Question #21

Hey 9-05, as you may know we were suppose to make a post for questions we got assigned from the text book. I was assigned question 21. Also I'm really sorry for the picture quality!

Calculate:

a)

For question A you had to use pedmas. So you first had to solve what was in the brackets. Next was the multiplication. Last was the adding. My answer was the simplified version of 8/30. I got that version by finding the common denominator which was 2, then all you had to do was show how many times 2 went into the numbers.

b)
For question b you had to use reciprocals. So basically the opposite of the factors. For dividing you end up multiplying and when doing that you can cancel out factors that have common factors. For instance I canceled out 4 and 8 because 4 went into both 8 and itself. Then you would replace the factor with the number that goes into it.


c)

For question c you had to use pedmas again. This question was probably the hardest one fro my to solve, because I had to multiply negative numbers. But overall after trying and trying to figure it out all you had to do was solve what was in the brackets, then multiply and finally add. After all of the trouble it was pretty easy to figure out when actually looking at the work.

That's my post! Please comment and tell me if I did anything wrong, or to compliment me (:

a.) The question is asking for how many hours St. John's is ahead of Brandon and to get the answer you have to find the difference of the time in St. John's and Brandon. In other much simpler words, you have to subtract it.
So the time in St. John's is -3 1/2 and the time in Brandon is -6, you have to subtract those two:
-3 1/2 - (-6) = -3 1/2 + 6/1

* now here comes the explaining part:
Why did it turn into a plus sign and where did the negative sign from the -6 go? and why is it 6/1 when it is only 6?

answer to those questions:
It turned into a plus sign and the negative sign from the 6 disappeared because it is now a positive number. When you have a question like this: a - (-b)=c, it is an "oopsie". I think it turns into a positive automatically because the question really is saying: a - 1 (-b)=c. So if you substitute those letters with numbers it will be like this:

-3 1/2 - (-6) = -3 1/2 -1 (-6)...... because of BEDMAS (order of operations) you have to get rid of the brackets first so you have to do -1 times -6 so it turns into +6.
Then it is 6/1 because mathematicians are lazy, they wrote 6 instead of 6/1 because they know that 6 and 6/1 are the same. It is just like the whole "oppsies" thing.

Now to solve it: - WOW that was a very long explanation -___- sorry guys.
-3 1/2 - (-6) = -3 1/2 + 6/1
= -7/2 + 12/2 (I just turned into an improper fraction because it is easier for me)
= 5/2 or 2 1/2 hours
St. John's is ahead of Brandon by 2 1/2 hours.

b.) The question is practically saying how many hours do you need to add to -8 to get to 5 1/2.
Here's a number line to make it easier (:

















There's 13 1/2 hours.

c.) This question is asking for the difference of the time in Tokyo and Kathmandu. So all you have to do is subtract it.
9 - (5 3/4) = 9/1 - (23/4)
= 36/4 - 23/4 (equivalent fractions. Least common denominator because it needs the same denominators)
= 13/4 or 3 1/4 hours
There's 3 1/4 hours time difference between Tokyo and Kathmandu.

d.) This question is also asking for the difference of the time in Chatam Islands and St. John's. You also have to subtract.
12 3/4 - (-3 1/2) = 51/4 + 7/2 ( if you're asking about this equation again look up to the first one, the very long explanation )
= 51/4 + 14/4
= 65/4 or 16 1/4 hours
There's 16 1/4 hours time difference between Chatam Islands and St. John's.

e.) The question is asking you what location has the same time as the difference of Istanbul and Alice Springs halfway. It is asking you to subtract The time in Istanbul, +2, from the time in Alice Springs, +9 1/2 then divide in to t2 because it says "halfway" then see what other location in the list has the same number.
(9 1/2 + 2) ÷2 = (19/2 + 2/1) ÷2
= (19/2 + 4/2) ÷2
= 23/2 ÷ 2/1
= 23/2 x 1/2 ( you have to multiply the dividend by the divisors reciprocal)
= 23/4 or 5 3/4 hours
Kathmandu, Nepal has the same time so Kathmandu, Nepal is the location that has the same time as the difference of Istanbul and Alice Springs halfway.


Sorry if I didn't explain it that well. I tried to explain it and make it as detailed as possible. I guess I just made it long and broing -___-. At least I tried and finished my work ! :D

Question # 17

Hi guys! So the question is:

To calculate -3/4 +(-2/ 3), Amy decided to convert the fractions to decimals and convert the decimals on a scientific calculator.
a) Explain why she had difficulty in determining the the exact answer by this method.
b) How should she calculate to get an exact answer?

a) -2/3 is a repeating decimal. That would mean she would have to round off to add the fractions together, which would not give her an exact answer. Although she could still find the decimal equivalent for -1 5/12. To do that, she would have to divide -5 by 12, and add that to -1.

