Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
2. Suppose a pizza is cut into 4 equal slices
Addition and Subtraction of Fractions
3. Suppose a pizza is cut into 4 equal slices
Addition and Subtraction of Fractions
4. Suppose a pizza is cut into 4 equal slices and Joe takes
one slice or ¼ of the pizza,
Addition and Subtraction of Fractions
1
4
5. Suppose a pizza is cut into 4 equal slices and Joe takes
one slice or ¼ of the pizza, Mary takes two slices or 2/4 of
the pizza,
Addition and Subtraction of Fractions
1
4
2
4
6. Suppose a pizza is cut into 4 equal slices and Joe takes
one slice or ¼ of the pizza, Mary takes two slices or 2/4 of
the pizza, altogether they take
+
Addition and Subtraction of Fractions
1
4
2
4
1
4
2
4
7. Suppose a pizza is cut into 4 equal slices and Joe takes
one slice or ¼ of the pizza, Mary takes two slices or 2/4 of
the pizza, altogether they take
+
Addition and Subtraction of Fractions
1
4
2
4
= 3
4
of the entire pizza.
1
4
2
4
8. Suppose a pizza is cut into 4 equal slices and Joe takes
one slice or ¼ of the pizza, Mary takes two slices or 2/4 of
the pizza, altogether they take
+
Addition and Subtraction of Fractions
1
4
2
4
= 3
4
of the entire pizza. In picture:
+ =
1
4
2
4
3
4
9. Suppose a pizza is cut into 4 equal slices and Joe takes
one slice or ¼ of the pizza, Mary takes two slices or 2/4 of
the pizza, altogether they take
+
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Same
Denominator
1
4
2
4
= 3
4
of the entire pizza. In picture:
+ =
1
4
2
4
3
4
10. Suppose a pizza is cut into 4 equal slices and Joe takes
one slice or ¼ of the pizza, Mary takes two slices or 2/4 of
the pizza, altogether they take
+
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Same
Denominator
To add or subtract fractions of the same denominator,
keep the same denominator, add or subtract the numerators
1
4
2
4
= 3
4
of the entire pizza. In picture:
±
a
d
b
d
=
+ =
1
4
2
4
3
4
11. Suppose a pizza is cut into 4 equal slices and Joe takes
one slice or ¼ of the pizza, Mary takes two slices or 2/4 of
the pizza, altogether they take
+
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Same
Denominator
To add or subtract fractions of the same denominator,
keep the same denominator, add or subtract the numerators
1
4
2
4
= 3
4
of the entire pizza. In picture:
±
a
d
b
d
=
d
+ =
1
4
2
4
3
4
12. Suppose a pizza is cut into 4 equal slices and Joe takes
one slice or ¼ of the pizza, Mary takes two slices or 2/4 of
the pizza, altogether they take
+
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Same
Denominator
To add or subtract fractions of the same denominator,
keep the same denominator, add or subtract the numerators
then simplify the result.
1
4
2
4
= 3
4
of the entire pizza. In picture:
±
a
d
b
d
= a ± b
d
+ =
1
4
2
4
3
4
15. Example A.
a. 7
12
+ =
7 + 11
12
18
12
Addition and Subtraction of Fractions
11
12 =
16. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 18/6
12/6
=
Addition and Subtraction of Fractions
11
12 =
17. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
Addition and Subtraction of Fractions
11
12 =
18. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ =b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
11
12 =
19. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
11
12 =
20. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
21. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
22. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
Subtraction of Whole Numbers with Fractions
23. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
Subtraction of Whole Numbers with Fractions
Example B. a. Bolo ate of 1 pizza, what’s left?
8
5
24. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
Subtraction of Whole Numbers with Fractions
Example B. a. Bolo ate of 1 pizza, what’s left?
8
5
5
8Treating 1 as 8
8,
what’s left is: =
8
8 –
5
81 –
25. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
Subtraction of Whole Numbers with Fractions
Example B. a. Bolo ate of 1 pizza, what’s left?
8
5
5
8Treating 1 as 8
8,
what’s left is: =
8
8 –
5
8 =
3
8.1 –
26. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
Subtraction of Whole Numbers with Fractions
Example B. a. Bolo ate of 1 pizza, what’s left?
