Mathematics GRADE 6
Transcript of Mathematics GRADE 6
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Page 1 of 43
Grade 6 Lesson
Common Fractions
Resources Sasol Inzalo book, textbooks, DBE workbooks
DAY 1
INTRODUCTION: NOTE:
We need to understand what a fraction is and what are the parts that make
up a fraction.
Define:
1. Fractions 2. Denominator 3. Numerator
Comparing and ordering fractions
CLASS WORK ACTIVITY 1
Work through the following introductory activity and answer the questions in your classwork
book.
1. Complete the fraction wall below by writing in the fractions.
1 WHOLE
Mathematics
GRADE 6
CONCEPTS & SKILLS TO BE ACHIEVED:
At the end of the lesson learners should be able to:
● Describe and order fractions
● Calculating with fractions
● Solving Problems with fractions
● Percentage
- Working with hundredths
- Finding percentages of whole numbers
- Word problems involving percentage
TOPIC: FRACTIONS
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Page 2 of 43
Grade 6 Lesson
Common Fractions
2. Comparing fractions using a fraction wall
Let us compare halves (1
2) and thirds (
1
3)
1
2
1
2
1
3
1
3
1
3
(a) Which is bigger? 1
2 or
1
3
(b) Which is bigger? 1
2 or
2
3
3. Compare the following fractions using the fraction wall in number 1 by writing <, > or =
(a)1
4 ___
2
3 (b)
1
2 ___
2
6 (c)
1
7 ___
4
8 (d)
1
6 ___
2
12
(e) 1
3 ___
3
9 (f)
1
5 ___
2
10 (g)
3
4 ___
5
8 (h)
1
2 ___
1
9
Hundredths
The fraction strip shows fifths. The strip is divided into 5 equal parts.
We can call this a fifth strip.
The strip can be changed into a fifteenths strip, by dividing each fifth into three equal parts:
ACTIVITY 2
1. (a) Describe how a fifths strip can be changed into a tenths strip.
If you wish, you can make a rough drawing to help you do it.
(b) Describe how a fifths strip can be changed into a twentieths strip.
2. Describe how a tenths strip can be changed into a hundredths strip.
3. How many hundredths of each strip below are coloured? Explain your answers.
(a)
(b)
TIP Shade each fraction before comparing
If something is divided into 10 equal parts, each part is called a tenth of the
whole.
If something is divided into 100 equal parts, each part is called a hundredth of
the whole.
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Page 3 of 43
Grade 6 Lesson
Common Fractions
4. There are 100 square tiles on this floor.
The two diagrams below may help you to find the answers
to these questions. (a) How many tenths of all the tiles are grey?
(b) How many hundredths of all the tiles are grey?
(c) How many twentieths of all the tiles are grey?
5. Are any of the following statements about the floor on the right
false?
(a) 37
100 of the floor is grey.
(b) 2
10 +
17
100 of the floor is grey.
(c) 3
10 +
7
100 of the floor is grey.
6. Describe in three different ways what part of the floor in question 5
is white.
COMPARING FRACTIONS
ACTIVITY 3
1. A box has 24 smarties with the following number of colour sweets in it.
i) blue – 6 ii) brown - 2 iii) green - 1 iv) pink - 3 v) purple – 5 vi) red – 7
(a) Shade the colours in the areas below, using pencil crayons.
(b) Shade the diagram according to the colours of your smartie box. (Use colouring pencils)
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Page 4 of 43
Grade 6 Lesson
Common Fractions
Using the diagram above, represent these as fractions from the biggest to the smallest
(descending order)
_____;_____;_____;_____;_____;_____;_____;_____
2. Here is a fraction wall that has been broken up into parts. Complete the wall.
1
8
1
5
(a) (b)
(c)
1
10
1
10 1
10
1
10
(d) 1
4
3. Rewrite these fractions in order from smallest to largest using the fraction wall.
4. Place these fractions on the number line: 𝟒𝟎
𝟓𝟎 ;
𝟏
𝟓;
𝟏
𝟐;
𝟑
𝟏𝟎;
𝟕
𝟏𝟎
5. Eight (8) cups of milk was served to each of three children. Lisa drank 2 cups of milk. Her
sister Angie drank 5 cups, and her brother Mark 1 drank cups.
(a) What part of the total cups did each child drink?
(b) Who drank the smallest part of the cups?
(c) Who drank the largest part of the cups?
Child Milk
Drank Fraction
Lisa 2 cups 2
8
Angie 5 cups.
Mark 1 cups
(d) Order the fractions in ascending order: _____;_____;_____
TIP
Write the part of the cup that each
child drank as a fraction, and then
*order from least/ smallest to
greatest/ largest (ascending order)
*arrange
4
5
2
5
9
10
7
10
3
10
⬚
⬚
⬚
⬚
⬚
⬚
⬚
⬚
⬚
⬚
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Page 5 of 43
Grade 6 Lesson
Common Fractions
6. It takes Jack three-fifths of an hour to complete his math homework, two-tenths of an
hour to complete his reading homework, and two-twentieth of an hour to complete his
science homework.
