816 Math Blog

Hey sorry its late but we forgot to post it yesterday! So here it is..ENJOY!







Adding Fractions
Adding fractions is pretty easy, just follow these step and you'll be good to go!



Sorry its a link people but I don't know how to post google docs in blogger so, SORRY!

Addition
Adding fractions is easy once you get the hang of it you can get subtraction as well. First you have to make all your fractions improper to start here is the first example.

Hey Everyone! Last fraction post here and I'm gonna show you how to add, subtract, multiply and divide fractions! Let's start with adding!

Here's an example: 2/4 + 1/4
Since the denominators are the same, all you have to do is add the numerators together.
2 + 1 is 3 so... 3/4!

What if the denominators weren't the same?? :O! Well it's still easy! :) Just MAKE the denominators the same!
For example: 2/4 + 2/8
Now, how do you make the denominators of 4 and 8 the same? Divide 8 by 2! 8 divided by 2 is 4, which is the same as the other denominator. And whatever you do to one side, you do to the other. Now you have to divide the numerator by 2 'cuz you did it to the bottom. The numerator is 2 so 2 divided by 2 is 1. The fraction is 1/4!
2/4 + 1/4 = 3/4 ...hard? I think not!

Subtracting Fractions isn't very hard neither. I'll give you one example with the same denominators and another with different denominators.
Example 1: 4/10 - 2/10
Just subtract the numerators since denominators are the same. 4 - 2 = 2. 2/10 is the answer.

Example 2: 4/10 - 6/30
The denominators are 10 and 30. Divide 30 by 3 to equal 10, an equal denominator to 10! Whatever you do down there, you do up there, too. Divide 6 by 3 to get 2. The equation is 4/10 - 2/10 = 2/10

Multiplying Fractions gets a bit complicated, but not if you know what you're doing.
Example 1: 2/3 x 4/5
The first step is to multiply the numerators. 2 x 4 equals 8. Then multiply the denominators. 3 x 5 equals 15. Your fraction is 8/15! EEEEAASSYYY!!....if you know how to do it :)

Example 2: 2 1/2 x 1/2
Woah! That's hard, eh? NOT! Do you know what an improper fraction is? It's a fraction that has a greater numerator than denominator, meaning its total value is more than 1 whole. All you need to do is convert 2 1/2 into an improper fraction, then use the 2 steps from example 1! To convert a mixed number into an improper fraction, multiply your wholes (2) by your denominator (2) and then add it to your numerator (1). 2 x 2 = 4 + 1 =5. Then use the same denominator. 5/2 is the fraction so you're multiplying 5/2 by 1/2. Multiply Numerators (5 x 1 = 5) and denominators (2 x 2 = 4) to get the fraction 5/4. That's your answer!

Everything is easy so far, right? Well, how do you think dividing will be? EASY! I'll teach you on the way!
Example 1: 9/10 ÷ 3/4

The reciprocal is just a way to find the answer easier. The question is 9/10 ÷ 3/4. Take 3/4 and multiply it by its "opposite". 3/4 x 4/3 is 1 whole. Whatever you do down there, you do up there. Now you multiply 9/10 by 4/3 because you did it to the bottom fraction. Your answer is shown above. Just simplify the improper fraction into a mixed number.

Example 2: Mixed Numbers!
3 1/2 ÷ 7
First, convert your mixed number!
Whole x denominator + numerator...
3 x 2 = 6 + 1 = 7
7/2 is your fraction.
You also have to convert the 7. Let's use the denominator of 2! 7 x 2 is 14. 14/2 is 7 wholes!
7/2 ÷ 14/2 ...use the reciprocal now!


Dividing fractions isn't so bad...

Now let's get to word problems :)

#1: It takes 2 1/4 scoops of flour to make one cake. How many cakes do 15 scoops make?
Let's draw pictures!



As you can see by the indicated colors, 15 scoops of flour can make 6 cakes and 2/3 of a cake.

#2:
One day in Winnipeg with 10 1/2 hours of daylight, it was sunny for 1/3 of that time. For how many hours was it sunny that day?
Convert 10 1/2 into improper to make it easier...
10 x denominator (2) + numerator (1).
10 x 2 = 20 + 1 = 21
21/2 is equal to 10 1/2.
We're trying to find 1/3, so just divide it by 3 if you can, and take 1 piece because you have 1 thirds.