8
5
5
8Treating 1 as 8
8,
what’s left is: =
8
8 –
5
8 =
3
8.1 –
27. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
Subtraction of Whole Numbers with Fractions
Example B. a. Bolo ate of 1 pizza, what’s left?
8
5
5
8Treating 1 as 8
8,
what’s left is: =
8
8 –
5
8 =
3
8.1 –
b. There were 3 pizzas on
the table and Bolo ate
of 1 pizza, what’s left?
9
7
28. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
Subtraction of Whole Numbers with Fractions
Example B. a. Bolo ate of 1 pizza, what’s left?
8
5
5
8Treating 1 as 8
8,
what’s left is: =
8
8 –
5
8 =
3
8.1 –
Of the 3 pizzas, 2/9 is left of the eaten one, and 2 pizzas
are untouched.
b. There were 3 pizzas on
the table and Bolo ate
of 1 pizza, what’s left?
9
7
29. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
Subtraction of Whole Numbers with Fractions
Example B. a. Bolo ate of 1 pizza, what’s left?
8
5
5
8Treating 1 as 8
8,
what’s left is: =
8
8 –
5
8 =
3
8.1 –
Of the 3 pizzas, 2/9 is left of the eaten one, and 2 pizzas
+ 29
7 = 1 –
9
7are untouched. So 3 –
b. There were 3 pizzas on
the table and Bolo ate
of 1 pizza, what’s left?
9
7
30. Example A.
a. 7
12
+ =
7 + 11
12
18
12
= 3
2
18/6
12/6
=
+ = 8 + 4 – 2
15
= 2
3
=b.
Addition and Subtraction of Fractions
8
15
4
15
– 2
15
10
15
11
12 =
Subtraction of Whole Numbers with Fractions
Example B. a. Bolo ate of 1 pizza, what’s left?
8
5
5
8Treating 1 as 8
8,
what’s left is: =
8
8 –
5
8 =
3
8.1 –
Of the 3 pizzas, 2/9 is left of the eaten one, and 2 pizzas
+ 2 =9
7 = 1 –
9
7
9
2
2are untouched. So 3 – pizzas are left.
b. There were 3 pizzas on
the table and Bolo ate
of 1 pizza, what’s left?
9
7
31. Addition and Subtraction of Fractions
c. There were 8 pizzas on the table and Bolo ate pizzas,
5
2
3
how much pizzas are left?
32. Addition and Subtraction of Fractions
c. There were 8 pizzas on the table and Bolo ate pizzas,
5
2
3
how much pizzas are left?
Of the 8 pizzas, 3 are eaten with 5 left, then another of one
is eaten.
5
2
33. Addition and Subtraction of Fractions
c. There were 8 pizzas on the table and Bolo ate pizzas,
5
2
3
how much pizzas are left?
Of the 8 pizzas, 3 are eaten with 5 left, then another of one
5
2= 8 – 3 –is eaten.
5
2
5
2
3 = 5 – 5
2So 8 –
34. Addition and Subtraction of Fractions
c. There were 8 pizzas on the table and Bolo ate pizzas,
5
2
3
how much pizzas are left?
Of the 8 pizzas, 3 are eaten with 5 left, then another of one
5
2= 8 – 3 –is eaten.
5
2
5
2
3 = 5 – 5
2 = 4 5
3So 8 – are left.
35. Addition and Subtraction of Fractions
c. There were 8 pizzas on the table and Bolo ate pizzas,
5
2
3
how much pizzas are left?
Of the 8 pizzas, 3 are eaten with 5 left, then another of one
5
2= 8 – 3 –is eaten.
5
2
5
2
3 = 5 – 5
2 = 4 5
3So 8 – are left.
To add/subtract (±) mixed fractions of the same denominator,
(±) the whole number parts first, then (±) the fractional parts
of which it might be necessary to carry or borrow.
36. Addition and Subtraction of Fractions
c. There were 8 pizzas on the table and Bolo ate pizzas,
5
2
3
how much pizzas are left?
Of the 8 pizzas, 3 are eaten with 5 left, then another of one
5
2= 8 – 3 –is eaten.