Order the time spent to complete Jack's homework by subject from least to greatest.
Maths: 3
5=
3×4
5×4=
12
20
Reading: 2
10=
2×2
10×2=
4
20
Science: 2
20=
2×1
20×1=
2
20
Order the fractions in ascending order: ____;____;____
HOMEWORK ACTIVITY 4
1. (a) How many tenths of the strip below are green?
(b) How many hundredths of the strip are green?
(c) How many hundredths of the strip are yellow?
(d) What part of the strip below is grey?
(e) Will it be wrong to say that four-tenths of this strip is dark grey?
2. The coloured strip below is 120 mm long. It is divided into 5 equal parts.
(a) What fraction part of the whole strip is green?
(b) Calculate how long the green part is, then check your answer by measuring it.
(c) What fraction part of the whole strip is red?
(d) How many hundredths of the strip are red?
3. Complete this equivalent fraction number line. The first two have been done for you.
TIP
1. Write each time as a fraction, and
2. Ensure that the denominators are
the same.
3. *Order from smallest to
largest (ascending order)
*arrange
Equivalent means that the fractions are equal
GREEN YELLOW
YELLOW RED RED RED GREEN
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Page 6 of 43
Grade 6 Lesson
Common Fractions
DAY 2
INTRODUCTION: REVISION NOTE: 1. Definitions (Revise)
A fraction is one equal part of a number of equal parts that forms a whole.
The denominator tells us into how many equal parts the whole has been divided into.
The numerator tells us how many equal parts out of the whole number are being referred to.
2. Comparing and ordering fractions (Revise)
(a) Ensure that the denominators are identical to start comparing.
(b) Find the equivalent fractions to ensure the denominators are identical.
(c) Compare numerators.
(d) Order fractions.
Calculations of common fractions
CLASSWORK:
Addition of fractions with common denominators
1
4 +
2
4 =
Subtraction of fractions with common denominators
3
4 -
2
4 =
Number Lines
Diagram
𝟏
𝟒
𝟏
𝟒
𝟏
𝟒
𝟏
𝟒
Calculation
𝟏
𝟒 +
𝟐
𝟒 =
𝟑
𝟒
Number Lines
Diagram
𝟏
𝟒
𝟏
𝟒
𝟏
𝟒
𝟏
𝟒
Calculation
𝟑
𝟒 -
𝟐
𝟒 =
𝟏
𝟒
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Page 7 of 43
Grade 6 Lesson
Common Fractions
CLASSWORK: ACTIVITY 5
Complete the following activity in your writing book. 1. What part of a litre of milk will you get if you add a fifth of a litre to 3 twentieths of a litre?
You may find the diagrams below helpful.
2.
(a) How many twentieths are equal to one fifth?
(b) Is 1
5 =
5
20 or is
1
5 =
4
20 ?
(c) Is 1
5 +
3
20 =
4
20 +
3
20 ?
3. Calculate
(a) 1
5 +
3
5 (b)
2
12 +
5
12 (c)
3
5 +
2
5
(d) 3
8 +
5
8 (e)
1
2 +
1
4 (f)
1
3 +
3
8
Equivalent Fractions
Fractions that are equal or equivalent to each other.
4. Is it true that 5
12 +
1
3 =
3
4 ?
It is easy to add fractions that are expressed with the same denominator, like
5
12 and
3
12 :
5 twelfths + 3 twelfths = 8 twelfths
To add fractions with different denominators, we have to use equivalent fractions.
For example, to calculate 5
12 +
1
3 we have to replace
1
3 with
4
12:
5
12 +
1
3 =
5
12 +
4
12 and 5 twelfths + 4 twelfths is 9 twelfths.
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Page 8 of 43
Grade 6 Lesson
Common Fractions
CLASSWORK: ACTIVITY 6 1. Match the equivalent fractions in the top row with the fractions underneath by drawing a line to
connect them. The first one has been done for you.
2. Complete these equivalent fraction models by writing the equivalent fraction:
HOMEWORK: ACTIVITY 7
(a) Drake rode his bike for three-quarters of a kilometre and Usher rode his bike for one-
quarter of a kilometre. Which boy rode his bike further?
(b) Each of the boys below, cycled a certain distance. Who cycled the furthest?
