We know going down, the distance from here to here is 8 degrees and then starting from
zero, the distance from zero all the way to the top is 24 degrees, so we want to look
for the net increase in temperature, complete increase in temperature, we just simply add
these two, because first of all you have to get to zero and then you go 24 degrees up.
So you just go 24 plus 8 you add them up we get 32 degrees Fahrenheit ok? another way
to do this we can just do the Hi minus the Lo, alright that would give us the answer,
so the Hi is 24 degrees and then we subtract it from the Lo which is negative 8 degrees.
Remember any time you're multiplying signs, minus times minus is a plus alright, so 24
plus 8, what's 24 plus 8?
32 degrees.
Alright?
so your answer is E. Ok moving along to question 3, it says if (3/4 minus 2/3) plus (1/2 plus
1/3) is calculated and the answer reduced to simplest terms, what is the denominator
of the resulting fraction?
So let's do this, so we have 3 over 4 minus 2 over 3 plus 1 over 2 plus 1 over 3, so we're
going to resolve, remember all of our operations, we're going to do the fractions in parenthesis
first and then we're going to combine the resulting fractions ok?
So let's do the left side first, what is the LCD of 4 and 3?
What is the LCD of 4 and 3?
The LCD of 4 and 3 is 12 right?, that is the smallest number that they both can go into,
so we need to make these two denominators 12.
So to do that we're going to multiply on the left, multiply the denominator by 3, because
4 times 3 is 12, the target LCD, whatever you multiply by the denominator multiply by
the top and this one I need this to be 12 so I just multiply by 4 top and bottom.
So that changes that fraction into 9 over 12, we multiply across, 3 times 3 is 9, 4
times 3 is 12, minus 8 over 12 ok? plus now let's take a look at this side right here,
now what is the LCD of 2 and 3?
The LCD of 2 and 3 is 6 so i need to make these 2 denominators 6.To accomplish that
for the left fraction, multiply this by 3 to make it 6 in the denominator and then the
numerator the same thing, so you don't change the problem.
I need this to become 6 so i multiply 2 top and bottom.
so now we're going to have 3 over 6 plus 2 over 6, alright now let's do the fractions
one by one and then we're going to combine the resulting fractions.
So 9 minus 8 is simply 1 over 12 plus 3 plus 2 is 5 over 6.
Now to resolve these two fractions, we need to find the LCD so that we can make the denominators
identical.
And then we can add the two fractions.
So what is the LCD of 12 and 6?
the LCD of 12 and 6 is 12, you know 6 goes into 12.
So this is already the LCD so we don't need to bother with it.
This one we need to make it into 12 so we times it by 2 top and bottom, because 6 times
2 equals 12.
so this becomes 1 over 12 plus 10 over 12 alright?and then you're final answer is 11
over 12.
The question asks, what is the denominator of the resulting fraction?
so the denominator is all i care about, so the denominator is 12 so that's your answer.
Alright so our answer is 3.
ok let's move along to question number 4.
for question 4 we're asked, we're going to be evaluating this.
So let's go ahead and do it.
we have 1/2 + (2/3 divided by 3/4) - (4/5 x 5/6).
Now this is an order of operations problem again, we're going to do the parenthesis first,
then we'll do the addition and subtraction later.
So just leave the 1/2 alone plus, now 2/3, whenever you're dividing two fractions, you
just drop, change, flip.
you multiply the first fraction by the reciprocal of the second.
So you just bring down the 2/3, change the division to a times and then you flip this
to 4/3.
minus, and then this one, it's already a multiplication alright so what we're going to just do is
just multiply across, so 4 times 5 is 20, 5 times 6 is 30.
now let's focus on this, this needs further simplification, so just bring down 1/2 plus
multiply this, 2 times 4 is 8, 3 times 3 is 9, minus 20/30, you can divide both sides
by 10 right?
so divide both sides by 10, the zeros go away so you have 2/3.
Alright, now we have 3 fractions.
I can drop the parenthesis, since there are no operations to be done with this, so 1/2
plus 8/9 minus 2/3.
Now what is the LCD of the denominators, what is the LCD of 2, 9 and 3?
The LCD of 2, 9 and 3 is 18, so the LCD of these three numbers is 18.
So what we're gong to do is, we're going to do, try to make all of the denominators 18
ok?
So let's go ahead and do that.
In order to make 2, 18 i need to multiply by 9, in order to make 9, 18 i need to multiply
by 2, in order to make 3, 18 i need to multiply by 6.
So when I multiply all of these values together I'm going to have 9/18 plus 16/18 minus 12/18
ok? alright, No that these denominators are Identical, I can combine them into one.
