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Mathematics

Common fractions

Educator section

Memorandum

14. a) denominator

b) common denominator

c) multiple

d) tellers

e) number

f) fractions

g) improper fractions

h) simplify

15.2 a)

= 12 21 size 12{ { { size 8{"12"} } over { size 8{"21"} } } } {} + 14 21 size 12{ { { size 8{"14"} } over { size 8{"21"} } } } {}

= 26 21 size 12{ { { size 8{"26"} } over { size 8{"21"} } } } {}

= 1 5 21 size 12{ { { size 8{5} } over { size 8{"21"} } } } {}

b)

= 5 10 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} + 6 10 size 12{ { { size 8{6} } over { size 8{"10"} } } } {}

= 11 10 size 12{ { { size 8{"11"} } over { size 8{"10"} } } } {}

= 1 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}

c)

= 36 45 size 12{ { { size 8{"36"} } over { size 8{"45"} } } } {} - 25 45 size 12{ { { size 8{"25"} } over { size 8{"45"} } } } {}

= 11 45 size 12{ { { size 8{"11"} } over { size 8{"45"} } } } {}

d)

= 4 6 size 12{ { { size 8{4} } over { size 8{6} } } } {} - 3 6 size 12{ { { size 8{3} } over { size 8{6} } } } {}

= 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {}

16.

a)

= 11 2 3 size 12{"11" { { size 8{2} } over { size 8{3} } } } {} + 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {}

= 11 14 21 size 12{"11" { { size 8{"14"} } over { size 8{"21"} } } } {} + 3 21 size 12{ { { size 8{3} } over { size 8{"21"} } } } {}

p = 11 17 21 size 12{"11" { { size 8{"17"} } over { size 8{"21"} } } } {}

b)

= 3 1 4 1 9 size 12{3 { { size 8{1} } over { size 8{4} } } - { { size 8{1} } over { size 8{9} } } } {}

= 3 9 36 4 36 size 12{ { { size 8{9} } over { size 8{"36"} } } - { { size 8{4} } over { size 8{"36"} } } } {}

t = 3 5 36 size 12{ { { size 8{5} } over { size 8{"36"} } } } {}

= 6 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} – (3 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} )

= 6 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 3 3 6 size 12{ { { size 8{3} } over { size 8{6} } } } {} + 4 6 size 12{ { { size 8{4} } over { size 8{6} } } } {}

= 6 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 4 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {}

= 2 9 12 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} - 2 12 size 12{ { { size 8{2} } over { size 8{"12"} } } } {}

g = 2 7 12 size 12{ { { size 8{7} } over { size 8{"12"} } } } {}

d)

= 9 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {} - (4 9 12 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} + 8 12 size 12{ { { size 8{8} } over { size 8{"12"} } } } {} )

= 9 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 5 5 12 size 12{ { { size 8{5} } over { size 8{"12"} } } } {}

= 4 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 5 12 size 12{ { { size 8{5} } over { size 8{"12"} } } } {}

= 4 21 24 size 12{ { { size 8{"21"} } over { size 8{"24"} } } } {} - 10 24 size 12{ { { size 8{"10"} } over { size 8{"24"} } } } {}

v = 4 11 24 size 12{ { { size 8{"11"} } over { size 8{"24"} } } } {}

Leaner section

Content

Activity: addition and subtraction of fractions [lo 1.7.3]

14. Addition and subtraction of fractions

LET US REVISE.

The answers to the following questions are hidden below.

Circle them when you find them and then complete the sentences.

a b t t t s o n k o f m n
d e n o m i n a t o r y u
e d e l u o a e n r a j m
n k l l l e a m d o c p e
o h a e t m l e i n t o r
m m v r i e d r g e i o a
i n i s p r f e s g o g t
n s u x l m g p t t n h o
a e q k e l v o l e s t r
t d e f s h j r k l e e s
o q w e r t y p y o l u h
r s d a z d o m u b g e s
s i m p l i f i e d e l h

a) We can only add or subtract fractions if the.................................................. are the same.

b) If the denominators differ, we must find .................................................. fractions with the same denominators.

c) We can find the common denominator easily by using ..................................................

d) We only add the.................................................. together.

e) The .................................................. stays unchanged when we add or subtract.

f) When we add mixed numbers together, we first add the natural numbers and then

the ..................................................

g) When we subtract mixed numbers, we can first change them to ................................................. fractions.

h) Answers must always be .................................................. as far as possible.