(c ) Which fraction is the biggest? (Show your calculations)
A. 1
3 B.
3
6 C.
5
12
Bruno
Drake
Chris
Drake Usher
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Page 9 of 43
Grade 6 Lesson
Common Fractions
DAY 3
Fractions
Revise the definitions of:
(a) Fractions (b) Denominator (c) Numerator (d) Equivalence
Addition of fractions with a denominator that are multiples of the other
3
4 +
1
2 =
Number Lines
Step 1
Draw 2 number lines
Step 2
Indicate fractions on each
A: 3
4 B:
1
2
Step 3
Divide each fractional part 1
4 (A) in
half AND
Divide each fractional part 1
4 (B) in
quarters
We have eight equal parts on A and B
Step 4
Add A to B
A+ B
6
8 +
4
8
= 10
8
= 12
8 = 1
1
4
Diagram
Step 1
Draw 2 rectangular shapes of
equal length
Step 2
Divide each rectangle according to
the fractions on each.
A: 3
4 B:
1
2
Step 3
Divide each fractional part 1
4 (A) in
half AND
Divide each fractional part 1
4 (B) in
quarters
We have eight equal parts on A and B
Step 4
Add A to B
A+ B
6
8 +
4
8
= 10
8
= 12
8 = 1
1
4
Calculation Step 4
Add A to B
A+ B
6
8 +
4
8
= 10
8
= 12
8 = 1
1
4
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Page 10 of 43
Grade 6 Lesson
Common Fractions
DAY 3
Subtraction of fractions with a denominator that are multiples of the other
3
4 -
1
2 =
Number Lines
Step 1
Draw 2 number lines
Step 2
Indicate fractions on each
A: 3
4 B:
1
2
Step 3
Divide each fractional part 1
4 (A) in
half AND
Divide each fractional part 1
4 (B) in
quarters
We have eight equal parts on A and B
Step 4
Subtract B from A
A - B
6
8 -
4
8
= 2
8
= 1
4
Diagram
Step 1
Draw 2 rectangular shapes of equal
length
Step 2
Divide each rectangle according
to the fractions on each.
A: 3
4 B:
1
2
Step 3
Divide each fractional part 1
4 (A) in
half AND
Divide each fractional part 1
4 (B) in
quarters
We have eight equal parts on A and
B
Step 4
Subtract B from A
A - B
6
8 -
4
8
= 2
8
= 1
4
Calculation Step 4
Subtract B from A
A - B
6
8 -
4
8
= 2
8
= 1
4
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Grade 6 Lesson
Common Fractions
DAY 3
CLASSWORK ACTIVITY 8
Calculate:
Use the above strategies to assist you.
(a) 3
8 +
5
8 +
7
8 (b)
2
3 +
1
6 +
5
6 (c)
3
8 +
3
8 +
3
8
(d) 3
8 -
3
8 (e)
3
8 +
3
8 +
3
8 +
3
8 (f)
7
8 -
3
8
(g) 15
16 -
3
16 (h)
15
16 -
3
8 (i)
17
20 +
3
10 -
2
5
(j) 7
12 +
3
4 (k)
3
4 +
3
8 +
3
16 (l)
3
5 +
2
15 +
4
5 -
7
15
HOMEWORK ACTIVITY 9
Calculate the following in your writing book.
(a) 1
6 +
3
12 +
7
12 (b)
2
5 +
4
20 (c)
2
10 +
6
10 -
14
20
(e) 1
2 -
4
12 (e)
1
16 +
7
8 -
1
2 (f)
80
100 -
3
10
(h) 15
18 -
3
9 (h)
12
24 -
3
8 (i)
1
5 +
3
10 -
2
5
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Page 12 of 43
Grade 6 Lesson
Common Fractions
DAY 4 & 5
INTRODUCTION Classwork Activity
Addition of fractions with mixed numbers 3 +
3
4 =
1 + 2 3
4 =
14
5 + 2
3
5 =
Number Lines
Diagram
Calculation
3 + 3
4 = 3
3
4
Number Lines
Diagram
Calculation
1 + 2 3
4
= 1 + 2 + 3
4
= 3 + 3
4
= 33
4
Number Lines
Diagram
Calculation
14
5 + 2
3
5
= 1 + 2 + 4
5 +
3
5
= 3 + 7
5 (
𝟕
𝟓 =
𝟓
𝟓 =1 +
𝟐
𝟓)
= 3 + 5
5 +
2
5
= 3 + 1 + 2
5
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Page 13 of 43
Grade 6 Lesson
Common Fractions
Additional explanation to support mixed number calculations above
Subtraction of fractions with mixed numbers
3 - 3
4 =
51
4 – 2
3
4 =
Number Line
Diagram
Calculation
14
5 + 2
3
5
= 1 + 2 + 4
5 +
3
5
= 1 + 2 + 5
5 +
2
5
= 1 + 2 + 1 + 2
5
= 2 + 2 +2
5 = 4
2
5
Number Lines
Diagram
Calculation
3 - 3
4 =2
1
4
Number Lines
Diagram
Calculation
51
4 - 2
3
4
= 51
4 – 2 -
3
4
= 31
4 -
3
4
= 21
2
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Page 14 of 43
Grade 6 Lesson
Common Fractions
ACTIVITY 10
1. Try Judy’s method or your own menthod to calculate 91
4− 6
3
8
2. It helps to be able to do certain calculations mentally. Try to calculate these in your head,
without doing any writing.