I'm just going to compute 9 plus 16 minus 12.
so using the order of operations here, you just do addition, subtraction, which ever
shows first from left to right you execute that first ok?
So starting from the left plus comes first so 9 plus 16 is 25 , minus 12 over 18, and
25 minus 12 is 13/18, so there goes your final answer.
The final answer is C. Alright let's move on to question number 5.
it says that Mr. Brown went grocery shopping to buy meat for his annual office picnic.
He bought 7 3/4 pounds of hamburger, 17.85 pounds of chicken and 6 1/2 pounds of steak.
How many pounds of meat did Mr. Brown buy?
So we're just going to add all the fractions together, and then that will give us our answer.
So we're going to add 7 3/4 plus 17.85 and 6 1/2.
So let's go ahead and add all of this.
wait a minute, we have decimals and fractions here what on earth?
It's kind of complicated to execute the addition because they're all all over the place, different
kinds of representations here.
You look at our alternatives, they're all decimals ok? so that's a hint to me that I
need to convert everything to decimal.
So 3/4 as a decimal is like 3 quarters, so 3 quarters, if you add 3 quarters you're going
to get 75 cents.
So this 7 and 3 quarters is like 7.75, this is already in decimal form, so leave it alone,
17.85.
And then 6 1/2, half of a dollar is 50 cents, so that is just 6.50.
alright now that they all are in decimal form we can now execute our addition.
So 5 plus 5 is 10, zero carry the 1.
8 plus 8 is 16 plus 5 is 21.
1 carry the 2 and 7 plus 7 is 14, plus 2, 16, plus 6 is 22.
2 carry 2, and then 2 plus 1 is 3 so you have 32.10 pounds.
So the answer to number 5 is A. let's move on to question number 6.
It says four students about to purchase concert tickets for $18.50 for each ticket discover
that they may purchase a block of 5 tickets for $80.00.
How much would each of the 4 save if they can get a fifth person to join them and the
5 people equally divide the price of the 5-ticket block?
So how do we do this?
hmmm, now let's see, so what is the original cost for each?
original cost for each student.
Original price for each student is $18.50.
So with this new option, how much will each student pay?
total cost for all 5 is $80.00, ok for 5 students, it's $80.00.
So the new cost for each, is going to be what?
Using this $80.00 total cost price.
The new cost for each is simply going to be the total which is 80 divided by the number
of people that are going to get the tickets.
so $80 divided by 5 you can divide that out, 5 goes into 8, 1 time, ok 5 goes into 30,
6 times.
ok so it's going to be $16 each person is going to be paying $16 here ok?
The way I divided it here, you can use your long division or your calculator, if your
calculators are approved for this, so 5 goes into 8, 1, 1 times 5, 5.
and then you have 30 and then you have 6 ok?
So this is the new cost, this is the original cost so what i'm going to do is I'm going
to look for the difference between the original cost and the new cost.
so that's the savings that each of the 5 will have.
So we're going to go $18.50 minus $16.00 when you subtract it, zero, 5, 8 minus 6 is 2,
1 minus 1 is zero so it's $2.50.
You're answer is B. So for number 6 your answer is B, each person will save $2.50.
Ok let's move on to question number 7, it says, In scientific notation what is 20,000
plus 3.4 million?
We're going to add them first, then we're going to convert our results to scientific
notation.
So let's put the bigger number on top, 3.4 million and then we're going to add 20,000
to that.
ok so if we execute that, our summation, what are we going to get?
we're going to have 3,420,000.
Alright How can we write this in scientific notation?
Now scientific notation requires that there be only one digit to the left of the decimal
ok, so we're going to start from here, and we're going to move the decimal point, one,
two, three, four, five, six.
We moved it 6 units to the right, so that there's one digit here.
When i'm moving the decimal to the front 6 units, it's as though I'm dividing this number
by 100,000, so in order to compensate for that division I need to multiply by something,
so what do I multiply by?
Now you got to note that this is the front of the number right here, this is the front
and this is the back.
if you're moving to the front, you're going to be positive, and if you're going to the
back it's going to be negative.
So since we're going to the front, 6 times, one, two, three, four, five, six, this is
equivalent to dividing by 1 million, in order to compensate for this we're going to multiply
this number by 10 to the positive 6, 10 to the positive 6 alright?
so to write this in scientific notation it's going to be 3.42, you get this from that by
dividing this number by a million and to compensate for that division you have to multiply by
10 to the 6th ok?
Remember every time you're moving your decimal to the front the power is going to be positive
had it been that you were moving it to the back to accomplish a digit to the left of
the decimal the power would be negative ok? so you're answer to this is 3.42 times 10
to the positive 6th, answer is A. Thank you so much for watching this presentation.
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