3 1/2 hours of that sunlight were sunny on that day in Winnipeg, out of 10 1/2 hours.

Oh! Before I go, remember to always simplify your fractions if possible, and to always have simple sentence answers to any word problem! Cya guys later!!

Our first question is 2/3 multiplied by 9/10. First what we do is to multiply the numerators which is 2 and 9. So 2 x 9 equals to 18.

Now all that is left to do is to multiply the denominators. So 3 multiplied by 10 equals to 30.


Now the fraction we have is 18/30. So we simplify it and we get 3/5.


So our answer is 3/5 .

Question 2


Now we move on to dividing fractions. Our first Question is 1/4 divided by 3/4. When dividing fractions it always helps when using a ratio table.


Now we have to make it into a mixed fraction. First we have to figure out how many times does 4 go into 12 ? 3 , so 3 becomes the whole number. Since 4 goes into 12 perfectly and there are no left over 3 also becomes our numerator and the denominator stays the same.

Adding and Subtracting Fractions

Question 1

First what we do is look at the Denominators. Then we look at what the two Denominators both go into, then we multiply. 2 multiplied by 7 would give us the total of 14.

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Now that we multiplied both our numerators. All that is left to do is add both second fractions that we got which was 7 over 14 and 4 over 14.

So all we did for the last step was add the numerators and kept the denominators the same, which gave us the total fraction of 11 over 14.

Question 2

First we look at the Denominators, then we figure out what they both go into so 3 times 10 equals 30. Now we make a set of fractions that could go into 30. Now we divide. We divide 3 into 30 and also divide how many times 10 goes into 30.

The last thing we do now is to take away from the numerator which is 10 and 9. So 10 take away 9 equals to one. Then we keep the denominators the same and we have a fraction of 1 over 30.

Word Problems

Question 2

Question 3

Adding Fraction:

Well what I've learned about adding fractions from all the teaching Mr.H taught us, I actually found that adding fractions were simple. Just like 1 2 and 3

And just like I said...1

Perhaps the question was 5/9 + 1/3..
The first step would be to do cross multiplication...

Then....2

you then simply add the two numerators(15 and 9)

and the last step......3

To simplify your answer to the lowest terms, you find the number that is able to divide the numerator and denomerator and the number happens to be 3...

Subtraction is the exact same thing as adding fractions but at the second step you just subtract instead.

Now for adding when you have a mixed number is also very simple, if you think that adding fractions were difficult at this point you must be crazy.

Adding Mixed Fractions

Step 1:

Perhaps the question was....2 4/9 + 5 1/2
You just add the whole fractions together first (2 and 5) which will equal 7

now what would be left is 4/9 and 1/2, so now you do the procedure as if this question was like the very first one in this post.

Your answer should now be 17/18 and all you do now is put the two answers together which would become 7 17/18

Now here's a presentation for multiplying and dividing fractions....



This is the end of my final post for FRACTIONS

~THE END~

Adding and Subtracting Fractions

Question 1:






First of all, we have to look at the denominators and see what 4 and 8 both go into. We can do this by multiplying 4 by 8 which is 32. Maybe some people would choose to use 32 as the next denominator, but using 8 is much easier since 4 and 8 both go into 8.











Then, we make another set of fractions, but with the denominator of 8. First we look at the denominators. How many times does 4 have to be counted to go into 8? 2. How many times does 8 have to be counted to go to 8? 1.












What we do to the bottom, we do to the top. So since 4 was multiplied by 2, then the numerator (3) has to be multiplied by 2. And since 8 was multiplied by 1, then the numerator (1) has to be multiplied by one. 3 x 2? 6. 1 x 1? 1.








The last thing we have to do is subtract the numerators. So 6 take away one is 5. The denominator stays the same, so the overall answer is 5 over 8!

Question 2:







First of all, we have to look at the denominators and see what 2 and 7 both go into. So we multiply both of them to see what number they both fit in. 2 multiplied by 7 results as 14.