3.
(a) 1
8 +
3
8 (b) 3 -
3
5 (c)
5
8 +
5
8 (d) 3 - 2
1
4
(e) 3 + 6
5 (f) 5 -
4
7 (g)
7
8 +
5
8 (h) 2
3
5 +
4
5
4. Problem Solving with mixed numbers
(a) Jose has 83
4 kg of bananas t his fruit stand. If he sells 2
1
4 kg of bananas, how
many kilograms does he have remaining?
(b) Steven has 101
4 pages of homework. If he finishes 2
1
2 pages every ten
minutes, how many pages will Steven have left after 20 minutes?
HOMEWORK: ACTIVITY 11
1.
(a) 101
3 - 2
5
6 (b) 7
3
8 + 2
3
4 -
1
2
(c) 3 7
12 + 4
5
6 -
1
3 (d) 5
1
4 + 2
1
2 -
7
8
2.
(a) Juanita will work for 4 7
8 hours at her job on Saturday. If she also volunteers for
2 1
3 hours at the hospital, how many hours will she be working and
volunteering on Saturday?
7 3
10 - 3
4
5 can be calculated like this
7 3
10 – 3 4
3
10 -
4
5 3
1
5 +
3
10 3
2
10 +
3
10 3
5
10 = 3
1
2
Judy calculates 7 3
10 - 3
4
5 like this:
7 3
10 – 3 4 -
4
5 3
1
5 +
3
10 3
2
10 +
3
10 3
5
10 = 3
1
2
Is Judy correct?
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Page 15 of 43
Grade 6 Lesson
Common Fractions
(b) Stephanie runs three days a week. She ran 32
3𝑘𝑚 on Monday, 4
1
6𝑘𝑚
onWednesday, and 23
12 𝑘𝑚 on Friday. What distance did she cover for the
week?
(c) Carlos and Franklin are giving away books at a fair. They have 10 boxes, and
each box holds 20 books. On the first day, they gave away 33
4 boxes.On the
second day, they gave away 42
5 boxes. How many boxes of books do they
have left?
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Page 16 of 43
Grade 6 Lesson
Common Fractions
DAY 6 INTRODUCTION: Equal sharing
CLASSWORK:
ACTIVITY 12:
Work through the following activity and write the answers in your classwork
a. Sharing
Share the following chocolate bar equally amongst three (3) friends. Draw a sketch to
explain your division.
How many equal parts did each friend receive? _____________________
What fraction did each one receive? _________________________
b. Grouping (Partitioning)
How many groups can you share 12 counters amongst, so that there is 3 in each group?
Draw your solutions .
Divide the 3 chocolate bars amongst 4 of your
friends. Ensure that each friend receives, a part
of every bar.
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Page 17 of 43
Grade 6 Lesson
Common Fractions
DAY 6
CLASSWORK ACTIVITY
a. Finding fractions of whole numbers
Using the diagram below, find 2
3 of 12.
Draw your solutions before calculating the answer
Calculation
(Any strategy below is acceptable)
2
3 of 12
= 2
3 x 12 =
2×12
3× 1 =
24
3 = 8
2
3 of 12
= 12 ÷ 3 x 2= 8
ACTIVITY 13:
1. There are 24 hours in a day and scientists tell us that we should sleep for 3
8 of the day.
How much time should we spend sleeping?
2. The National History Museum has collected 125 dinosaurs. George has collected 3
5 of
this amount. How many dinosaurs has George collected?
3. Mr. Murray is 160cm tall and his brother Tom is 7
8as tall as him. How tall is Tom?
4. The weather forecaster says that it is 20° C in London but only 7
10 as hot in New York.
How hot is it in New York?
DIAGRAM
1
3
1
3
1
3
1. Divide into 3 equal groups as
indicated by denominator
2. Each part is a third. (1
3).
3. We must find 2
3.
4. Observation 3
3 = 12
1
3 = 4, then
2
3 = 8
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Page 18 of 43
Grade 6 Lesson
Common Fractions
5. Skateboards cost R36 each in my local store. The shopkeeper says if I buy one I can
buy another for only 7
9 of the normal price. How much would a second skateboard
cost?
HOMEWORK: Complete the exercises in your classwork book before you
consult the memorandum at the end of the lesson ACTIVITY 14:
(a) 5
8 of 16 (b)
2
9 of 63 (c)
5
6 of 42
(d) 7
8 of 144 (e )
2
5 of 70 (f)
2
7 of 35
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Page 19 of 43
Grade 6 Lesson
Common Fractions
DAY 7 Fractions: Problem solving
REMEMBER THE FOLLOWING WHEN YOU SEE A PROBLEM: ➢ Read the problem.
