<< Chapter < Page Chapter >> Page >

2. What is of cardinal importance before attempting to add or subtract fractions?

3. Show whether you are able to do the following:

3.1 8 - 4 3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {}

3.2 3 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} - 1 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

  • Note this : The denominators must be similar when you add fractions together or subtract them from one another.

e.g. 2 4 7 size 12{ { { size 8{4} } over { size 8{7} } } } {} - 1 6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {}

2 – 1 = 1 and

4 7 size 12{ { { size 8{4} } over { size 8{7} } } } {} - 6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {}

( 4 – 6 --- this is not possible. Carry one whole: 1 = 7 7 size 12{ { { size 8{7} } over { size 8{7} } } } {} )

( 4 + 7 = 11 --- yes, 11 – 6 = 5)

Answer: 5 7 size 12{ { { size 8{5} } over { size 8{7} } } } {}

  • You could also reduce compound numbers to improper fractions and make the denominators similar.
  • e.g.. 18 7 13 7 = 5 7 size 12{ { { size 8{"18"} } over { size 8{7} } } - { { size 8{"13"} } over { size 8{7} } } = { { size 8{5} } over { size 8{7} } } } {} (18 – 13 = 5: The denominators are the same. Subtract one numerator from the other.)

4. Do the following:

4.1 4 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} + 4 16 42 size 12{ { { size 8{"16"} } over { size 8{"42"} } } } {}

4.2 36 - 15 6 11 size 12{ { { size 8{6} } over { size 8{"11"} } } } {}

4.3 1 8 + 0, 625 3 8 size 12{ { { size 8{1} } over { size 8{8} } } +0,"625" - { { size 8{3} } over { size 8{8} } } } {}

4.4 4 5 10 + 7 1 2 + 6 3 4 size 12{4 { { size 8{5} } over { size 8{"10"} } } +7 { { size 8{1} } over { size 8{2} } } +6 { { size 8{3} } over { size 8{4} } } } {}

4.5 7 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} - 4 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}

4.6 7 a - a 4 size 12{ { { size 8{a} } over { size 8{4} } } } {} a / 4

4.7 9 a + 6 ab 3 b size 12{ { { size 8{9} } over { size 8{a} } } + left ( { { size 8{6} } over { size 8{ ital "ab"} } } - { { size 8{3} } over { size 8{b} } } right )} {}

4.8 - 6 + 2 6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {}

4.9 5 - (4 4 9 size 12{ { { size 8{4} } over { size 8{9} } } } {} + 2 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} )

4.10 3 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} a - 2 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} a

Activity 1.5

Multiplication and division of rational numbers (fractions)

[lo 1.2.6, 1.6.2]

  • You did this in grade 7 – let's refresh the memory.

1. Multiplication:

  • Important : Write all compound numbers as fractions.Then do crosswise cancellation.

Try the following:

  • 1 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} × 2 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} × 4

2. Division:

  • The reciprocal plays an important role in the division of fractions.

Use an example to explain this term.

e.g. 1 3 ÷ 2 3 size 12{ { { size 8{1} } over { size 8{3} } } div { { size 8{2} } over { size 8{3} } } } {}

  • Both numbers are fractions
  • Change ÷ to the × sign and obtain the reciprocal of the denominator (fraction following the ÷ sign).
  • Do cancellation as with multiplication.

3. Do the following:

3.1 8 ÷ 8 11 size 12{ { { size 8{8} } over { size 8{"11"} } } } {}

3.2 18 ÷ 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}

3.3 5 6 ÷ 5 2 size 12{ { { size 8{5} } over { size 8{6} } } div { { size 8{5} } over { size 8{2} } } } {}

3.4 -2 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} ÷ -1 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {}

3.5 6 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} mn ÷ -6 m 3

3.6 4 xy 3 ab ÷ 2x 3a size 12{ { { size 8{ - 4 ital "xy"} } over { size 8{3 ital "ab"} } } div { { size 8{ - 2x} } over { size 8{3a} } } } {} -

