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Did you know?

2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} is a proper fraction. The numerator is smaller than the denominator.
9 4 size 12{ { { size 8{9} } over { size 8{4} } } } {} is an improper fraction. The numerator is bigger than the denominator.
1 2 3 size 12{1 { { size 8{2} } over { size 8{3} } } } {} is a mixed number . A mixed number is always bigger than 1 and consists of a whole number (1) plus a fraction ( 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} ).

Activity 3:

To calculate by means of computations that are suitable to be used in adding ordinary fractions [lo 1.8.3]

1. Can you still remember how to add fractions? Let us see. Work together with a friend. Take turns to say the answers. Choose any two fractions and add them. Give your answer first as an improper fraction and then as a mixed number.

Ask your teacher’s help if you struggle.

1.1
1.2

Activity 4:

To recognise and use equivalent forms [lo 1.5.1]

1. Look carefully at the following questions and then complete them as neatly as possible.

EQUIVALENT FRACTIONS

1.1 Colour 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} of the figure in blue:
1.2 Colour 2 4 size 12{ { { size 8{2} } over { size 8{4} } } } {} of the figure in green:
1.3 Colour 4 8 size 12{ { { size 8{4} } over { size 8{8} } } } {} of the figure in yellow:
1.4 Colour 8 16 size 12{ { { size 8{8} } over { size 8{"16"} } } } {} of the figure in red:
  • What do you notice?
1.6 Complete:
1
2
=
....
4
=
4
....
=
....
16

Did you know?

We call fractions that are equal in size, equivalent fractions. The word equivalent means ‘the same as’ . Thus the fractions are equal.

Do you remember?

1 unit
1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {}
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 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {}
1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {}
1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {}
1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {}
1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {}
1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}
1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {}
1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {}

2. The following activity will prepare you for the addition and subtraction of fractions. Use your knowledge of equivalent fractions and answer the following. Where you are in doubt, use the diagram above.

2.1: 1 2 = 10 size 12{ { { size 8{1} } over { size 8{2} } } = { { size 8{ dotslow } } over { size 8{"10"} } } } {}

2.2: 2 3 = 6 size 12{ { { size 8{2} } over { size 8{3} } } = { { size 8{ dotslow } } over { size 8{6} } } } {}

2.3: 5 = 8 10 size 12{ { { size 8{ dotslow } } over { size 8{5} } } = { { size 8{8} } over { size 8{"10"} } } } {}

2.4: 1 4 = 12 size 12{ { { size 8{1} } over { size 8{4} } } = { { size 8{ dotslow } } over { size 8{"12"} } } } {}

2.5: 5 = 10 12 size 12{ { { size 8{5} } over { size 8{ dotslow } } } = { { size 8{"10"} } over { size 8{"12"} } } } {}

2.6: 4 10 = 5 size 12{ { { size 8{4} } over { size 8{"10"} } } = { { size 8{ dotslow } } over { size 8{5} } } } {}

2.7: 1 3 = 3 size 12{ { { size 8{1} } over { size 8{3} } } = { { size 8{3} } over { size 8{ dotslow } } } } {}

2.8: 6 = 1 2 size 12{ { { size 8{ dotslow } } over { size 8{6} } } = { { size 8{1} } over { size 8{2} } } } {}

2.9: 3 6 = 12 size 12{ { { size 8{3} } over { size 8{6} } } = { { size 8{ dotslow } } over { size 8{"12"} } } } {}

2.10: 4 6 = 9 size 12{ { { size 8{4} } over { size 8{6} } } = { { size 8{ dotslow } } over { size 8{9} } } } {}

Assessment

Learning outcomes(LOs)
LO 1
Numbers, Operations and RelationshipsThe learner is able to recognise, describe and represent numbers and their relationships, and counts, estimates, calculates and checks with competence and confidence in solving problems.
Assessment standards(ASs)
We know this when the learner:
1.1 counts forwards and backwards fractions;
1.2 describes and illustrates various ways of writing numbers in different cultures (including local) throughout history;
1.3 recognises and represents the following numbers in order to describe and compare them:
  • common fractions to at least twelfths;
1.5 recognises and uses equivalent forms of the numbers listed above, including:
1.5.1 common fractions with denominators that are multiples of each other;
1.6 solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as:
  • financial (including buying and selling, profit and loss, and simple budgets);
LO 5
Data handlingThe learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.
We know this when the learner:
5.3 organises and records data using tallies and tables;
5.5 draws a variety of graphs to display and interpret data (ungrouped) including:
  • a pie graph.

