1. Fractions: Addition & Subtraction
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Fractions: Addition & Subtraction
Lesson 1f

2. Fractions Reminder Fractions have two parts: A Numerator &
A Denominator
Numerator
Denominator
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3. Finding Common Denominators
Before you can learn to add or subtract fractions you must first learn how to find the Least Common Denominator (LCD).
A Common Denominator is a common multiple of all of the denominators
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4. Finding Common Denominators
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Finding Common Denominators
Cont. . .
Example 1:
Write and as fractions with a common denominator.
A common denominator of and is a common multiple of 3 and 4.
List the multiples of 4 until you have a common multiple of 3 and 4.
Is 4 a multiple of 3? No 4 8 12 16
Is 8 a multiple of 3? No
Is 12 a multiple of 3?
Yes
12 is a common denominator of and .
12 is the Least Common Denominator (LCD).

5. Finding Common Denominators
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Finding Common Denominators
Cont. . .
Example 1: cont . . .
Now it is time to find the fractions equal to and that have a denominator of 12.
1 x ? 3
= 3
2 x ? 4
= 8 8 ? ? ? ? ? ? ? ? ? ? 3 = =
3 x ? = 12 4 4 4 4
4 x ? = 12 3 3 3 3 = =

6. Finding Common Denominators
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Finding Common Denominators
Cont. . .
Example 2:
Write , and as fractions with a common denominator.
List the multiples of 8 until you have a common multiple of 2, 3 and 8.
Is 8 a multiple of 2 & 3? No 8 16 24
Is 16 a multiple of 2 & 3? No
Is 24 a multiple of 2 & 3?
Yes
24 is a common denominator of , & .
24 is the Least Common Denominator (LCD).

7. Finding Common Denominators
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Finding Common Denominators
Cont. . .
Example 2: cont . . .
Now it is time to find the fractions equal to , & that have a denominator of 24.
1 x ? 8
= 8 3
= 15
1 x ? 12
=12
5 x ? 12 ? ? ? ? ? ? ? ? ? ? 8 15 ? ? ? ? = = =
2 x ? =24 12 12 12 12
3 x ? =24 8 8 8 8
8 x ? =24 3 3 3 3 = = =

8. Finding Common Denominators
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Finding Common Denominators
Cont. . .
Your turn: On a separate sheet of paper, write the following fractions with common denominators.
Click here to check your answers!

9. Finding Common Denominators
Next
Finding Common Denominators
Cont. . .
Your turn: On a separate sheet of paper, write the following fractions with common denominators.
LCD = 20
LCD = 6
LCD = 10 15 4 2 5 8 5
LCD = 24
LCD = 30
LCD = 30 4 9 20 21 9 25

10. Adding & Subtracting Fractions
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Adding & Subtracting Fractions
To add fractions that already have common denominators, add the numerators.
For example:
Reduce to lowest terms 12 ?
To subtract fractions that already have common denominators, subtract the numerators.
For example:
Reduce to lowest terms ? 4

11. Adding & Subtracting Fractions
Next
Adding & Subtracting Fractions
Cont. . .
Your turn: On a separate sheet of paper, add or subtract the following fractions.
Click here to check your answers!

12. Adding & Subtracting Fractions
Next
Adding & Subtracting Fractions
Cont. . .
Your turn: On a separate sheet of paper, add or subtract the following fractions. ? 7 ? 16 ? 4 ? 1 ? 6 ? 2

13. Adding & Subtracting Fractions
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Adding & Subtracting Fractions
Cont. . .
To add fractions that do not have common denominators, you must first write each fraction with a common denominator. Then add the numerators.
Example 1: ? ? ? 6 ?
Example 2: 8 ? ? ? ? ? ? ? ? 9

14. Adding & Subtracting Fractions
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Adding & Subtracting Fractions
Cont. . .
To subtract fractions that do not have common denominators, you must first write each fraction with a common denominator. Then subtract the numerators.
Example 1: 14 ? ? ? ?
Example 2: 18 ? ? ? ? 15 ? ? ? ?

15. Adding & Subtracting Fractions
Next
Adding & Subtracting Fractions
Cont. . .
Your turn: On a separate sheet of paper, add or subtract the following fractions.
Click here to check your answers!

16. Adding & Subtracting Fractions
Next
Adding & Subtracting Fractions
Cont. . .
Your turn: On a separate sheet of paper, add or subtract the following fractions. 2 ? ? ? ? 10 ? ? ? ? 12 ? ? ? ? 15 ? ? ? ? 14 ? ? ? ? ? ? ? ? 7 4 ? ? ? ? ? ? ? ? 9 ? ? ? ? 2 16 ? ? ? ? ? ? ? ? 9

17. Next
Adding Mixed Numbers
To add mixed numbers you must first write each fractional part with common denominators.
Example 1:
This can be rewritten as: 10 ? ? ? ? ? ? ? ? 9

18. Next
Adding Mixed Numbers
Cont. . .
To add mixed numbers you must first write each fractional part with common denominators.
Example 2:
This can be rewritten as: 6 ? ? ? ?

19. Next
Click here to check your answers!
Adding Mixed Numbers
Cont. . .
Your turn: On a separate sheet of paper, add the following fractions.

20. Next
Adding Mixed Numbers
Cont. . .
Your turn: On a separate sheet of paper, add the following fractions. 4 ? ? ? ? 8 ? ? ? ? 15 ? ? ? ?

21. Subtracting Mixed Numbers
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Subtracting Mixed Numbers
To subtract mixed numbers you must first write each fractional part with common denominators.
Example 1:
This can be rewritten as: 8 ? ? ? ? 2
– 2 10 7 6

22. Subtracting Mixed Numbers
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Subtracting Mixed Numbers
Cont. . .
To subtract mixed numbers you must first write each fractional part with common denominators.
Example 1:
must be rewritten.
We must borrow 1 from the 6 in order to subtract the fractions.
This can be rewritten as: 5 6 ? ? ? ?
– 4 9 5 1

23. Subtracting Mixed Numbers
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Subtracting Mixed Numbers
Cont. . .
Your turn: On a separate sheet of paper, subtract the following fractions.
Click here to check your answers!

24. Subtracting Mixed Numbers
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Subtracting Mixed Numbers
Cont. . .
Your turn: On a separate sheet of paper, subtract the following fractions. 8 4
– 2
– 3 6 2 5 4 1 6

25. The End
Time to move on to
the next lesson