816 Math Blog

This is another skills homework assignment. I'm that that great at borrowing, so sorry if there is any mistakes.

This is my first question : 3 1/4 - 1 1/2 = ?

To make life easy the first thing we should do is figure out and find the lowest common denominator.
3 1/4 1 1/2
3 1/4 1 2/4

You can't subtract 2/4 form 1/4. So you have to make 1/4 bigger by borrowing the whole or in
other words 4/4. But you can subtract 1 from 3.

3-1=2 4|4 + 1|4= 5/4 2 + 5/4 = 2 5/4

So why don't we start solving
2 5/4 - 1 2/4
2-1=1
5/4 - 2/4 = 3/4
1= 3/4 = 1 3/4

This is our next question : 50 1\10 - 25 4\5=

The first thing we should do is find the lowest common denominator .
1/10 4/5
1/10 8/10

50 1/10 - 25 8/10

Now you can take away 25 from 50, you have to make the 1/10 bigger by
borrowing 1 whole or another way to say it is 10/10.

50-1=49
1/10 + 10/10= 11/10
49 11/10 - 25 8/10
49 - 25 = 24
11/10 - 8/10 = 3/10
24 + 3/10 = 24 3/10

Now you are finished !!!!

In skills we have to show how to multiply fractions

This is one way of doing it
(denominator x whole number + numerator)

for ex. 2 2/4 below is how you multiply it
(2 x 4) then add the numerator
(2 x 4 + 2)= 10

Here's another example
1 1/2
(1 x 2) then add the numerator
(1 x 2 + 1)= 3

In skills class today, we learned that multiplying improper fractions are easier than multiplying mixed numbers.

Are 2/5 of 3/4 the same as 3/4 of 2/5 ?

He gave us two fractions and told us to figure out if 2/5 of 3/4 is the same as 3/4 of 2/5. So to find out going to use decimals and pictures. So first ill find out the decimals the first one is 6/20 which is 0.3 and I found out so is the other. that is one fact that says they are both the same and now im going to use pictures just to make sure... Both facts say that the fractions are equal.

Decimals

To find the decimal you have to divide the numerator by the denominator.

2 divided by 3 = 0.6 repeated
4 divided by 6 =0.6 repeated

Once more to to get a decimal you have to divide the numerator by the denominator.

1 divided by 4 = 0.25
1 divided by 8 = 0.125

So in conclusion we found out that to get a decimal you have to divide the numerator by the denominator.

I am not exactly sure how to borrow, but I will try my very best to do this.

My first question is 3 1/4 - 1 1/2 = ?

First we are going to find the lowest common denominator.
3 1/4 1 1/2
3 1/4 1 2/4

You can subtract 1 from 3, but you can't subtract 2/4 from 1/4. So you have to make the 1/4 bigger by borrowing 1 whole or in this case 4/4.
3-1=2
4/4 + 1/4= 5/4
2 + 5/4 = 2 5/4

Now we solve!
2 5/4 - 1 2/4
2-1=1
5/4 - 2/4 = 3/4
1= 3/4 = 1 3/4


The next question is 50 1/10 - 25 4/5=.

First we find the lowest common denominator.
1/10 4/5
1/10 8/10

50 1/10 - 25 8/10
Now you can take away 25 from 50, but you can't take away 1/10 from 8/10 so you have to make the 1/10 bigger by borrowing 1 whole or in this case 10/10.

50-1=49
1/10 + 10/10= 11/10
49 11/10 - 25 8/10
49 - 25 = 24
11/10 - 8/10 = 3/10
24 + 3/10 = 24 3/10

How to subtract mixed by making improper fractions

3 1/4 - 1 1/2

Borrowing

50 1/10 - 25 4/5

49 10/10 + 1/10

49 11/10

25 4/5

24 5/5 + 1/5

24 6/5 - 49 11/10

There are many ways to find the difference between fractions but we will only consider 2. One way is to find its decimal value. We will do this for 2/3 and 4/6.

To find the decimal value of a fraction, you must divide numerator by the denominator.
2/3 =0.666
4/6 =0.666
As you can see both numbers equal the same amount.

Another way we can find out which fraction is smaller is by finding the common denominator. We will use this method to find the smaller piece between 1/4 and 1/8.

