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Fun with Fractions

VOLUME: 1
by

Courtney S

on 15 November 2012

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Transcript of Fun with Fractions

Fun with Fractions By: Alyssa Gainer and
Courtney Skelton Fun with Fractions Adding and Subtracting Multiplying and Dividing Reciprocals Word Problems and more Mixed Numbers and improper
fractions Dictionary VOLUME: 1 In this section we will be learning how to add and subtract using common denominators In this chapter we will learn how to create a reciprocal Definitions of all the subjects we have worked on Table of Contents: Chapter 1- The first step to fractions
Chapter 3- Mixed Numbers
Chapter 4- Reciprocals
Chapter 5- Multiplying and Dividing
Chapter 6- Word Problems and More The First Step To Fractions Practice Problems Adding and Subtracting Practice Problems More Of- First Step To Fractions Fractions are a part over a whole. For example . The 5 is part of 10. The top number is the numerator. The bottom number is the denominator. A good way to remember it is the denominator starts with a D, so does the word down. So Denominator Down. Now you have to reduce. Reducing is when you can divide the same number evenly into both the numerator and denominator. So would reduce to because 5 can go into 5, 1 time and 5 can go into 10 2 times. Some fractions cannot reduce... An example is . It can't reduce because they have no common factors. So to know if your fraction is reduced all the way, it can't be divided equally by the same number.
Lastly we will talk about common denominators. 5 10 5 10 1 2 1 3 Reduce all fractions!! 10 20 = _______ *Reduce all fractions to their lowest terms!!

*Fractions do not have decimals in their numerators and denominators
*Even if something seems like it can't be reduced, put the fraction in the empty space anyways 5 20 = _______ 3 9 = _______ In this chapter we will
mixed numbers and
improper fractions!! We are going to work on mixed numbers and improper fractions. A mixed number is when there is a whole number along with a fraction. This is an example of what one looks like: . This is a mixed fraction! Now, an improper fraction is when the numerator is larger than the denominator. Unlike a normal fraction where the denominator is larger than the numerator. Now, let's use our example from Chapter 2 : . The first step to changing an improper fraction to a mixed number is to see how many times the denominator goes into the numerator. 9 18 = _______ 1. 2. 3. 4. 5. 6. 7 21 The First Step to Fractions: = _______ 6 18 Common Denominators _______ = Common denominators are when you have two fractions with the same denominator. To find a common denominator, you must first list multiples of both denominators. So lets say we have 3/4 and 5/6. We need to add these two numbers together. First we need to list multiples for the denominator. Here is the list of multiples (multiples are a number that contains another number an integral number of times without a remainder)
3/4= 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
5/6= 6, 12, 18, 24, 30, 36, 42
Now underline or circle the numbers that appear in both lists of multiples.
3/4= 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
5/6= 6, 12, 18, 24, 30, 36, 42 Our improper fraction will be . Now we are going to change this improper fraction into a mixed number. The first thing that we need to do is find out how many times the denominator can go into the numerator. The denominator can go into the numerator 4 times (12+12+12+12=48). So your mixed number would be just plain 4. Now if we had a improper fraction like then we see how many times the denominator can go into the numerator which is 4. So 4 is your whole number. Then you have 2 numbers left over (50-48=2) so you take the 2 as your numerator and 12 as your denominator (because the denominator always stays the same). So your mixed number is Now look for the smallest underlined number. In this case, it is 12. Now you would think 'what number would I multiply the denominator by to get the common denominator (which is 12)'. Once you find out that number, change it into a fraction (if the number was one, then it would be 1/1) (these numbers are called multiples.) 3/4 3/3 9/12 5/6
2/2
10/12 Next you will add your new products together. You will learn about this in the next chapter. change these mixed numbers into improper fractions! 1. 2. 3. Practice Problems 7.

8.

9.

10. 4. 5. 3 6 9 6 18 =_______ 20 5 24 7 8 = = 3 2 50 =_______ 10 = 35 153 =_________ 6 60 9 81 =________ 10 2 5 = = Find 5 multiples for each number 8 25 6 4 10 2 1 12 15 22 =__ __ __ __ __ =__ __ __ __ __ MORE =__ __ __ __ __ =__ __ __ __ __ =__ __ __ __ __ =__ __ __ __ __ =__ __ __ __ __ =__ __ __ __ __ =__ __ __ __ __ =__ __ __ __ __ More practice problems... change these improper fractions into mixed numbers! To begin this chapter, we will start off with adding. Let's continue our problem from chapter 1- The First Step to Fractions. Adding fractions is very simple. You can get confused if you do not pay attention. So make sure to be focused! To add fractions, ONLY ADD THE NUMERATOR! The denominator will stay the same.
Example:
9/12 9+10=19
+ 10/12 Denominator stays the same
--------------
19/12