Memorandum

ACTIVITY 1

1.1 Equal parts of a whole

1.2 Nominator

1.3 size 12{ div } {}

1.4 Say in how many equal parts the whole is divided

1.5 Smaller

1.6 Nominator

1.7 Equivalents

1.8 Larger

1.9 Say with how many equal parts I work / are coloured in

1.10 Divide the nominator and denominator by the same number

2. 2.1 b and c

  • c and e
  • a en b

2.4 Not equal parts

2.5 (i) 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

(ii) 2 8 size 12{ { { size 8{2} } over { size 8{8} } } } {} / 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

(iii) 4 8 size 12{ { { size 8{4} } over { size 8{8} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

(iv) 3 8 size 12{ { { size 8{3} } over { size 8{8} } } } {}

(v) 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

(vi) 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {}

(vii) 2 10 size 12{ { { size 8{2} } over { size 8{"10"} } } } {} / 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {}

(viii) 4 10 size 12{ { { size 8{4} } over { size 8{"10"} } } } {} / 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

(ix) 3 10 size 12{ { { size 8{3} } over { size 8{"10"} } } } {}

(x) 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

(xi) 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {}

ACTIVITY 2

1.

B 8 1 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 7 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}
C 6 1 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 5 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {}
D 8 1 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 7 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}
E 3 1 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} 2 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}
F 12 6 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 6 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
G 16 8 8 16 size 12{ { { size 8{8} } over { size 8{"16"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 8 8 16 size 12{ { { size 8{8} } over { size 8{"16"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
H 16 4 4 16 size 12{ { { size 8{4} } over { size 8{"16"} } } } {} / 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} 12 12 16 size 12{ { { size 8{"12"} } over { size 8{"16"} } } } {} / 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {}
I 8 2 2 8 size 12{ { { size 8{2} } over { size 8{8} } } } {} / 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} 6 6 8 size 12{ { { size 8{6} } over { size 8{8} } } } {} / 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {}
J 12 6 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 6 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
K 8 2 2 8 size 12{ { { size 8{2} } over { size 8{8} } } } {} / 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} 6 6 8 size 12{ { { size 8{6} } over { size 8{8} } } } {} / 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {}

ACTIVITY 4

1.5 Fractions all equal

1.6 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} = 2 4 size 12{ { { size 8{2} } over { size 8{4} } } } {} = 4 8 size 12{ { { size 8{4} } over { size 8{8} } } } {} = 8 16 size 12{ { { size 8{8} } over { size 8{"16"} } } } {}

2. 2.1 5 10 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} 2.6 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

2.2 4 6 size 12{ { { size 8{4} } over { size 8{6} } } } {} 2.7 3 9 size 12{ { { size 8{3} } over { size 8{9} } } } {}

2.3 8 10 size 12{ { { size 8{8} } over { size 8{"10"} } } } {} 2.8 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

2.4 3 12 size 12{ { { size 8{3} } over { size 8{"12"} } } } {} 2.9 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {}

2.5 10 12 size 12{ { { size 8{"10"} } over { size 8{"12"} } } } {} 2.10 6 9 size 12{ { { size 8{6} } over { size 8{9} } } } {}

3. 3.1 12 21 size 12{ { { size 8{"12"} } over { size 8{21} } } } {} 3.4 15 18 size 12{ { { size 8{15} } over { size 8{"18"} } } } {}

3.2 14 16 size 12{ { { size 8{"14"} } over { size 8{16} } } } {} 3.5 9 10 size 12{ { { size 8{9} } over { size 8{"10"} } } } {}

3.3 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} 3.6 21 27 size 12{ { { size 8{21} } over { size 8{"27"} } } } {}

4. 10 12 size 12{ { { size 8{"10"} } over { size 8{"12"} } } } {} = 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} = 6 9 size 12{ { { size 8{6} } over { size 8{9} } } } {} 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} = 4 6 size 12{ { { size 8{4} } over { size 8{6} } } } {}

3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} = 6 8 size 12{ { { size 8{6} } over { size 8{8} } } } {} 8 10 size 12{ { { size 8{8} } over { size 8{"10"} } } } {} = 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} 3 10 size 12{ { { size 8{3} } over { size 8{"10"} } } } {} = 6 20 size 12{ { { size 8{6} } over { size 8{"20"} } } } {}

Questions & Answers

show that the set of all natural number form semi group under the composition of addition
Nikhil Reply
what is the meaning
Dominic
explain and give four Example hyperbolic function
Lukman Reply
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
×/×+9+6/1
Debbie
Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
16
Makan
x=16
Makan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
please help me prove quadratic formula
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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Source:  OpenStax, Mathematics grade 5. OpenStax CNX. Sep 23, 2009 Download for free at http://cnx.org/content/col10994/1.3
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