To do this we need to find the common denominator of 4 and 8. One way you can do this is by multiplying the numbers. A different way is just by counting multiples until you find a common denominator. We will use the second way to answer this question.

If we keep counting by fours, we will get to eight right away. Eight is then the lowest common denominator. We know to get four to eight we need to multiply by 2, therefore we need to multiply the numerator by two too.

1/4 = 2/8
now we can compare or contrast.
2/8 > 1/8

Now we know that 1/4 is bigger than 1/8.

Skills; Fractions

In skills we had to prove 2 different ways, if these two fractions 2/3 and 4/6 were greater, less than, or equal too each other. I did it in decimals and pictures. A key word we needed to think about was "precise".

DECIMAL: When you divide fractions you always divide the numerator by the denominator. 2/3 is 2 divided 3. Your answer will be 0.666 (repeating) Then you divide 4 by 6 and get 0.666 (repeating) Now you know that both of the fractions are the same or equivalent.

PICTURE:



2/3 and 4/6 are equal but not completely the same...
Even though they have the same amount of entirety that pieces they are cut into are different . They are also written differently .


The second question we had to do was, 1/8 and 1/4. is 1/4 bigger - smaller - or equal to 1/8? To find the answer you need to do the same thing for this question like you did for the first. I'll show you in a decimal and a picture ...


DECIMAL: 1 divided by eight = 0.125
DECIMAL: 1 divided by four = 0.25

PICTURE


so you can see that 1/4 is bigger than 1/8
1/4 is cut into smaller pieces . would you rather have 1 out of four pieces or 1 out of eight pieces ?

PICTURES FROM: Rayna

skills homework (fractions)
Mr.Backe has been explaining to us for the last couple classes that even though fractions are equal in size they are not the same. Like my first example... 2/3 is greater, less then or equal to 4/6. Lets find out shall we :) Okay first we are going to find the decimals so we can compare them to see which is bigger.
DECIMALS

To find the decimal you have to divide the numerator by the denominator.

2 divided by 3 = 0.6(repeated)

4 divided by 6 =0.6(repeated)

so according to the decimals both fractions are equivalent, but we still aren't sure so lets try it with a picture.
PICTURE

Both the decimals and the pictures tell us that the fractions are equal, but they aren't the same. lets say we had a pizza and there was a chocolate and we cut it into 3 pieces and there was only two of us. All a sudden two more people come in and want some chocolate, so we cut each of the three piece in half. Now each of the four people get 1/6. Although the same amount was eaten, they got smaller pieces.

The next Example is 1/8 and 1/4, this one I will do the picture first.
PICTURE

Now according to the pictures 1/4 is bigger then 1/8, but just to b sure lets figure out the decimal.
DECIMAL

Once again to find the decimal you have to divide the numerator by the denominator.

1 divided by 4 = 0.25
1 divided by 8 = 0.125

Now that we also found the decimal we know that 1/4 is bigger hen 1/8 because if the whole is cut into 4 the pieces will be bigger then if you cut the whole into 8 pieces.

These are precise ways of figuring out the bigger fraction.

Skills Home Work
by Gennia
For our skills home work we were assigned some fraction questions. We are expected to solve them and make a post about it.

To find the decimal you have to divide the numerator by the denominator.

2 divided by 3 = 0.6 (repeated)
4 divided by 6 = 0.6 (repeated)

This way the decimals should all be equivalent. Lets be sure by looking at this photo.











Picture taken by Rayna:P
This picture shows us that the decimals and the fractions are equivalent, but not the same.

Okay so .. our next question is 1/8 and 1/4. Here is the picture for that.










What the picture is showing us it that 1/4 is bigger than 1/8.
You always have to double check though, so to make sure lets figure out the decimal.

1 divided by 4 = 0.25
1 divided by 8 = 0.125

So we found the decimals and prouved that 1/4 is bigger than 1/8.
If the whole is cut into 4 the pieces will be bigger then if you cut the whole into 8 pieces.

How is 2/3 and 4/6 the same or different? And is 1/8 and 1/4 the same?
(Explain in 2 different ways)

1. We can convert these fractions into Percents

2/3= 66%

4/6= 66%

2. We can convert them into decimals

2/3= 0.66

4/6= 0.66



1. Is 1/4 and 1/8 the same?

No they're not the same

We can convert them into another fractions using different numbers but still be the same amount.

1/4 = 75/100


1/8 = 2/16