1. Addition and Subtraction of Fractions

2. Warm up Convert these Mixed numbers as improper fractions 5 8/8 = 48/8
5 8/8 = 48/8
4 5/6 = 29/6
3 3/5 = 18/5
4) Write 3 improper fractions with 4 as denominator 9/4 , 13/4, 23/4
5) Write a fraction for 26 minutes in an hour. Is it proper or an improper fraction?
26/60 proper fraction
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3. A fraction in which the numerator is greater than the denominator
Lets review of our last lesson
Improper Fraction
A fraction in which the numerator is greater than the denominator
Mixed Number
A mixed number (fraction) is a number that has a part that is a whole number and a part that is a fraction
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4. Conversion from an improper fraction in to a mixed fraction
Divide the numerator by the denominator
The remainder you get put it over the denominator (i.e. in the numerator)
The quotient in the place of the whole number
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5. The mixed fraction will look like
Remainder
Quotient
Divisor
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6. Multiply the whole number times the denominator
Conversion from a mixed fraction
in to a improper fraction
Multiply the whole number times the denominator
Add your answer to the numerator
Put your new number over the denominator
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7. The improper fraction will be written as
(Whole number x Denominator) + Numerator
Denominator
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8. Change this mixed number to an improper fraction
Multiply the whole number times the denominator.
Add your answer to the numerator.
Put your new number
over the denominator. + 3 43 8 = x 5 5
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9. Lets get Started Addition of Fractions more sets
Addition means combining objects in two or
more sets
the objects must be of the same type, i.e. we
combine bundles with bundles and sticks with
sticks.
in fractions, we can only combine pieces of the
same size. In other words, the denominators
must be the same.
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10. Addition of Fractions with
equal denominators
Example 1 8 3 8 + +
= ?
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11. + + = Addition of Fractions with equal denominators Example 1 8 3 8
The answer is (1+3) 8
Which can be simplified to 1 2
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12. Addition of Fractions with equal denominators
(1+3)
(8+8)
is NOT the right answer because the denominator tells us how many pieces the whole is divided into, and in this addition problem, we have not changed the number of pieces in the whole. Therefore the denominator should still be 8.
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13. 1 Examples of Addition with equal denominators 2 1 3 5 5 5 + = + = + = = 1 + =
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14. + + = Addition of Fractions with different denominators 1 2 3 5 +
Prime denominators
In this case, we need to first convert them into equivalent fraction with the same denominator
Example: +
An easy choice for a common denominator is 3×5 = 15
1 x x x x = = = = + = + =
Therefore,
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15. Addition of Fractions with different denominators
Remember
When the denominators are co-prime, we need to multiply the two denominators to get the common denominator
When the two denominators have a common factor we find the least common denominator by factoring
When one denominator is a multiple of the other denominator the multiple is the denominator
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16. Examples of each type of denominators
Multiple Denominators
3 x 2
4 x 2
6 1
8 8
6 + 1 8 = = 7 8 + = = +
8 is multiple of 4
Prime Denominators
3 2
5 7 +
3 x x 5
5 x x 5 + + = = = =
5 and 7 are both prime
Common Factor
5 4
6 9
5 x x 2
6 x x 2 23 18 + + 18 = + = = =
Take LCM of 6 and 9
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17. Add the fractions together and the whole numbers together
Adding Mixed Numbers 1 5 3 5 1 5 3 5 + + + 3 + 2
= 3 2
1 + 3 5 = 4 5
= 5 + 4 5
= 5
Add the fractions together and the whole numbers together
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18. Subtraction of Fractions
subtraction means taking objects away
the objects must be of the same type,
i.e. we can only take away apples from a group of apples
- in fractions, we can only take away pieces of the same size. In other words, the denominators must be the same
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19. Subtraction of Fractions with equal denominators - 3 12
This means to take away
from 11 12 11 12
take away
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20. Subtraction of Fractions with equal denominators - 3 12 11 12
This means to take away
from 11 12
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21. Subtraction of Fractions with equal denominators -
Now you can see that there are only 8 pieces left,
therefore - = 8 12 =
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22. Lets see some more examples
Equal Denominators - = =
Different denominators
x x
x x - = - = =
Do same as in Addition
Multiple Take the multiple
Common Factors Take LCM
Prime Multiply the two
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23. Subtraction of mixed numbers1 4 1 2 - 3 1
Example:
Since 1/4 is not enough to be subtracted by 1/2, we have to convert all mixed numbers into improper fractions first then compute 1 4 1 2
3 x x 2 + 1 - - 3 1 = - = - = 7 4 3 4 = = 1
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24. Your Questions 3/8 + 5/8 1 2/9 + 3/5 37/45 9/10 -3/4 3/20
3/8 + 5/
2/9 + 3/ /45
9/10 -3/ /20
To make a salad, Henry used ¾ pound of Boston lettuce and 2/3 pound of red lettuce. How much lettuce did he use in all? 17/12 pounds
8/15 – 2/ /15
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25. Questions galore 6) 7/9 - 1/6 11/18 7) 3 ¼ + 6 ½ 39/4
6) 7/9 - 1/ /18
7) 3 ¼ ½ /4
8) 11/12 - 1/ /12
9) 6/9 - 18/
10) 28/12 – 48/ /3
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26. Lets take a Break
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27. 6/1/5 Dividing Integers
GAME
Click here to play a Game
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28. Emma takes lesser time by 9/20 minutes
Jason takes 11/5 minutes to walk across the park. Emma takes 7/4 minutes to do the same. Who takes less time and by what fraction?
Emma takes lesser time by 9/20 minutes
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29. 2) Alice painted 2/3 of the wall space in her room
2) Alice painted 2/3 of the wall space in her room. Sabrina helped her by painting 1/3 of the wall space. How much did they paint together?
They painted the complete wall.
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30. 3) Bob’s hat size is 27/4. Betty’s hat size is 57/8
3) Bob’s hat size is 27/4 .Betty’s hat size is 57/8. How much larger is Betty’s size than Bob’s?
3/8 of a size
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31. Addition of Fractions Lets recap what we have learned in this lesson
Addition means combining objects in two or
more sets
the objects must be of the same type, i.e. we
combine bundles with bundles and sticks with
sticks.
in fractions, we can only combine pieces of the
same size. In other words, the denominators
must be the same.
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32. Addition of Fractions + With equal denominators Example 1 8 3 8
The answer is (1+3) 8
Which can be simplified to 1 2
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33. Addition of Fractions with different denominators
Remember
When the denominators are co-prime, we need to multiply the two denominators to get the common denominator
When the two denominators have a common factor we find the least common denominator by factoring
When one denominator is a multiple of the other denominator the multiple is the denominator
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34. Subtraction of Fractions
subtraction means taking objects away
the objects must be of the same type,
i.e. we can only take away apples from a group of apples
- in fractions, we can only take away pieces of the same size. In other words, the denominators must be the same
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35. Subtraction of fractions
Example: - - = 8 12 =
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36. You had a Great Lesson Today
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