➢ Understand the problem ➢ Use the strategy of drawing possible solutions to the problem which may assist you in the
calculations.
CLASSWORK ACTIVITY 15: 1. A chocolate slab is divided into 24 small blocks.
Copy this table and write your answers to questions (a), (b), (c)and (e) below
in the table.The answers for 2 people sharing equally have been done for you.
(a) How many people can equally share this slab without remainders?
(b) How many blocks will each person get in each case as indicated in the table?
(c) What part (fraction) of the slab will each person get in each case?
(d) Did you find all possible answers to question (a)? How do you know?
(e) Try to write each fraction that you wrote in the third row of the table in another way.
Do this in the last row.
2. Ben paints the garden wall red. The wall consists of 24 panels
(divisions) of the same size.
(a) On the first day, Ben painted 1
3 of the wall. How many
panels did he paint?
(b) The following day he painted another 1
6 of the wall. What fraction of the wall was then
painted red?
(c) On the third day, Ben painted another 1
4 of the wall. His friend, Nick helped him and
painted 1
8 of the wall. What fraction of the wall did the two of them paint that day?
(d) How many panels of the wall were still not painted red after three days?
(e) What fraction of the whole wall is still not painted red after three days?
Number of people
who share 2 3 4 5 6 7 8
Number of blocks
per person 12
Fractions per person 1
12
Fractions written in
another way
2
24
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Page 20 of 43
Grade 6 Lesson
Common Fractions
3. 16 Vienna sausages are shared equally by a number of children.
Each child gets 22
3 sausages. How many children are there?
Use the diagram below to assist you.
4. A packet of Vienna sausages is shared equally by 9 children. Each child gets 41
3
sausages. How many sausages were there in the packet?
HOMEWORK: ACTIVITY 16
Use the strategy of drawing possible solutions to the problem which may assist you in the
calculations.
1. There are 600 houses in Township A and 240 houses in Township B.
150 of the houses in Township A have running water, and 80 houses in Township
B have running water.
(a) What fraction of the houses in each township don’t have running water?
(b) In which township is the situation the best, with respect to the provision of running
water?
2. The cricket team (consisting of 11 members) receives three (3) oranges after the match.
The coach instructs the captain that they should divide the oranges equally.
He also mentions that the following players should
receive an extra wedge.
➢ Top batsman
➢ Top bowler
➢ Top fielder
➢ Man of the match
Orange A has 7 wedges, while orange B has 8 wedges. The last orange has 11 wedges.
Share these equally.
Questions
(a) How many wedges are there in total?
(b) What was the minimum amount of wedges that each player received?
(c) What was the maximum amount of wedges that the top players received?
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Page 21 of 43
Grade 6 Lesson
Common Fractions
DAY 8 Introduction:
Working with hundredths.
What does percentage mean?
"Percent" comes from the Latin Per Centum. The Latin word Centum which means
100, for example a century is 100 years.
HOMEWORK: Complete the exercises in your classwork book; before you consult the
memorandum at the end of the lesson.
ACTIVITY 17 1. What fraction of each square is shaded?
Complete the table in percentage, fractional and decimal notation.
2. What PART of each of the figures above is not shaded?
Square Fraction Decimal
fraction Percentage
A
B
C
D
Square Fraction Decimal
fraction Percentage
A
B
C
D
“Percentage” is another word for “hundredths”.
23% means 23
100 , which is the same as
2
10 +
3
100 or 0,23.
Instead of saying 23 hundredths we can say 23%.
A B C D
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Page 22 of 43
Grade 6 Lesson
Common Fractions
DAY 8 3. Write each of the decimal as percentages.
(a) 0,45 (b) 0,7 (c) 0,03
(d) 0,95 (d) 0,20 (f) 2,5
4. Write the fractions as percentages.
(a) 2
5 (b)
7
10 (c)
3
4 (d) 2
1
2
( e) 13
20 (f) 1
11
50 (g)
14
25 (h)
6
5
CLASSWORK: ACTIVITY 18
Finding percentages of whole numbers
1. If you have a calculator available, use it to do the following:
(a) 123 ÷ 10 (b) 123 ÷ 100 (c) 123,4 ÷ 10 (d) 1 234 ÷ 100
It is necessary that you know how to divide by 10 and 100 without a
calculator, so that you can see what actually happens!
2. The pattern is easy to see and to explain.
(a) What happens to the place value parts when you divide by 10?
Explain in your own words.
(b) What happens to the place value parts when you divide by 100?
Explain in your own words.
3. Now do the following mentally.
(Remember to think about the place value parts first!)