Assessment

Learning outcomes(LOs)
LO 1
Numbers, Operations and RelationshipsThe 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 standards(ASs)
We know this when the learner:
1.2 recognises, classifies an represents the following numbers to describe and compare them:
1.2.2 decimals, fractions and percentages;
1.2.5 additive and multiplicative inverses;
1.2.6 multiples and factors;
1.2.7 irrational numbers in the context of measure­ment (e.g. π size 12{π} {} and square and cube roots of non-perfect squares and cubes);
1.3 recognises and uses equivalent forms of the rational numbers listed above;
1.6 estimates and calculates by selecting and using operations appropriate to solving problems that involve:
1.6.1 rounding off;
1.6.2 multiple operations with rational numbers (including division with fractions and decimals);
1.7 uses a range of techniques to perform calculations, including:
1.7.1 using the commutative, associative and distributive properties with rational numbers;
1.7.2 using a calculator;
1.9 recognises, describes and uses:
1.9.1 algorithms for finding equivalent fractions;
1.9.2 the commutative, associative and distributive properties with rational numbers (the expecta­tion is that learners should be able to use these properties and not necessarily to know the names of the properties).

Memorandum

ACTIVITY 1

1. Natural numbers

Counting numbers

Integers

Real numbers

2. a b size 12{ { {a} over {b} } } {} ; b ≠ 0

2 size 12{ sqrt {2} } {}

3.1 Q

  • Q 1

4.

size 12{ {2} wideslash {7} } {} 0 1 size 12{ sqrt {1} } {} 3 size 12{ sqrt {3} } {} 9 3 size 12{ nroot { size 8{3} } {9} } {} 8 3 size 12{ nroot { size 8{3} } {8} } {} 2,47 1, 45 size 12{ sqrt {1,"45"} } {} size 12{ sqrt { {4} wideslash {8} } } {} size 12{ sqrt { {"16"} wideslash { sqrt {9} } } } {}
Rational
Irrational
  • 1 + 4 size 12{ sqrt {4} } {} ; -4
  • 2 3 size 12{ { { - 2} over {3} } } {} ; 12 1 5 size 12{ { {1} over {5} } } {}
  • 9 + 4 size 12{ sqrt {9+4} } {} ; 1 + 2 2 size 12{ { {1+ sqrt {2} } over { sqrt {2} } } } {}

6. Equal in value

7. 4 14 size 12{ { {4} over {"14"} } } {} = 6 24 size 12{ { {6} over {"24"} } } {} etc

  • Proper fraction
  • Inproper fraction
  • Mixed number
  • Decimal number
  • Recurring decimal number
  • Percentage

ACTIVITY 2

1. 2,15

  • 0,625
  • 3,25
  • 5,75
  • 2,875
  • 6, 000 7 size 12{ { {6,"000"} over {7} } } {} = 0,8571 . . . ≈ 0,86
  • 7, 000 9 size 12{ { {7,"000"} over {9} } } {} = 0,777 . . . = 0, 7 size 12{ {7} cSup { size 8{ cdot } } } {} or 0,8
  • 6 8 1000 size 12{ { {8} over {"1000"} } } {} = 6 1 125 size 12{ { {1} over {"125"} } } {}
  • 4 65 100 size 12{ { {"65"} over {"100"} } } {} = 4 13 20 size 12{ { {"13"} over {"20"} } } {}
  • 375 1000 size 12{ { {"375"} over {"1000"} } } {} = 3 8 size 12{ { {3} over {8} } } {}
  • 7 75 1000 size 12{ { {"75"} over {"1000"} } } {} = 7 3 40 size 12{ { {3} over {"40"} } } {}
  • 13 65 100 size 12{ { {"65"} over {"100"} } } {} = 13 13 20 size 12{ { {"13"} over {"20"} } } {}
  • 125 1000 size 12{ { {"125"} over {"1000"} } } {} = 1 8 size 12{ { {1} over {8} } } {}

5.1 7, 000 9 size 12{ { {7,"000"} over {9} } } {} = 0, 7 size 12{ {7} cSup { size 8{ cdot } } } {}

5.2 -5,8 3 size 12{ {3} cSup { size 8{ cdot } } } {} 5, 000 6 size 12{ { {5,"000"} over {6} } } {} = 0,8333 . . .

5.3 3, 1 size 12{ {1} cSup { size 8{ cdot } } } {} 3 size 12{ {3} cSup { size 8{ cdot } } } {} 13 , 0000 99 size 12{ { {"13","0000"} over {"99"} } } {} = 0,1313 . . .