Then we make another set of fractions but with the denominator of 14. We look at the denominators first. What does 2 have to be multiplied by to get to 14? 7. What does 7 have to be multiplied by to get to 14? 2.











What we have to do to the bottom, we have to do to the top! So since 2 was multiplied by 7, the numerator (1) has to be multiplied by 7. And since 7 was multiplied by 2, the numerator (2) has to be multiplied by 2.. too!






So now we take away the old fractions, and use the new one! All we have to do is add the numerators together. 7 + 4 results as 11, and the denominator stays the same.

Question 3:





Now we are dealing with mixed fractions. First, we put the whole numbers 20 and 4 out of the way.







Now it looks like a normal subtraction fraction question. Now we have to find out what 3 and 10 both go into. So 3 X 10 = 30.












Then we make a set a fractions that have a denominator of 30. First, we look at the denominators. How many times does 3 have to be multiplied by to get to 30? 10. How many times does 10 have to be multiplied to get to 30?3.












Now, we have to multiply the top fraction numerators by the number that their denominators were multiplied by. So 1 multiplied by 10 is 10, and 3 multiplied by 3 is 9.






Then we take away the old fractions and use the new ones. We have to subtract numerator 9 from numerator 10.The answer to that is 1. And of course, we keep the denominator the same.





Then we bring back the whole numbers and we just use simple subtraction.






Now, we just combine the whole number 16 and the fraction 1 over 30. So the answer to question 3 is 16 and 1 thirtieths!




Multiplying Fractions

Question 1:








Now we are dealing with multiplying fractions. It's not that hard once you get it.














To answer a multiplying fraction question, all you have to do is multiply the numerator to the other, and the same goes to the denominators.











So 3 multiplied by 2 makes 6. 4 multiplied by 5 is 20. So that makes 6 over 20. Then we just simplify by finding a number 6 and 20 both go into, like 2. So 6 divided by 2 is 3, and 20 divided by 2 is 10.



Question 2:






Now we are going to start multiplying mixed fractions.


















Since these fractions are mixed, we can turn them into improper fractions. We can do this by going denominator multiplied by whole number plus numerator.















Now with the improper fractions, the multiplication question looks like this.














Then we multiply 5 by 11, and 2 by 10. Which results as 55 twentieths.












We then simplify the improper fraction, then turn it back into a mixed fraction.







So then the answer to this mixed fraction multiplication question is 2 and 7 fourths!



Dividing Fractions

Question 1:







Now it's onto dividing fractions!

















To divide fractions, we can use a ratio table to help us. The paint cans and the room labels are just there to help us.. Like we have 4 fifths of a paint can the filled up 2 sevenths of the room. What we're supposed to do in this ratio table is to make 2 sevenths into a whole number. So what we do first is divide the numerator by 2, so that makes 1 seventh. Then we multiply one by 7, which makes 7 sevenths, a whole number. If we did those on one side, we have to do it to the other. So divide the numerator by 2, so that makes 2 fifths.Then we multiply 2 by 7, which makes 14 fifths.









Then we change the 14 fifths into a mixed fraction. How many 5's are in 14? 2. So 2 becomes the whole number. How much do you have to add to 2 groups of 5 to get to 14? 4. So 4 becomes the numerator. The denominator stays the same as 5.







So the answer to this fraction division question is 2 and 4 fifths!



Question 2:







Here is a fraction division question with a mixed number and a whole number.
















Then we turn 8 and 1 third into an improper fraction. We make the whole number 7 a fraction by making it a numerator and making the denominator 1.









So this is what the division question looks like now.













To help us with this question, we'll use something that's a fraction over fraction. 25 fifths is the numerator, and 7 over 1 is the denominator. To make 7 over 1 completely whole, we'll use something called a reciprocal. We multiply 7 over 1 by 1 over 7 which results as 1. Then we multiply 25 thirds by 1 over 7 which equals 25 over 21.









We then turn 25 over 21 into an improper fraction. 21 goes into 25 once, and we have to add 4 more to get to 25.







So the answer to this division question is 1 and 4 twenty-fifths!

Word Problem #2 :













Word Problem #3 :