5
2
5
2
3 = 5 – 5
2 = 4 5
3So 8 – are left.
To add/subtract (±) mixed fractions of the same denominator,
(±) the whole number parts first, then (±) the fractional parts
of which it might be necessary to carry or borrow.
+
Example C. Calculate.
a.
8
5
4 8
8
7
37. Addition and Subtraction of Fractions
c. There were 8 pizzas on the table and Bolo ate pizzas,
5
2
3
how much pizzas are left?
Of the 8 pizzas, 3 are eaten with 5 left, then another of one
5
2= 8 – 3 –is eaten.
5
2
5
2
3 = 5 – 5
2 = 4 5
3So 8 – are left.
To add/subtract (±) mixed fractions of the same denominator,
(±) the whole number parts first, then (±) the fractional parts
of which it might be necessary to carry or borrow.
+
Example C. Calculate.
a.
8
5
4 8
8
7
= 4 + 8 +
8
5
8
7
+
38. Addition and Subtraction of Fractions
c. There were 8 pizzas on the table and Bolo ate pizzas,
5
2
3
how much pizzas are left?
Of the 8 pizzas, 3 are eaten with 5 left, then another of one
5
2= 8 – 3 –is eaten.
5
2
5
2
3 = 5 – 5
2 = 4 5
3So 8 – are left.
To add/subtract (±) mixed fractions of the same denominator,
(±) the whole number parts first, then (±) the fractional parts
of which it might be necessary to carry or borrow.
+
Example C. Calculate.
a.
8
5
4 8
8
7
= 4 + 8 +
8
5
8
7
+
= 12 +
8
12
39. Addition and Subtraction of Fractions
c. There were 8 pizzas on the table and Bolo ate pizzas,
5
2
3
how much pizzas are left?
Of the 8 pizzas, 3 are eaten with 5 left, then another of one
5
2= 8 – 3 –is eaten.
5
2
5
2
3 = 5 – 5
2 = 4 5
3So 8 – are left.
To add/subtract (±) mixed fractions of the same denominator,
(±) the whole number parts first, then (±) the fractional parts
of which it might be necessary to carry or borrow.
+
Example C. Calculate.
a.
8
5
4 8
8
7
= 4 + 8 +
8
5
8
7
+
= 12 +
8
12
= 12 +
2
1
1
= 13 2
1
45. Addition and Subtraction of Fractions
Fractions with different denominators can’t be added directly
since the “size” of the fractions don’t match.
c.
5
4
35
2
= 3
8 –
5
4
35
2
8 –
5
2
8 – – =
5
4
5
2
5 –
5
4
=
5
21 –
5
44 + = 5
–
5
4 + 7 4 = 4
5
3
Borrow 1 to
subtract 4/5
46. Addition and Subtraction of Fractions
Fractions with different denominators can’t be added directly
since the “size” of the fractions don’t match. For example
+
1
2
1
3
=
?
?
c.
5
4
35
2
= 3
8 –
5
4
35
2
8 –
5
2
8 – – =
5
4
5
2
5 –
5
4
=
5
21 –
5
44 + = 5
–
5
4 + 7 4 = 4
5
3
Borrow 1 to
subtract 4/5
47. Addition and Subtraction of Fractions
Fractions with different denominators can’t be added directly
since the “size” of the fractions don’t match. For example
+
1
2
1
3
=
?
?
To add them, first find the LCD of ½ and 1/3, which is 6.
c.
5
4
35
2
= 3
8 –
5
4
35
2
8 –
5
2
8 – – =
5
4
5
2
5 –
5
4
=
5
21 –
5
44 + = 5
–
5
4 + 7 4 = 4
5
3
Borrow 1 to
subtract 4/5
48. Addition and Subtraction of Fractions
Fractions with different denominators can’t be added directly
since the “size” of the fractions don’t match. For example
To add them, first find the LCD of ½ and 1/3, which is 6.
We then cut each pizza into 6 slices.
+ =
?
?
1
3
1
2
c.
5
4
35
2
= 3
8 –
5
4
35
2
8 –
5
2
8 – – =
5
4
5
2
5 –
5
4
=
5
21 –
5
44 + = 5
–
5
4 + 7 4 = 4
5
3
Borrow 1 to
subtract 4/5
49. Addition and Subtraction of Fractions
To add them, first find the LCD of ½ and 1/3, which is 6.