7.1 3 9 size 12{ { {3} over {9} } } {} = 1 3 size 12{ { {1} over {3} } } {}

7.2 45 99 size 12{ { {"45"} over {"99"} } } {} = 5 11 size 12{ { {5} over {"11"} } } {}

7.3 23 990 size 12{ { {"23"} over {"990"} } } {}

7.4 3 900 size 12{ { {3} over {"900"} } } {} = 1 300 size 12{ { {1} over {"300"} } } {}

9. 0, 4 size 12{ {4} cSup { size 8{ cdot } } } {} 5 size 12{ {5} cSup { size 8{ cdot } } } {} = x

x = 0,4545 . . . 

100 x = 45,4545 . . .

  • –  99 x = 45

x = 45 99 size 12{ { {"45"} over {"99"} } } {} = 5 11 size 12{ { {5} over {"11"} } } {}

ACTIVITY 3

2.1 17 x5 20 x5 size 12{ { {"17"x5} over {"20"x5} } } {} = 85%

2.2 19 40 size 12{ { {"19"} over {"40"} } } {} x 100 1 size 12{ { {"100"%} over {1} } } {} = 47,5%

2.3 38 x2 50 x2 size 12{ { {"38"x2} over {"50"x2} } } {} = 76%

2.4 45 60 size 12{ { {"45"} over {"60"} } } {} x 100 1 size 12{ { {"100"%} over {1} } } {} = 75%

3.1 55 100 size 12{ { {"55"} over {"100"} } } {} = 11 20 size 12{ { {"11"} over {"20"} } } {}

3.2 15 , 5 100 size 12{ { {"15",5} over {"100"} } } {} = 0,155 = 155 1000 size 12{ { {"155"} over {"1000"} } } {} = 31 200 size 12{ { {"31"} over {"200"} } } {}

3.3 33 200 size 12{ { {"33"} over {"200"} } } {}

3.4 2 0 30 { 0 size 12{ { {2 { {0}}} over {"30 {"{0}}} } } {} = 2 30 size 12{ { {2} over {"30"} } } {}

4.a) 33 800 size 12{ { {"33"} over {"800"} } } {} x 25500 1 size 12{ { {"25500"} over {1} } } {} size 12{ approx } {} 1 052

b) 3 5 size 12{ { {3} over {5} } } {} x 25500 1 size 12{ { {"25500"} over {1} } } {} = 15 300

c) 85 1000 size 12{ { {"85"} over {"1000"} } } {} x 25500 1 size 12{ { {"25500"} over {1} } } {} = 2 167,5 size 12{ approx } {} 2 168

  • (14,5) 15300 1052 size 12{ { {"15300"} over {"1052"} } } {} = 7650 526 size 12{ { {"7650"} over {"526"} } } {} = 3825 263 size 12{ { {"3825"} over {"263"} } } {}
  • 25 500 – 18 520 = 6 980

4.4

4.5 3 5 size 12{ { {3} over {5} } } {} x 2 1 size 12{ { {2} over {1} } } {} = 6 5 size 12{ { {6} over {5} } } {} = 1 1 5 size 12{1 { {1} over {5} } } {}

ACTIVITY 4

1.1 39 7 size 12{ { {"39"} over {7} } } {}

1.2 70 9 size 12{ { {"70"} over {9} } } {}

2. Numbers must be the same

3.1 3 4 7 size 12{3 { {4} over {7} } } {}

3.2 2 2 9 18 size 12{2 { {2 - 9} over {"18"} } } {} = 1 20 9 18 size 12{1 { {"20" - 9} over {"18"} } } {} = 1 11 18 size 12{1 { {"11"} over {"18"} } } {}

4.1 29 7 size 12{ { {"29"} over {7} } } {} + 184 42 size 12{ { {"184"} over {"42"} } } {} = 174 + 184 42 size 12{ { {"174"+"184"} over {"42"} } } {} = 358 42 size 12{ { {"358"} over {"42"} } } {} = 8 22 42 size 12{8 { {"22"} over {"42"} } } {} = 8 11 21 size 12{8 { {"11"} over {"21"} } } {}

4.2 21 - 6 11 size 12{ { {6} over {"11"} } } {} = 20 5 11 size 12{"20" { {5} over {"11"} } } {}

  • 0,125 + 0,625 – 0,375 = 0,375
  • 17 10 + 10 + 15 20 size 12{"17" { {"10"+"10"+"15"} over {"20"} } } {} = 17 35 20 size 12{"17" { {"35"} over {"20"} } } {} = 18 15 20 size 12{"18" { {"15"} over {"20"} } } {} = 18 3 4 size 12{"18" { {3} over {4} } } {}
  • 3 3 21 24 size 12{3 { {3 - "21"} over {"24"} } } {} = 2 11 24 size 12{2 { {"11"} over {"24"} } } {}
  • {} 28 a 2 a 4 size 12{ { {"28"`a rSup { size 8{2} } - a} over {4} } } {}