(a) 23 ÷ 100 (b) 234 ÷ 100 (c) 230 ÷ 100
(d) 3 523 ÷ 100 (e) 4 006 ÷ 100 (f) 5 ÷ 100
Now that we have answered the questions above, we can say:
Finding a percentage of a whole number is similar to finding a fraction of a whole number.
We can also say:
A percentage is a fraction written in a different notation.
So, to find 6% of 65 is the same as finding 6
100 of 65.
This requires dividing by 100. It can easily be done mentally. We need to practise the skill.
19 ÷ 10 = 19
10 = 1,9 and 19 ÷ 100 =
19
100 = 0,19
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Page 23 of 43
Grade 6 Lesson
Common Fractions
DAY 8 HOMEWORK: ACTIVITY 19
1. Write down the numbers that can replace the letters (a) to (g) to complete this flow
diagram.
Example: 56 ÷ 100 = 0,56 ( 56 ÷ 100 = 5,6 ÷ 10)
2. Write down the numbers that can replace the letters (a) to (e) to complete this flow
diagram.
Example: 76 x 5 = 380 ÷ 100 = 3,8 ( 380 ÷ 100 = 38 ÷ 10)
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Page 24 of 43
Grade 6 Lesson
Common Fractions
DAY 9 Calculating Percentage using a different strategy.
Determine percentage
(a) 15% of 200 pupils were girls. How many girls were there?
Step 1: Find 10 % of 200
We can say 200 ÷ 10 = 20
Step 2: Find 5% of 200 or 1
2 of 20
If 10% of 200 = 20 then 5% of 200 = 10
Step 3
Therefore 20 + 10 = 30 girls
(b) 12% of 450
Step 1: Find 10 % of 450
We can say 450 ÷ 10 = 45
Step 2: Find 1% of 450
If 10% of 450 = 45 then 1% of 450 = 4,5 ( or 45 ÷ 10)
Then 2% = 4,5 x 2 =9
Step 3
Therefore:
45 + 9= 54
(c) 6% of 65
Step 1: Find 10 % of 65
We can say 65 ÷ 10 = 6,5
Step 2: Find 1% of 65
If 10% of 65 = 6,5 then 1% of 65 = 0,65 ( or 6,5 ÷ 10)
Then 6% = 0,65 x 6 =3,9
CLASSWORK: ACTIVITY 20
1. Calculate:
(a) 6% of 65 (b) 20% of 300 (c) 12% of 450
(d) 25% of 244 (e) 3% of 60 (f) 14% of R150
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Page 25 of 43
Grade 6 Lesson
Common Fractions
CLASSWORK ACTIVITY 21
1. A Skateboard is reduced 25% in price in a sale. The old price was R120.
What is the new price? (Show calculations)
2. Ms. Jones gave an A grade to 15 out of every 100 students and Mr. McNeil gave
an A grade to 3 out of every 20 students. What percent of each teacher's
students received an A symbol? (Show calculations)
3. One team won 19 out of every 20 games played, and a second team won 7 out of every 8
games played. Which team has a higher percentage of wins?
4. Nomsi plays netball. During her last match she tried to score a goal 10 times. She was
successful 6 of the times she tried.
(a) What fraction of her attempts to score a goal was successful?
(b) What percentage of her attempts was successful?
(c) What percentage of her attempts was not successful?
5. Andiswa got 21 out of 30 for her Mathematics test.
What percentage did she get?
6. Many children had flu in winter. One day during this time, 120 out of 800 children were
absent from school. What percentage was absent?
HOMEWORK: ACTIVITY 22
1. John spends R50 in this way:
R3 for an apple R6 for a bus ticket R8 for a tin of juice
R13 for a meat pie R12 for a taxi R8 for milk
What percentage of the money did he spend on:
(a) travel
(b) food?
2. Peter scored 78% in a test. The test was out of 150. What was Peter’s mark?
3. Mimi bought a camera that was marked R850 in the shop. She got 20% discount. How
much did she pay for the camera?
4. Miss Pula could enter the top 30% of her Mathematics learners for a competition.
There are 46 learners in her class. How many learners could she enter?
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Page 26 of 43
Grade 6 Lesson
Common Fractions
DAY 10 Revision
CLASSWORK: ACTIVITY 23
1. What fraction is shaded in the shapes below
(a) (b) (c)
2. Complete the following by writing in <; > or =
(a) 2
3 *
4
5 (b)
2
3 *
1
2 (c)
7
14 *
9
18
(d) 4
5 *
7
10 *
3
6 (e) 75% *
4
5 (f)
2
5 * 40%
3. Provide the percentage represented by the following fractions:
a) 3
5 b)
1
5 c)
3
10 d)
4
25 e)
4
25 f)
3
20
4. Two netball teams play a game. There are 14 children all together. The sports teacher wants
to give each child of an orange. How many oranges does she need?