We then cut each pizza into 6 slices. Both fractions may be
converted to have the denominator 6.
+ =
Fractions with different denominators can’t be added directly
since the “size” of the fractions don’t match. For example
?
?
1
3
1
2
c.
5
4
35
2
= 3
8 –
5
4
35
2
8 –
5
2
8 – – =
5
4
5
2
5 –
5
4
=
5
21 –
5
44 + = 5
–
5
4 + 7 4 = 4
5
3
Borrow 1 to
subtract 4/5
50. Addition and Subtraction of Fractions
To add them, first find the LCD of ½ and 1/3, which is 6.
We then cut each pizza into 6 slices. Both fractions may be
converted to have the denominator 6. Specifically,
1
2
=
3
6
1
3
=
2
6
+ =
Fractions with different denominators can’t be added directly
since the “size” of the fractions don’t match. For example
?
?
1
3
1
2
c.
5
4
35
2
= 3
8 –
5
4
35
2
8 –
5
2
8 – – =
5
4
5
2
5 –
5
4
=
5
21 –
5
44 + = 5
–
5
4 + 7 4 = 4
5
3
Borrow 1 to
subtract 4/5
51. Addition and Subtraction of Fractions
Fractions with different denominators can’t be added directly
since the “size” of the fractions don’t match. For example
To add them, first find the LCD of ½ and 1/3, which is 6.
We then cut each pizza into 6 slices. Both fractions may be
converted to have the denominator 6. Specifically,
1
2
=
3
6
1
3
=
2
6
Hence,
1
2
+
1
3
=
3
6
+
2
6
=
5
6
+
3
6
2
6
=
5
6
c.
5
4
35
2
= 3
8 –
5
4
35
2
8 –
5
2
8 – – =
5
4
5
2
5 –
5
4
=
5
21 –
5
44 + = 5
–
5
4 + 7 4 = 4
5
3
Borrow 1 to
subtract 4/5
52. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
Addition and Subtraction of Fractions
53. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator.
Addition and Subtraction of Fractions
54. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator. We list the steps below.
Addition and Subtraction of Fractions
55. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator. We list the steps below.
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Different
Denominator (The Traditional Method)
56. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator. We list the steps below.
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Different
Denominator (The Traditional Method)
1. Find their LCD
57. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator. We list the steps below.
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Different
Denominator (The Traditional Method)
1. Find their LCD
2. Convert all the different-denominator-fractions to the have
the LCD as the denominator.
58. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator. We list the steps below.
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Different
Denominator (The Traditional Method)
1. Find their LCD
2. Convert all the different-denominator-fractions to the have
the LCD as the denominator.
3. Add and subtract the adjusted fractions then simplify the
result.
59. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator. We list the steps below.
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Different
Denominator (The Traditional Method)
1. Find their LCD
2. Convert all the different-denominator-fractions to the have
the LCD as the denominator.
3. Add and subtract the adjusted fractions then simplify the
result.
Example D.
5
6
3
8
+a.
60. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator. We list the steps below.
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Different
Denominator (The Traditional Method)
1. Find their LCD
2. Convert all the different-denominator-fractions to the have
the LCD as the denominator.
3. Add and subtract the adjusted fractions then simplify the
result.
Example D.
5
6
3
8
+a.
Step 1: To find the LCD, list the multiples of 8
61. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator. We list the steps below.
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Different
Denominator (The Traditional Method)
1. Find their LCD
2. Convert all the different-denominator-fractions to the have
the LCD as the denominator.
3. Add and subtract the adjusted fractions then simplify the
result.
Example D.
5
6
3
8
+a.
Step 1: To find the LCD, list the multiples of 8 which are
8, 16, 24, ..
62. We need to convert fractions of different denominators to
a common denominator in order to add or subtract them.
The easiest common denominator to use is the LCD, the least
common denominator. We list the steps below.
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions With the Different
Denominator (The Traditional Method)
1. Find their LCD
2. Convert all the different-denominator-fractions to the have
the LCD as the denominator.
