1. Home
  2. Mathematics grade 7
  3. Term 2
  4. Fractions - 07

2.11 Fractions - 07

<< Chapter < Page
  Mathematics grade 7     Page 1 / 2
Chapter >> Page >

Mathematics

Common fractions

Educator section

Memorandum

18.1

ADDITION

1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {} + 3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {}

2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} + 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} + 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}

2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} + 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} + 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} + 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

PRODUCT

2 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

1 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {}

2

1 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {}

b) numerators x numerators

denominators x denominators

d)

(i) 21 10 size 12{ { { size 8{"21"} } over { size 8{"10"} } } } {}

= 2 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}

(ii) 12 3 size 12{ { { size 8{"12"} } over { size 8{3} } } } {}

= 4

(iii) 84 9 size 12{ { { size 8{"84"} } over { size 8{9} } } } {}

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

18.2 3 1 2 8

  1. (i) 15 x 4 (ii) 18 x 40

8 5 25 27

2 1 5 3

k = 3 2 size 12{"" lSub { size 8{ {} rSub {} rSup {} } } lSup {} { {3} over {2} } } {} = 1 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} c = 16 15 size 12{ { { size 8{"16"} } over { size 8{"15"} } } } {} = 1 1 15 size 12{ { { size 8{1} } over { size 8{"15"} } } } {}

7 4 3

18.3 b) (i) = 38 x 16 (ii) = 17 x 9

4 5 3 10

m = 28 n = 51 10 size 12{ { { size 8{"51"} } over { size 8{"10"} } } } {}

n = 5 1 10 size 12{5 { { size 8{1} } over { size 8{"10"} } } } {}

6

(iii) = 18 x 8

5 3

1

= 48 5 size 12{ { { size 8{"48"} } over { size 8{5} } } } {}

p = 9 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {}

19.1

a) 1

b) 1

c) 1

d) 1

19.2 Product is 1 every time

19.4 a) 20 17 size 12{ { { size 8{"20"} } over { size 8{"17"} } } } {}

b) 1 40 size 12{ { { size 8{1} } over { size 8{"40"} } } } {}

c) 5 31 size 12{ { { size 8{5} } over { size 8{"31"} } } } {}

d) 8 73 size 12{ { { size 8{8} } over { size 8{"73"} } } } {}

19.5 c) 5 31 size 12{ { { size 8{5} } over { size 8{"31"} } } } {} : First make an improper fraction ( 31 5 size 12{ { { size 8{"31"} } over { size 8{5} } } } {} )

d) 8 73 size 12{ { { size 8{8} } over { size 8{"73"} } } } {} : First make an improper fraction ( 73 8 size 12{ { { size 8{"73"} } over { size 8{8} } } } {} )

20. a) 1 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} x 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

= 5 3 size 12{ { { size 8{5} } over { size 8{3} } } } {} x 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

= 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} m = 83, 3 . size 12{ {3} cSup { size 8{ "." } } } {} cm

b) 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} x 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} = 5 18 size 12{ { { size 8{5} } over { size 8{"18"} } } } {} m

= 27, 7 . size 12{ {7} cSup { size 8{ "." } } } {} cm

22.

(a) 32

(b) 15

(c) 25

(d) 25

(e) 45

(f) 2

(g) 8

(h) 7

(i) 7

(j) 6

(k) 6

(l) 8

(m) 8

(n) 8

(o) 100

Leaner section

Content

Activity: multiplication of fractions [lo 1.7.3, lo 2.1.5]

18. MULTIPLICATION OF FRACTIONS

18.1 Multiplication of fractions with natural numbers

You already know that multiplication is repeated addition.

a) See if you can complete the following table:

SUM SKETCH REPEATED ADDITION PRODUCT
e.g. 5 × 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 1 2 + 1 2 + 1 2 + 1 2 + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } + { { size 8{1} } over { size 8{2} } } + { { size 8{1} } over { size 8{2} } } + { { size 8{1} } over { size 8{2} } } + { { size 8{1} } over { size 8{2} } } } {} 2 1 2 size 12{2 { { size 8{1} } over { size 8{2} } } } {}
6 × 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} .................................................. .................
2 × 3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {} .................................................. .................
3 × 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} .................................................. .................
4 × 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} .................................................. .................

b) Look carefully at the completed table. Can you think of a shorter way/method to find the answers?

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

c) TAKE NOTE!

You could also follow this method:

1. Write both numbers as fractions e.g. 6 × 1 4 = 6 1 × 1 4 size 12{6 times { { size 8{1} } over { size 8{4} } } = { { size 8{6} } over { size 8{1} } } times { { size 8{1} } over { size 8{4} } } } {}

2. Multiply the numerators: 6 × 1 = 6

3. Multiply the denominators: 1 × 4 = 4

4. Simplify the answer: 6 4 = 1 2 4 = 1 1 2 size 12{ { { size 8{6} } over { size 8{4} } } =1 { { size 8{2} } over { size 8{4} } } =1 { { size 8{1} } over { size 8{2} } } } {}

d) Calculate:

(i) 7 × 3 10 size 12{7 times { { size 8{3} } over { size 8{"10"} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

(ii) 2 3 × 6 size 12{ { { size 8{2} } over { size 8{3} } } times 6} {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

(iii) 12 × 7 9 size 12{"12" times { { size 8{7} } over { size 8{9} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

e) We would represent 6 × 1 4 size 12{6 times { { size 8{1} } over { size 8{4} } } } {} in another way using a number line:

f) Represent the following on a number line: x = 4 × 2 3 size 12{x=4 times { { size 8{2} } over { size 8{3} } } } {}

18.2 Multiplying fractions with fractions

a) Look carefully at the following examples:

(i) Half ( 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} ) of three quarters ( 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} ) can be shown like this:

Questions & Answers

what is microbiology
Agebe Reply
What is a cell
Odelana Reply
what is cell
Mohammed
how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Mathematics grade 7' conversation and receive update notifications?

Ask