5. Complete the table below.
10
5 5
6. Which piece is the longest?
(a) 1
2 metre or
1
10 metre (b)
1
5 metre or
5
10 metre
7. Calculate the following
a) 2
3 +
4
15 (b)
4
16 +
3
8 (c)
4
9 +
3
9 -
1
9
(d) 2
12 +
4
6 (e)
1
6 +
1
3 +
3
12 (f) 4
4
9 + 6
1
3 + 5
3
18
(g) 62
14 + 3
1
2 - 3
5
14
8. (a) 2
3 of 21 (b)
4
9 of 81 (c)
2
6 of 42
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Page 27 of 43
Grade 6 Lesson
Common Fractions
9. A fashion retailer has a 20% off sale. This means that the
clothes on sale will sell for 20% less than the normal price.
Calculate what the sale price will be if the original price is:
(a) R400
(b) R120
(c) R150
(d) R60
(e) R70
(f) R1 250
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Page 28 of 43
Grade 6 Lesson
Common Fractions
DAY 1 MEMORANDUM Define
1. Fractions : equal part of the whole
2. Denominator: the number of equal parts the whole has been divided into.
3. Numerator: the number of equal parts out of the whole.
ACTIVITY 1
1.
1 whole
1
2
1
2
1
3
1
3
1
3
1
4
1
4
1
4
1
4
1
5
1
5
1
5
1
5
1
5
1
6
1
6
1
6
1
6
1
6
1
6
1
7
1
7
1
7
1
7
1
7
1
7
1
7
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12
2. (a) 1
2 (half) (b)
2
3 (two-thirds)
3. (a)1
4 <
2
3 (b)
1
2 >
2
6 (c)
1
7 <
4
8 (d)
1
6 =
2
12
(e) 1
3 =
3
9 (f)
1
5 =
2
10 (g)
3
4 >
5
8 (h)
1
2 >
1
9
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Page 29 of 43
Grade 6 Lesson
Common Fractions
ACTIVITY 2
1. (a) Divide each fifth into two equal parts.
(b) Divide each fifth into four equal parts.
2. Divide each tenth into ten equal parts.
3. (a) 30 hundredths (b) 70 hundredths
4. (a) 6 tenths (b) 60 hundredths (c) 12 twentieths
5. None of them is false.
(a) True (b) True (c) True
6. 63
100 or
6
10 +
6
100 or
5
10 +
13
100 or
1
2 +
13
100 of the floor is white.
COMPARING FRACTIONS
ACTIVITY 3
(a)
(b)
BLU
E
BLU
E
BLU
E
BLU
E
BLU
E
BLU
E
BR
OW
N
BR
OW
N
GR
EEN
PIN
K
PIN
K
PIN
K
PU
RP
LE
PU
RP
LE
PU
RP
LE
PU
RP
LE
PU
RP
LE
RED
RED
RED
RED
RED
RED
RED
(c) 7
24;
6
24;
5
24;
3
24;
2
24;
1
24
Blue
Brown
Green
Pink
Purple
Red
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Page 30 of 43
Grade 6 Lesson
Common Fractions
HOMEWORK ACTIVITY 4
1. (a) 4 tenths (b) 40 hundredths (c) 60 hundredths
(d) 8 twentieths or 4 tenths or 2 fifths (e) No
2. (a) 1 fifth (b) 24 mm (c) 3 fifths (d) 60 hundredths
3.
10
10
9
10
8
10
7
10
6
10
5
10
4
10
3
10
1
5
2
5
3
5
4
5
5
5
2
10
1
10
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Page 31 of 43
Grade 6 Lesson
Common Fractions
DAY 2: MEMORANDUM CLASSWORK: ACTIVITY 5
1.
3
20
1
5=
4
20
3
20 +
4
20 =
7
20
2. (a) 4 twentieths (b) 1
5=
4
20 (c)Yes;
1
5 +
3
20 =
3
20 +
4
20 =
7
20
3. (a) 4
5 (b)
8
12 (c)
5
5= 1 (d)
8
8= 1 (e)
2
4 +
1
4 =
3
4 (f)
2
8 +
3
8 =
5
8
4.
1
4=
3
12
2
12
1
3=
4
12
Yes, because: 5
12 +
1
3 =
5
12 +
4
12 =
9
12 =
3
4
ACTIVITY 6
1.
