817 Math Blog

On Tuesday, Mr Harbeck assigned us yet another skills blog post. For this post we have to define the word reciprocal, explain how it's used in math, and find at least 4 different ways.

For our skills post we had to look up the word Reciprocal. Reciprocal means; A number related to another in such a way that when its multiplied their product is one or you can called it Multiplicative Inverse.

We can use this and other techniques to get answers to our questions.
Here is an example:

Now I'll show you 3 ways I can do 3/4 divided by 3/5. First I'll show you with a ratio table

You can also estimate your answer so you know roughly where its around. Ask yourself how many groups of 3/4's are in 3/5's? Less than 1 or more than 1. Its less than one.

And heres an example of reciprocal.

Today in Skills, we have one more skill post and we have to find at least 4-5 different ways and what is the meaning of Reciprocal. So I got 4 different ways, I'll show you it in pictures. Here is one way.

Reciprocal: Also called Multiplicative inverse Mathematics. the ratio of unity to a given quantity or expression; that by which the given quantity or expression is multiplied to produce unity

The Ratio table!


Theirs Also another step with Ratio but its kinda confusing on this. You just change the Part R (N and D backwards ) Like 3/4 and you times for divide like divide by 3 and times 4

Next is pictures!



K well this is my last one and I think this will be the easy one! Its call something in Reciprocal.

Pictures:



Okay that's all the things I know how to find the answers! Sorry if I might get some wrong showing!

Last week Mr Harbeck assigned us our last skills assignment post, we were asked to explain if 2/5 of 3/4 are the same as 3/4 of 2/3 are actually the same just the fractions are switched around. Well let's prove it with pictures if 2/5 of 3/4 are the same as 3/4 of 2/3.

Guesstimate:

Today, we were assigned to do another blog post. We have to put the definition of the word reciprocal, explain how it's used in mathematics and show 2 examples.

Reciprocal, also called multiplicative inverse, is a number that you multiply so that the result equals 1. The easiest way to find it is to just flip the fraction over.

We use reciprocal or multiplicative inverse in math because it is faster, quicker and easier to understand. it can be used in a ratio table.

Example:

3/4 divided by 3/5
This question means - how many groups of 3/5 are in 3/4?
The reciprocal of 3/4 is 4/3 and the reciprocal of 3/5 is 5/3.

The answer is going to be more than 1 because 3/4 is larger than 3/5.
The ratio table:


















3/5 divided by 3/3
This question means - how many groups of 3/4 are in 3/5?
The reciprocal of 3/5 is 5/3 and the reciprocal of 3/4 is 4/3.

The answer is going to be less than 1 because 3/5 is smaller than 3/4.
The ratio table:

click the picture (:

Today in Skills, Mr.Herbeck gave us an assignment. This assignment would give us 10 extra mark so I might as well do it for extra marks.
Question: Are 2/5 of 3/4 the same as 3/4 of 2/5?
Well do they look the same to you? Well lets find out by using Pictures and numbers!

1. 2/5 and 3/4


Well Since the other one is still the same, do you think I'm still going to do it? Yes but in Picture!



Well I guess their both the same. Thank you for looking at my assignment! :)

For our third skills assignment we had to explain if 2/5 of 3/4 the same as 3/4 and 2/5?
Okay, 2/5 of 3/4 and 3/4 of 2/5 are actually the same but the fractions are just switched around. Okay lets draw a picture of them showing how they are equal.So I guess their the same! Thanks for viewing my assignment!!

In skills class, we were assigned to do another post about fractions. The question is: Are 2/5 of 3/4 the same as 3/4 of 2/5? We will find out by using pictures.

This is 2/5 of 3/4 :

To find out how to do this you need to multiply the fractions and to do that you have to multiply the numerators and the denominators.
numerators: 2 x 3 = 6
denominators: 5 x 4 = 20
So the answer is 6/20 or when simplified: 3/10


















This is 3/4 of 2/5:

numerators: 3 x 2 = 6
denominators: 4 x 5 = 20


















So, as you can see they're the same (:

One day In class Mr.Harbeck was teaching us about fractions and how 2 fractions can be the same, but one is more precise.