So our sum is 19/12. Now, you might wonder "Why is the numerator larger than the denominator?" Well, your question will be answered when we work on Chap.3

Subtracting is very similar to adding. It uses the same principal. Only subtract the numerators, DO NOT SUBTRACT THE DENOMINATOR. Let's try a problem 48 6 1. 2. 3. 4. 5. 102 3 10 5 64 18 155 15 = = = = = 8/1006
- 6/1006
---------------
2/1006 8-6=2 1. 2. Denominator stays the same Now that we have learned how to simply add and subtract, we can now move onto the practice problems Practice Problems The first step to fractions: In this section we will learn about 3 things: Fractions
Reducing
Common Denominators Add These Fractions Practice Problems Subtract These Fractions 6/10
+ 3/10

________ *These fractions need to be reduced if possible
*Your answer goes on the blue dashed line 4 2 3 12 19 1. 2. 2/6
+ 1/6

_______ 3. 1/3
+ 1/3

_______ 4. 5. 2/20
+ 15/20

__________ 9/15
+ 4/15

________ In this case the denominator goes into the numerator 1 time. This means that 1 will be your whole number in the mixed number. So, since 12 went in 19 only once, take 12, multiply it by 1 (12 1=12), and then take your product and subtract it from the numerator (19-12=7) Our answer is 7. That will be our numerator for the mixed fraction. Then, lastly, your denominator from your improper fraction still stays the same. So, in this case, it is still 12. Finally, our answer is .
Now, let's learn how to convert a mixed number into an improper fraction. We will use the mixed number we just made. To change it to an improper fraction, you will need to take the whole number (1) and multiply it by the denominator (12. So: 1 12=12). Then you add the numerator from the mixed fraction (7) and add it to the product you just got (7+12=19). That sum will now be your numerator. Then like we did before, the denominator will ALWAYS stay the same. Therefore your new improper fraction is . Fraction:
Reducing:
Common Denominators:
Subtracting:
Mixed Numbers:
Improper Fractions:
Multiplying:
Dividing:
Reciprocals:
Word Problems: part-to-whole comparison 1 7 12 to bring down to a smaller extent, size, amount, number, etc. a number that is a multiple of all the denominators of a set of fractions. to unite or join so as to increase the number to withdraw or take away, as a part from a whole. a number consisting of a whole number and a fraction as 4½ 1/2 a fraction having the numerator greater than the denominator In this chapter we will be learning how to multiply and divide fractions!! to make many; increase the number of When multiplying 2 fractions, we multiply the two numerators together. This product will make the new numerator. Then you have to take the 2 denominators and multiply them together, making that product your new denominator. Let's try a problem...

2 1 2 *Remember to reduce! 2 1
3 2 6 6 3

There! It's simple! Now let's try dividing fractions! The first thing that you have to do before dividing a fraction is, turn the second fraction in the problem into a reciprocal. Then after you complete that step, you have to multiply the factions together. Then you switch the second fraction back to its normal fraction. Let's try a problem!

2 1
3 2 These are the fractions that we will be using to answer this problem. Now you have to change the 2nd fraction into a reciprocal. to separate into parts, groups, sections, etc. Multiplying & Dividing fractions!
inversely related or proportional; opposite 1.
2. 6.

7.

8.

9.

10. 3/25
+ 2/25

____________

4/15
+ 1/15

____________

8/10
+ 1/10

____________

1/10
+ 4/10

___________

10/20
+ 5/20

____________ 7
19 1/503 Reduce 23/24 8/10
- 1/24 - 7/10

____________ _____________

3/10 2/3
- 1/10 - 1/2

____________ ______________

6/15 5/12
- 4/15 - 2/12

____________ _______________

6/7 3/4
- 5/7 - 1/4

___________ _______________

10/11 10/13
- 5/11 - 3/13

____________ ________________ = Reciprocals Reciprocals are very simple. All you have to do is switch the denominator with the denominator. So, if we had 2/3, its reciprocal is 3/2. Here's how it works: 2 3
3 2 6. 2 5 10 = 7. 1 2 62 = 8. 6 6 32 = 9. 2 4 45 = 10. 5 5 68 = 2 2
3 1 Then you multiply these fractions..... 2 2 4
3 1 3 = So this is your answer! So as you can see multiplying and dividing fractions are easy!!! Now let's try some practice problems! Practice Problems 1.

2.

3.

4.

5. 2 1 6. = 54 21 7. = 21 6 8. = 32 9. = 21 31 21 10. = = = Simple right? Because that's all a reciprocal is! Practice Problems 1. 6.

2. 7.

3. 8.

4. 9.

5. 10. * *All improper fractions do not need reduced *All mixed numbers do need reduced *To reduce a mixed number, do not mind the whole number, just reduce normally with the numerator and denominator *Turn the fraction into its reciprocal 1 36
2 5

51 100,001
2 100

5 52
1 21

32 654
5 22

6 39
1 4,648 5 6 *these fractions are NOT to be reduced
*Put your answer on the light blue line 1 1 2 6 5 15 2 8 1.