15.1 Do you still remember?

When we add or subtract e.g. one third ( 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} ) + four fifths ( 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} ) or five sixths ( 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} ) – two nineths ( 2 9 size 12{ { { size 8{2} } over { size 8{9} } } } {} ) we must first make the DENOMINATORS the same. To do this we must look for the Lowest Common Multiple (LCM) .

If we want the LCM of 3 and 5 we can work as follows:

3: 3 ; 6 ; 9 ; 12 ; 15 ; 18 ; 21 ; etc.

5: 5 ; 10 ; 15 ; 20 ; 25 ; etc.

Thus we change both denominators to 15:
1 × 5
3 × 5
=
5
15
en
4 × 3
5 × 3
=
12
15

Thus: 1 3 + 4 5 5 15 + 12 15 17 15 1 2 15 alignl { stack { size 12{ { { size 8{1} } over { size 8{3} } } + { { size 8{4} } over { size 8{5} } } } {} #= { { size 8{5} } over { size 8{"15"} } } + { { size 8{"12"} } over { size 8{"15"} } } {} # = { { size 8{"17"} } over { size 8{"15"} } } {} #=1 { { size 8{2} } over { size 8{"15"} } } {} } } {}

15.2 Calculate the following:

a) x = 4 7 + 2 3 size 12{x= { { size 8{4} } over { size 8{7} } } + { { size 8{2} } over { size 8{3} } } } {}

___________________________________________________

___________________________________________________

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b) y = 1 2 + 3 5 size 12{y= { { size 8{1} } over { size 8{2} } } + { { size 8{3} } over { size 8{5} } } } {}

___________________________________________________

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c) d = 4 5 5 9 size 12{d= { { size 8{4} } over { size 8{5} } } - { { size 8{5} } over { size 8{9} } } } {}

___________________________________________________

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d) k = 2 3 1 2 size 12{k= { { size 8{2} } over { size 8{3} } } - { { size 8{1} } over { size 8{2} } } } {}

___________________________________________________

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16. Work together with a friend and calculate:

a) p = 7 2 3 + 4 1 7 size 12{p=7 { { size 8{2} } over { size 8{3} } } +4 { { size 8{1} } over { size 8{7} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

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b) t = 5 1 4 2 1 9 size 12{t=5 { { size 8{1} } over { size 8{4} } } - 2 { { size 8{1} } over { size 8{9} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

c) g = 6 3 4 2 1 2 + 1 2 3 size 12{g=6 { { size 8{3} } over { size 8{4} } } - left (2 { { size 8{1} } over { size 8{2} } } +1 { { size 8{2} } over { size 8{3} } } right )} {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

d) v = 9 7 8 3 3 4 + 1 2 3 size 12{v=9 { { size 8{7} } over { size 8{8} } } - left (3 { { size 8{3} } over { size 8{4} } } +1 { { size 8{2} } over { size 8{3} } } right )} {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

17. CHALLENGE!

Divide into groups of three. Complete the following table by filling in the number of hours you spent doing homework last week:

NAME Mon Tues Wed Thur Fri
e.g Nomsa 1 1 2 size 12{1 { { size 8{1} } over { size 8{2} } } } {} 2 1 4 size 12{2 { { size 8{1} } over { size 8{4} } } } {} 3 3 4 size 12{3 { { size 8{3} } over { size 8{4} } } } {} 1 1 2 size 12{1 { { size 8{1} } over { size 8{2} } } } {} 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
1. ............................................... ............ ............ ............ ............ ............
2. ............................................... ............ ............ ............ ............ ............
3. ............................................... ............ ............ ............ ............ ............

Answer the following questions:

a) How many hours did each member of the group spend on homework last week?

1. _________________________________

2. _________________________________

3. _________________________________

b) Who spent the most time on homework? _______________________________

c) Who learnt the least? _________________________________

d) Calculate the difference between b en c’s answers.

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

e) Ask another group to check your answers.

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve:

1.7.3: addition, subtraction and multiplication of common fractions.

Questions & Answers

are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
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Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
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ya I also want to know the raman spectra
Bhagvanji
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Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
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Anam
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Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
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