Question 1. 2/3 or 3/4















They both look the same. 2/3 is 4/6 simplified. One is more precise.


4/6 is more precise than 2/3. That is true because if you were to turn those to fractions in to decimals ... it would be.. 0.6666667 ( 2/3 ) and.. 0.66666667 ( 4/6 ).


4/6 is more precise because it has more place value.

Question 2. 1/8 or 1/4

1/4 is obviously bigger than 1/8 ... but why ?
If you look at the picture above , 1/4 is a bigger portion than 1/8. When you look at the denominator you see that 8 is bigger than 4 , so many people might think that 1/8 is larger than 1/4. But when you look at a fraction... the lower the denominator , the bigger the piece. What would you rather have.. 1 of 4 slices from a pizza or 1 of 8 slices from a pizza? 1 of 4 right? Because its cut into less pieces which makes each piece bigger.

On Thursday Mr.Herbeck gave us a skill homework. Its about Fraction, I'll show you 2 ways of finding the answer in subtracting fractions. Here is one way of finding the answer. (In subtract)
This is Borrowing



Now there is another way of finding the answer in mixed subtract fraction. Here is another way. This is call the improper fraction way.



Well those are all the way of finding the answer of mixed subtracting fractions. You can find more but I don't their is more. Well thanks for looking at my assignment! BYE!!

In math class, we talked about subtracting fractions. To be able to subtract fractions, it has to have the same denominators. To get the same denominator you look for the lowest common denominator for example: 1/4 - 1/8, you can't subtract that because the denominators are different so you have to look for the lowest common denominator which is 8, you need to change 1/4 so the numerator is 2 and the denominator is 8. 2/8 - 1/8, is much better and you can now subtract. Mr. Harbeck also taught us how to subtract mixed fractions using two very effective techniques.

The first one is: turning it into an improper fraction, denominator x whole number + numerator = improper fraction. For example: 2 1/2 - 1 3/4 = ?, if you change it, it will be like this: 2 2/4 - 1 3/4. You can subtract 2 and 1 but you can't subtract 2 and 1 so you have to change it into an improper fraction: 10/4 - 7/4 = 3/4

The second one is: the borrowing technique, we use this when the numerator is too big. For example: 625 1/2 - 100 3/4 = ? or as an improper fraction: 1251/2 - 403 = ?, isn't that a bit more complicated? But, if you just borrow like this: ( 624 4/4 + 2/4) - 100 3/4 = ?, is much better because all you have to do is this:

Add 624 4/4 and 2/4 and the answer is 624 6/4. Then, you subtract 624 6/4 and 100 3/4 and the answer is 524 3/4.

Now, subtracting fractions are much easier whether it's improper, proper or mixed. (:

On Thursday we were had an assignment in Math Skills. This time we had to make a post about subtracting fractions using 2 techniques, one is good at some times and the other is good at other times. The two ways you can subtract mixed fractions is to make them improper first then subtract. Or if the mixed numbers are too big, we can use a borrow technique.

The proper time to borrow is when one of the mixed numbers is too big. It would just be harder to make it an improper fraction first then go from there on. For example:100 2/4 - 6 3/4. Unless you want to do like 1,000 push ups, do it the easier way, borrowing. As you can see you can't take 3 with you have only 2.
Okay now I'll show the proper time to use the improper way to subtract fractions. The proper time to use fractions is when the numbers are small and when you can't take away something bigger when you have something smaller to begin with. For example:
See how you can use both ways to subtract fractions! Sometimes one is more faster than the other but you can do either one, they both work!

Sometimes when subtracting fraction you first have to turn them into improper factions, you can also borrow from the fractions.

A good time to switch to improper factions first is when you find out you can't subtract the numerators and the fractions are small. ,
2 1/2 - 1 3/4 =
2 2/4 - 1 3/4 =
= ?