3. Add and subtract the adjusted fractions then simplify the
result.
Example D.
5
6
3
8
+a.
Step 1: To find the LCD, list the multiples of 8 which are
8, 16, 24, .. we see that the LCD is 24.
63. Addition and Subtraction of Fractions
Step 2: Convert each fraction to have 24 as the denominator.
64. Addition and Subtraction of Fractions
Step 2: Convert each fraction to have 24 as the denominator.
For , the new numerator is 24 * = 20,
5
6
5
6
65. Addition and Subtraction of Fractions
Step 2: Convert each fraction to have 24 as the denominator.
For , the new numerator is 24 * = 20,
5
6
5
6
5
6
=
20
24
so
66. Addition and Subtraction of Fractions
Step 2: Convert each fraction to have 24 as the denominator.
For , the new numerator is 24 * = 20,
5
6
5
6
5
6
=
20
24
For , the new numerator is 24 * = 9,
3
8
3
8
so
67. Addition and Subtraction of Fractions
Step 2: Convert each fraction to have 24 as the denominator.
For , the new numerator is 24 * = 20,
5
6
5
6
5
6
=
20
24
For , the new numerator is 24 * = 9,
3
8
3
8
so
3
8 =
9
24so
68. Addition and Subtraction of Fractions
Step 2: Convert each fraction to have 24 as the denominator.
For , the new numerator is 24 * = 20,
5
6
5
6
5
6
=
20
24
For , the new numerator is 24 * = 9,
3
8
3
8
Step 3: Add the converted fractions.
so
3
8 =
9
24so
69. Addition and Subtraction of Fractions
Step 2: Convert each fraction to have 24 as the denominator.
For , the new numerator is 24 * = 20,
5
6
5
6
5
6
=
20
24
For , the new numerator is 24 * = 9,
3
8
3
8
Step 3: Add the converted fractions.
5
6
3
8
+
=
20
24 +
9
24
So
so
3
8 =
9
24so
70. Addition and Subtraction of Fractions
Step 2: Convert each fraction to have 24 as the denominator.
For , the new numerator is 24 * = 20,
5
6
5
6
5
6
=
20
24
For , the new numerator is 24 * = 9,
3
8
3
8
Step 3: Add the converted fractions.
5
6
3
8
+
=
20
24 +
9
24
=
29
24
So
so
3
8 =
9
24so
(It’s reduced.)
71. We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
Addition and Subtraction of Fractions
72. We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
Addition and Subtraction of Fractions
73. We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5
Addition and Subtraction of Fractions
74. We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2,
Addition and Subtraction of Fractions
75. We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 =
Addition and Subtraction of Fractions
76. We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
Addition and Subtraction of Fractions
77. Addition and Subtraction of Fractions
Multiplier Method (for adding and subtracting fractions)
We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
Example E. a. 5
6
3
8
+
78. Addition and Subtraction of Fractions
Multiplier Method (for adding and subtracting fractions)
To add or subtract fractions, multiply the problem by the LCD,
distributive to find the numerator over the LCD for the answer.
We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
Example E. a. 5
6
3
8
+
79. Example E. a.
The LCD is 24.
Addition and Subtraction of Fractions
Multiplier Method (for adding and subtracting fractions)
To add or subtract fractions, multiply the problem by the LCD,
distributive to find the numerator over the LCD for the answer.
5
6
3
8
+
We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
80. Example E. a.
The LCD is 24. Multiply the problem by 24, then divide by 24.
Addition and Subtraction of Fractions
Multiplier Method (for adding and subtracting fractions)
To add or subtract fractions, multiply the problem by the LCD,
distributive to find the numerator over the LCD for the answer.
5
6
3
8
+
We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
81. Example E. a.
The LCD is 24. Multiply the problem by 24, then divide by 24.
5
6
3
8+( ) * 24 / 24
Addition and Subtraction of Fractions
Multiplier Method (for adding and subtracting fractions)
To add or subtract fractions, multiply the problem by the LCD,
distributive to find the numerator over the LCD for the answer.
5
6
3
8
+
We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
82. Example E. a.
The LCD is 24. Multiply the problem by 24, then divide by 24.
