Fractions Study Sheet

Rima and Krishna

Adding Improper Fractions

How To: Take both of your fractions and look at the denominators and find a common denominator. After you have done that what ever you did to the bottom to find the same denominator do to the top as well. Then last add up your fractions and simplify them if possible and convert into a mixed fraction.


Example: 7/4 + 9/8= ?


Step 1: Common Denominator= 8


Step2: Do the same to the top 4x2=8 8x1=8 14/8 + 9/8

7x2=14 9x1=9

Step 3: Add 14/8 + 9/8= 23/8


Step 4: Simplify if possible and convert to mixed fraction 23/8 can not be simplified so the answer would be 2 7/8

Video: https://www.educreations.com/lesson/view/how-to-add-improper-fractions/37234872/?s=D4RCpL&ref=link

Adding Proper Fractions

How To: Take both of your fractions and look at the denominators and find a common denominator. After you have done that what ever you did to the bottom to find the same denominator do to the top as well. Then last add up your fractions and simplify them if possible.


Example: 2/4 + 2/6= ?


Step 1: Common Denominator= 12


Step 2: Do the same to the top 4x3= 12 6x2=12 6/12 + 4/12

2x3= 6 2x2= 4

Step 3: Add 6/12 + 4/12= 10/12


Step 4: Simplify if possible 10/12 can be simplified to 5/6


Video: https://www.educreations.com/lesson/view/how-to-add-proper-fractions/37234688/?s=AKKYEN&ref=link

Adding Mixed Fractions

How to: You first look at your fractions denominators and find a common one. Then when you have found that whatever you did to the bottom also do to the top. When that is done add up the mixed number separately and add up the fractions separately. Lastly simplify the fractions if possible.


Example: 2 3/4 + 4 1/2


Step 1: Common Denominator= 4


Step 2: Do the same to the top 4x1=4 2x2=4 2 3/4 + 4 2/4

3x1=3 1x2=2

Step 3: Add 2 3/4 + 4/2/4=

Step 4: 6 5/4 which simplify to = 7 1/4


Video: https://www.educreations.com/lesson/view/how-to-add-mixed-fractions/37235117/?s=6PPRAD&ref=link

How to Subtract Fractions

Subtracting Fractions is very easy once you understand how to do it. When subtracting you must always remember to make the fractions the same, to do that you must do the following. To change the denominator, you must find the common denominator for both numbers, you either multiply them or find the common multiple. There is a rule for all fractions that whatever you do to the bottom, you must do to the top, so you will either multiply the numerator with the number you multiplied the denominators by, or check how many times the denominator fits into the multiple, and multiply by that number.


e.g. ⅔ - ⅘


multiply:

( 3 x 5 = 15)


common multiple:

( 3 = 3 , 6 , 9 , 12 , 15 , 18)

( 5 = 5 , 10 , 15 , 20)


Both denominators fit into 15, now you must multiply the numerator of the fraction ⅔ by 5, since that is what you multiplied the denominator by, or check how many times 3 fits into 15, which again is 5. For the fraction ⅘ , you will multiply 4 by 3, since that is what you multiplied the denominator by.


Now to subtract the two fractions together, you simply must subtract the two numerators together, but keep the denominator the same.
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Regular Fractions

To subtract regular fractions, you must find the common denominator then do what you did to the bottom to the top, then you subtract the two numerators by each other and keep the denominator the same.


e.g. 4/5 - 5/8


( 5 x 8= 40)


( 8 = 8 , 16 , 24 , 32 , 40 , 48)

( 5 = 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40)


4/5 = 8 x 4 = 32 5/8 = 5 x 5 = 25

8 x 5 = 40 5 x 8 = 40


32 - 25 = 7


32/40 - 25/40 = 7/40


Here are some questions you can try:


  1. 6/10 - 3/8

  2. 8/9 - 1/2

  3. 12/24 - 12/10

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Subtracting Proper Fractions with Unlike Denominators

Improper Fractions

Improper Fractions:


To subtract improper fractions, you must find the common denominator and then change the numerator by what you did to the denominator. To subtract the fractions, you need to subtract the numerators by each other and keep the denominators the same. Since you are subtracting improper fractions, sometimes the numerator will be larger than the denominator, and you could change the answer for it to become a mixed fractions. To do that you must see how many times the denominator fits into the numerator, then the answer will become a whole number, and the extra numbers will become the new numerator.


e.g. 5/4 - 8/5


( 4 x 5 = 20)


( 4 = 4 , 8 , 12 , 16 , 20)

( 5 = 5 , 10 , 15 , 20)



8/5 = 4 x 8 = 32 5/4 = 5 x 5 = 25

4 x 5 = 20 5 x 4 = 20


32 - 25 = 7


32/20 - 25/20 = 7/20


Here are some questions you can try:


  1. 10/5 - 7/5

  2. 4/1 - 3/2

  3. 30/7 - 9/2

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Subtracting Fractions with Unlike Denominators

Mixed Fractions

To subtract mixed fractions you must change the fraction to an improper fractions to subtract it properly. To do that in an easy way all you have to do it multiply the denominator by the whole number, then add the numerator. Once you do that you must find the common denominator for both fractions and change the numerator by how you changed the denominators. To subtract the fractions you must then subtract the numerators by each other and keep the numerators the same. Since this was a mixed fraction in the beginning, to change it back you must see how many times the denominator fits into the numerator and the extra numbers will be the new numerator and the denominator stays the same.


e.g. 2 4/5 - 1 5/8


5 x 2 = 10 + 4 = 14 8 x 1 = 8 + 5 = 13

14/5 13/8


( 5 x 8 = 40)


( 5 = 5 , 10 , 15 , 20 , 25 , 30 , 35, 40)

( 8 = 8 , 16 , 24 , 32 , 40)


14/5 = 8 x 14 = 112 13/8 = 5 x 13 = 65

8 x 5 = 40 5 x 8 = 40


112 - 65 = 47


112/40 - 65/40 = 47/40


40 goes into 47 once.


1 7/40



Here are some questions you can try:


  1. 1 3/4 - 3 2/8

  2. 2 9/12 - 5 2/5

  3. 4 6/10 - 6 3/6

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Subtracting Fractions (mixed numbers)