-1 + (-0.41666.....) = -1.4167 (answer has been rounded)

I still wouldn't advise using this method because 5/12 is a repeating fraction, meaning we would have to round off, which would not give her an exact answer.

b) She should have just added the fractions together.
-3/4 + (-2/3) = -9/12 + (-8/12)
= -17/12
= -1 5/12

Since this fractions cannot be simplified further, we are done. Well, I think that explains everything. If you have any questions or something is wrong, or if you just want to COMMENT, please do. Thanks for reading! :)

Question #20

Hello everyone! I am going to do question #20 (again) for those who didn't understand.

20) In a magic square, the sum of each row, column, and diagonal is the same. Copy and complete this magic square.

So first of all you find out the sum of the diagonal of the square.

And the sum is:

So now we know the sum, now we have to fill in the squares to make a sum of -2 1/2.

Next you have to do the easier ones first. The ones that have 2 squares filled in already.

You add up the two numbers and subtract it from -2 1/2

(-5/6)+(1/2)= -1/3

(-2 1/2)-(-1/3)= -2 1/6

1/2+(-1 1/6)= -2/3

-2 1/2-(-2/3)= -1 5/6

Then you do the same process again.

-1/2+(-2 1/6)= -2 2/3
-2 1/2-(-2 2/3)= 1/6

-1/2+(-1 5/6)= -2 1/3

-2 1/2-(-2 1/3)= -1/6

Now we have one more square to do. But you should always check your answer just in case.

We do the same thing, you could choose which numbers. You could go vertical or horizontal.

I'm going to do both ways to show that it doesn't really matter as long as you get the right answer.

1/6+(-1 1/6)= -1

-2 1/2-(-1)= -1 1/2

OR

-1/6+(-5/6)= -1
-2 1/2-(-1)= -1 1/2

I got the same answer so now we fill in the last square.

And that is how you do question #20!

Thanks for reading! Hope you enjoyed it. If you find a mistake, please comment and I'll fix it.

Question #14

Hi there my fellow 9-05 classmates! The question that I am going to be explaining is question number 14 from the text book.
Li and Ray shared a vegetarian pizza and a Hawaiian pizza of the same size. The vegetarian pizza was cut into eight equal slices. The Hawaiian pizza was cut into six equal slices. Li ate two slices of the vegetarian pizza and one slice of the Hawaiian pizza. Ray ate two slices of the Hawaiian pizza and one slice of the vegetarian pizza. a)Who ate more pizza?

In order to solve this question I decided to make a chart. I figured that it would help me to organize everything better.

First you add what Li ate, which was 1/6 of a pizza and 2/8 of a pizza, which will give you 10/24 (after you simplify). Then you add what Ray ate, which was 2/6 of a pizza, and 1/8 of a pizza, which will give you 11/24 (after you simplify).

So, Ray ate more pizza.

b)How much more did that person eat?

To figure this out, you just subtract what Ray ate from what Li ate.

11/24-10/24=
1/24

Ray ate 1/24 more of a pizza.

c)How much pizza was left over?

Since I like charts, I want to use one to figure out this one too.

The 1/2 comes from 3/6, which is how much of the Hawaiian pizza was left. The 5/8 comes from how much of the vegetarian pizza was left. First you find common denominators for 1/2 and 5/8, which is 8/16 + 10/16. That equals to 18/16, and when you simplify that, it is 1 and 1/8.

Thank you for reading my post. If there's anything wrong, or you don't understand anything, feel free to COMMENT :]

Question #15

Hi everyone! This is a post on question #15. The question is about patterns. The question is just basically saying to find three numbers, after the given numbers. Using patterns according to the numbers. So, it's really easy to do.




Here it is:

To do this first question, I changed the mixed numbers into improper fractions. Then, I found out the common denominator, for just the first two fractions. With those two fractions, I tried different operations, until I got to the pattern. Then you would have to see if the pattern actually works. so it's basically trial and error, for me.






On the second fraction, I did the same thing too. Except I only used the absolute value on the first fraction, to find out the pattern. This question, I had a longer time figuring out than the first one. Since the changing of signs (positive then to negative) caught me off guard. Then I remembered that a negative number, divided by a negative number is positive. Also a positive number divided by a negative number is negative. So the pattern must have been the number divided by a negative number. That gave me a clue. Sooner or later, I finally got it.

absolute value: only how far a number is from zero (eg. the absolute value of 6 is 6, and the absolute value of -6 is 6 also.

I guess that's it. I tried my best explaining this. I think that the easier question you get, the harder it is explaining it. Since there's nothing much to explain.

Have a good long weekend everyone! :D

AND:

Question #16

Hello, "THE CLASS" I am going to talk about Question #16.

Okay, so went over this in class, but in case you still don't understand I am going to explain.
So First you need to find how much cash Boris has.

So we know how much Boris has now, what about Charlie?

Alright Boris has $64, And Charlie has $19.20, and Anna has $ 25.60. The question asks us how much all three have together.


There a.) is Done HOORAY.

Now b.) the Question asks how much more money, Boris has then Charlie.

So here you need to subtract how much Boris has compared to Charlie. So $64.00 - $19.20= $44.20.

There is Question #16. Hope this made it clear. Please Comment!