You can't subtract 3 from 2 so you have to start the question with improper factions,
2 1/2 - 1 3/4 =
5/2 - 7/4 =
10/4 - 7/4
=3/4
These questions are an example of when you need to do switch to start with improper fractions.

A good time to borrow when subtracting fractions is when the fraction are huge,
625 1/2 - 100 3/4 =
625 2/4 - 100 3/4 =
= ?

When the question ends up with 2 subtracted by 3 is a good time to borrow,
625 1/2 - 100 3/4 =
625 2/4 - 100 3/4 =
(624 + 4/4 + 2/4)
624 6/4 - 100 3/4=
= 624 9/4
The question is now solved by borrowing fractions.

You can do any subtracting question now, you can do it normally, you can borrow, or you can use improper fractions

Sometime last week, we were assigned another assignment in Skills class. But instead, we have to make a post about subtracting fractions that should borrow, and fractions that should use improper.

The proper time to borrow is when you need to subtract the two fractions but need to use the whole number to do so or when the number is simply big. For example 12 2/11 - 4 9/11. I will explain to you by using pictures, step by step.

A few weeks ago now, we were given yet another skills assignment (skills post), still having to do with fractions. But instead we have to be able to make a post about subtracting fractions that should borrow, and fractions that should be improper fractions.

100 2/4 - 6 3/4

PICTURE:

In our Math class, Mr. Harbeck was teaching us about fractions, and how you compare them. During our Skills class, Mr. Harbeck told us to find two different ways between two fractions. We were assigned to show if the fractions were the same, smaller, or bigger. The way you find out if a fraction is bigger, smaller or the same is by using a picture, or a decimal.

The first fraction we were given was; 2/3 and 4/6. Is 2/3 bigger, smaller, or the same as 4/6? To find out, let's find the decimal of the two fractions.

DECIMAL :
First you divide 2 by 3, and you get 0.666 [repeating]. Then you divide, 4 by 6 and you get 0.666 [repeating]. So now, you know that these two fractions are the same! Another way you can say they're the same is saying that they are equivalent.

PICTURE :The second fraction Mr. Harbeck gave us was; 1/8 and 1/4. Is 1/8 bigger, smaller or the same as 1/4? To find the answer, we do the same thing as the first one.

DECIMAL :
First, you divide 1 by 8. You get, 0.125, and when you divide 1 by 4. You get, 0.25.
This proves that 1/4, is bigger than 1/8.

PICTURE :

My terrible thing xD.

2/3 and 4/6
two easy ways to find that they are equal :].
First look you can convert into %'s. How you can do this is you take 100 and divide it by the denominator. So you would split 100 into 3 parts and into 6 parts. When dividing 100 into 3 parts its 33.333 on going but we just say 33.3. So 1 part is 33% add another part to that and it equals 66%. 66% is when you have 2 thirds of a number. Finally you do the same thing to the 4/6 each part is around 16.6% on going so when you add two together its about 33.3 % 2/6 is equal to 1/3 add 2 to 2/6 which is another 30% and you have 2/3 and 4/6 being the same number [ 66% ].

Another way is simplying.
all you have to do is find out if you are able to half the numerator and denominator with it still being a whole number.
When you half 4/6 4 divided by 2 and 6 divided by 2 it is equal to 2/3 which is obviously equal to 2/3.


2 different ways to find which is greater between
1/8 and 1/4
For this you are definetly able to convert into %'s.
you know that 1/4 is 1 quarter of 100. Divide 100 by 4 and that equals 25%. 1/8 is half of 1/4 so that means that it is half of 25. 1/8 is equal to 12.5% which means for sure that 1/4 is bigger.

In decimals this may be a little confusing for some people

0.125 [1/8]
0.25 [1/4]

as you can see the 1/8 looks bigger. But it is not. This is something called place values. here is the example.

0.125[000]
0.25[0000]

It doesnt matter how many 0's are behind it the closest place value to the whole is whats determined to find the real answer.

okay I hope this made sense.