5
6
3
8+( ) * 24 / 24
Addition and Subtraction of Fractions
Multiplier Method (for adding and subtracting fractions)
To add or subtract fractions, multiply the problem by the LCD,
distributive to find the numerator over the LCD for the answer.
5
6
3
8
+
We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
distribute the multiplication
83. Example E. a.
The LCD is 24. Multiply the problem by 24, then divide by 24.
5
6
3
8+( ) * 24 / 24
4
Addition and Subtraction of Fractions
Multiplier Method (for adding and subtracting fractions)
To add or subtract fractions, multiply the problem by the LCD,
distributive to find the numerator over the LCD for the answer.
5
6
3
8
+
We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
distribute the multiplication
84. Example E. a.
The LCD is 24. Multiply the problem by 24, then divide by 24.
5
6
3
8+( ) * 24 / 24
4 3
Addition and Subtraction of Fractions
Multiplier Method (for adding and subtracting fractions)
To add or subtract fractions, multiply the problem by the LCD,
distributive to find the numerator over the LCD for the answer.
5
6
3
8
+
We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
distribute the multiplication
85. Example E. a.
The LCD is 24. Multiply the problem by 24, then divide by 24.
5
6
3
8+( ) * 24 / 24
4 3
29
24
Addition and Subtraction of Fractions
Multiplier Method (for adding and subtracting fractions)
To add or subtract fractions, multiply the problem by the LCD,
distributive to find the numerator over the LCD for the answer.
5
6
3
8
+
We introduce the following Multiplier-Method to add or subtract
fractions to reduce the amount of repetitive copying.
This method is based on the fact that
if we multiply a quantity x by a, then divide by a, we get back x.
For example, 2 * 5 / 5 = 10/5 = 2, 3 * 8 / 8 = 24/8 = 3.
= (4*5 + 3*3) / 24
=
distribute the multiplication
87. The LCD is 48. Multiply the problem by 48, expand the
multiplication, then divide the result by 48.
Addition and Subtraction of Fractions
b.
7
12
5
8
+ –
16
9
88. ( ) * 48 / 48
7
12
5
8+ – 16
9
The LCD is 48. Multiply the problem by 48, expand the
multiplication, then divide the result by 48.
Addition and Subtraction of Fractions
b.
7
12
5
8
+ –
16
9
89. ( ) * 48 / 48
7
12
5
8+ – 16
94
The LCD is 48. Multiply the problem by 48, expand the
multiplication, then divide the result by 48.
Addition and Subtraction of Fractions
b.
7
12
5
8
+ –
16
9
90. ( ) * 48 / 48
67
12
5
8+ – 16
94
The LCD is 48. Multiply the problem by 48, expand the
multiplication, then divide the result by 48.
Addition and Subtraction of Fractions
b.
7
12
5
8
+ –
16
9
91. ( ) * 48 / 48
67
12
5
8+ – 16
94 3
The LCD is 48. Multiply the problem by 48, expand the
multiplication, then divide the result by 48.
Addition and Subtraction of Fractions
b.
7
12
5
8
+ –
16
9
92. ( ) * 48 / 48
= (4*7 + 6*5 – 3*9) / 48
67
12
5
8+ – 16
94 3
The LCD is 48. Multiply the problem by 48, expand the
multiplication, then divide the result by 48.
Addition and Subtraction of Fractions
b.
7
12
5
8
+ –
16
9
93. ( ) * 48 / 48
= (4*7 + 6*5 – 3*9) / 48
= (28 + 30 – 27) / 48
67
12
5
8+ – 16
94 3
The LCD is 48. Multiply the problem by 48, expand the
multiplication, then divide the result by 48.
Addition and Subtraction of Fractions
b.
7
12
5
8
+ –
16
9
94. ( ) * 48 / 48
= (4*7 + 6*5 – 3*9) / 48
= (28 + 30 – 27) / 48
=
67
12
5
8+ – 16
94 3
The LCD is 48. Multiply the problem by 48, expand the
multiplication, then divide the result by 48.
Addition and Subtraction of Fractions
b.
7
12
5
8
+ –
16
9
48
31
The Multiplier–Method would be the main method used for
adding/subtracting fractional numbers and formulas through
out this and following courses.