2.

3. 4.

5. 6.

7.

8.

9.

10. 4 1 6 4 4 8 6 4 6 3 = = = = = 6.

7.

8.

9.

10. = = = = = = = = = = *answers must be reduced
yellow line 6 5 6 8 = 5 6 5 2 = 5 5 6 1 = 9 2 4 2 = 6 1 1 9 = YAY!.. We're almost done! Now all we have to do is a few basic word problems! Word problems are problems that are interpreted in words! all you have to do is figure out a way to pick out the correct numbers out of the problem and then figure it out. It's easy! Let's get started and try a couple! any mathematics exercise expressed as a hypothetical situation explained in words ANSWER KEY Word Problems! ANSWER KEY ANSWER KEY CHAPTER 1- The first step to fractions 1. 1. 1/2 8. 7/8
2. 1/4 9. 10/35
3. 1/3 10. 1/9
4. 1/2
5. 1/3
6. 1/3
2. Brandon's mom made a pie. she split it into 20 pieces. Oscar ate 2/5 of the pie. How many pieces did Oscar eat?
3.Maddie has 3/4 of the bag of candy. She divides it among her friends by 1/3. How much does one friend get?
4. Marley has 55 kit-kat's. Trevor wanted some so Marley gave him 3/5 of the candy she had. How many kit-kat's does Trevor get?
5. Zoe had a whole bag of Warheads, she gave 3/5 of the waheads to Megan. Zoe had 4/10 of the bag. There were 100 warheads. How many warheads did Zoe get and how many did Megan get? First set of practice problems 5. 8, 16, 24, 32, 40, etc.
6. 10, 20, 30, 40, 50, etc.
7. 25, 50, 75, 100, 125, etc
8. 12, 24, 36, 48, 60, etc.
9. 15, 30, 45, 60, 75, etc.
10. 22, 44, 66, 88, 110, etc 1. 1, 2, 3, 4, 5, etc.
2. 2, 4, 6, 8, 10, etc.
3. 4, 8, 12, 16, 24, etc.
4. 6, 12, 18, 24, 30, etc. Second set of practice problems Chapter 2- Adding and Subtracting 9/10 1/5
1/2 1/3
2/3 9/10
17/20 1/2
13/15 3/4 1. 6.
2. 7.
3. 8.
4. 9.
5. 10. First set of Practice Problems Second Set of Practice Problems More Word Problems! 6. Patrick had 5/12 krabby patties, Spongebob had 10/24 Krabby patties. Who had more?
7. Ethan had 454 songs out of a possible 500. Brytney had 1/2 of the songs Ethan had. How many songs did Brytney have?
8. Courtney and Alyssa were making a prezi. They have 65 slides out of a possible 100. Mrs.Hack, Mrs.Monoski and Mrs.Kurtz made a prezi that had 3/5 as many slides as Courtney and Alyssa. How many slides did they have?
9. Zofina's Dad went to karate class with her sister Mirabelle. Her dad chopped 10 wooden boards. Mirabelle chopped 1/5 as many as her dad. How many did they chop all together?
10. I have 20 erasers. I give you 1/4. How many do I have left *These fractions need to be reduced if possible
*if the denominators are different
that means you have to find a common
denominator 11/12 1/10
1/5 1/6
2/15 1/4
1/7 1/2
5/11 7/13 1. 6.
2. 7.
3. 8.
4. 9.
5. 10. Chapter 3: Mixed Numbers and Improper fractions First Set Of Practice Problems Second Set Of Practice Problems 1.

2.

3. 168 9186 64 346
18 60 62 5

485 52 198
24 5 32

152 25 94
50 10 45 4.

5.

6. 7. 10.

8.

9. 8 3 2 1

34 10 3

2 2 1 5
9 1
3 10
21 1
7 11
32 10
21 1. 4. 7. 10.

2. 5. 8.

3. 6. 9. Chapter 4: Reciprocals 2/1 5/32 100/100001

2/51 1/6 21/52 4648/39

1/5 5/36 22/654 1. 4. 7. 2. 5. 8. 10. 3. 6. 9. Chapter 5: Multiplying and Dividing 1.

2.

3.

4.

5. 2 3 3 3 4 1 8 3 1 8 2 3 6.

7.

8.

9.

10. 5 8 3 4 1 6 2 1 4 2 3 Practice Problems Continued... 1.

2.

3.

4.

5. 8 4 2 3 / = 32 1 16 2 / = 7 14 7 14 / = 2 4 6 4 3 5 2 6 / / = = 1.

2. 1

3. 1

4. 3

5. 3 1 1 4 5 chapter 6: Word Problems 1. Madison (60)

2. 8 pieces

3. 1

4. 33 Kit-Kat's