4.7+ ( 6 3a ab ) size 12{\( { {6 - 3a} over { ital "ab"} } \)} {} = 9b + 6 3a ab size 12{ { {9b+6 - 3a} over { ital "ab"} } } {}

4.8 6 1 size 12{ { { - 6} over {1} } } {} + 20 7 size 12{ { {"20"} over {7} } } {} = 42 + 20 7 size 12{ { { - "42"+"20"} over {7} } } {} = 22 7 size 12{ { { - "22"} over {7} } } {} = 3 1 7 size 12{ - 3 { {1} over {7} } } {}

  • 5 – 6 4 + 6 9 size 12{ left (6 { {4+6} over {9} } right )} {} = 5 – 6 10 9 size 12{6 { {"10"} over {9} } } {} = 5 – 7 1 9 size 12{7 { {1} over {9} } } {}

=– 64 9 size 12{ { {"64"} over {9} } } {}

= 45 64 9 size 12{ { {"45" - "64"} over {9} } } {}

= 19 9 size 12{ { { - "19"} over {9} } } {} = 2 1 9 size 12{ - 2 { {1} over {9} } } {}

  • 10 a 3 size 12{ { {"10"a} over {3} } } {} 5a 2 size 12{ { {5a} over {2} } } {} = 20 a 15 a 6 size 12{ { {"20"a - "15"a} over {6} } } {}

= 5a 6 size 12{ { {5a} over {6} } } {}

ACTIVITY 5

1. 5 1 4 size 12{ { {5} over { {} rSub { size 8{1} } { {4}}} } } {} x 5 2 size 12{ { {5} over {2} } } {} x 4 1 1 size 12{ { { { {4}} rSup { size 8{1} } } over {1} } } {} = 25 2 size 12{ { {"25"} over {2} } } {} = 12 1 2 size 12{"12" { {1} over {2} } } {}

3.1 8 1 size 12{ { {8} over {1} } } {} ÷ 8 11 size 12{ { {8} over {"11"} } } {} = 8 1 1 size 12{ { { { {8}} rSup { size 8{1} } } over {1} } } {} x 11 8 1 size 12{ { {"11"} over { { {8}} rSub { size 8{1} } } } } {} = 11

3.2 18 1 size 12{ { {"18"} over {1} } } {} x 8 7 size 12{ { {8} over {7} } } {} = 144 7 size 12{ { {"144"} over {7} } } {} = 20 4 7 size 12{"20" { {4} over {7} } } {}

3.3 5 1 6 3 size 12{ { { { {5}} rSup { size 8{1} } } over { { {6}} rSub { size 8{3} } } } } {} x 2 1 5 1 size 12{ { { { {2}} rSup { size 8{1} } } over { { {5}} rSub { size 8{1} } } } } {} = 1 3 size 12{ { {1} over {3} } } {}

3.4 8 1 3 1 size 12{ { { - { {8}} rSup { size 8{1} } } over { { {3}}"" lSub { size 8{1} } } } } {} x 9 3 1 6 2 size 12{ { { - { {9}} rSup { size 8{3} } } over { { {1}} { {6}} rSub { size 8{2} } } } } {} = 3 2 size 12{ { {3} over {2} } } {} = 1 1 2 size 12{1 { {1} over {2} } } {}

3.5 2 7 9 mn 4 size 12{ { { { {2}} { {7}} rSup { size 8{9} } ital "mn"} over {4} } } {} x 1 6 2 m 3 size 12{ { {1} over { - { {6}}"" lSub { size 8{2} } m rSup { size 8{3} } } } } {} = 9n 8m 2 size 12{ { { - 9n} over {8m rSup { size 8{2} } } } } {}

3.6 4 2 xy 3 1 a b size 12{ { { - { {4}} rSup { size 8{2} } ital "xy"} over { { {3}}"" lSub { size 8{1} } { {a}}b} } } {} x 3 a 2 x size 12{ { { { {3}} { {a}}} over { - { {2}} { {x}}} } } {} = 2y b size 12{ { {2y} over {b} } } {}

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

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 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Mathematics grade 8' conversation and receive update notifications?

Ask