2. (a) 3
4=
6
8 (b)
1
4=
2
8 (c)
2
5=
4
10 (d)
1
2=
4
8
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Page 32 of 43
Grade 6 Lesson
Common Fractions
HOMEWORK 7
(a) Drake (b) Bruno (c) 3
6
DAY 3: MEMORANDUM
CLASSWORK ACTIVITY 8 CALCULATIONS:
(a) 3
8 +
5
8 +
7
8 (b)
2
3 +
1
6 +
5
6
= 15
8 =
4
6 +
1
6 +
5
6
= 17
8 =
10
6 = 1
4
6
(c) 3
8 +
3
8 +
3
8 (d)
3
8 -
3
8 = 0
= 11
8
= 13
8
(e) 7
8 -
3
8 =
4
8 (f)
15
16 -
3
16 =
12
16
(g) 17
20 +
3
10 -
2
5 (h)
7
12 +
3
4
= 17
20 +
6
20 -
8
20 =
7
12 +
9
12
= 23
20 -
8
20 =
16
12
= 15
20 =
3
4 = 1
4
12 = 1
1
3
(i) 3
4 +
3
8 +
3
16 (j)
3
5 +
2
15 +
4
5 -
7
15
= 9
16 +
6
16 +
6
16 =
9
5 +
2
15 +
12
15 -
7
15
= 21
16 = 1
5
16 =
23
15 -
7
15
= 16
15 - 1
1
15
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Page 33 of 43
Grade 6 Lesson
Common Fractions
HOMEWORK: ACTIVITY 9
(a) 1
6 +
3
12 +
7
12 (b)
2
5 +
4
20 (c)
2
10 +
3
10 -
14
20
=2
12 +
3
12+
7
12 =
8
20 +
4
20 =
8
20 +
6
20 -
14
20
= 12
12 = 1 =
12
20 =
7
10 =
14
20 -
14
20 = 0
(d) 1
2 -
4
12 (e)
1
16 +
7
8 -
1
2 (f)
80
100 -
3
10
= 6
12 −
4
12 =
1
16 +
14
16 -
8
16 =
80
100 - -
30
100
= 2
12 =
1
6 =
15
16 -
8
16 =
7
16 =
50
100 =
1
2
(h) 15
18 -
3
9 (h)
12
24 -
3
8 (i)
1
5 +
3
10 -
2
5
= 15
18 -
6
18 =
12
24 -
9
24
= 9
18 =
1
2 =
3
24 =
1
8
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Page 34 of 43
Grade 6 Lesson
Common Fractions
DAY 4 & 5 MEMORANDUM
CLASSWORK: ACTIVITY 10
1. 9 1
4 – 6 3
1
4 -
3
8 2
5
8 +
1
4 2
5
8 or 9
1
4 - 6
3
8 8
5
4 - 6
3
8 8
10
8 - 6
3
8 = 2
7
8
3. (a) 4
8 or
1
2 (b) 2
2
5 (c)
10
8 = 1
2
8 (d)
3
4
(e) 41
5 (f) 4
3
7 (g)
12
8 = 1
4
8 = 1
1
2 (h) 3
2
5
(a) 83
4 - 2
1
4
= 62
4kg
(b) 21
2 pages for every 10 minutes
5 pages after 20 minutes
21
2 + 2
1
2 = 5
101
4 - 5
= 51
4
HOMEWORK: ACTIVITY 11
(a) 71
2 (b) 9
5
8 (c) 8
1
12 e) 6
7
8
2.
(a) 4 7
8 + 2
1
3
=67 × 3
8 × 3 + 2
1 × 8
3 × 8
= 821
24 + 2
8
24
= 10 29
24
= 10 + 24
24 +
5
24
= 10 + 1 +5
24
= 115
24 ure
(b) 32
3 + 4
1
6 + 2
3
12
=32×4
3 × 4 + 4
1×2
6 × 2 + 2
3×1
12 × 1
= 38
12 + 4
2
12 + 2
3
12
=9 + 13
12
= 9 + 12
12 +
1
12
= 9 + 1 + 1
12
= 101
12
(c) 33
4 + 4
2
5
= 32×5
4 × 5 + 4
2×4
5 × 4
= 3 10
20 + 4
8
20
= 718
20 handed out
10 - 718
20
=3- 20
20 +
18
20
= 3 – 38
20
= 3- 1 +2
20
= 22
20
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Page 35 of 43
Grade 6 Lesson
Common Fractions
DAY 6 MEMORANDUM
ACTIVITY 12
(a) Each child to receive 4 parts; 41
3
(b) Any acceptable variation
Look at the denominator- 3- divide into 3 equal groups then multiply by numerator (2)
12 ÷ 3 = 4 x 2 = 8 or 3
4 of 12 =
3×12
4×1 =
36
4= 9
ACTIVITY 13
1. 24÷ 8= 3 x 3 = 9 hours or 3
4 of 24 =
3×24
4×1 =
72
4= 9 hours
2. 125 ÷ 5= 25 x 3 = 75 or 3
5 of 125 =
3×125
5×1 =
375
5= 75
3. 160 ÷ 8= 20 x 7 = 140 or 7
8 of 160 =
7×160
8×1 =
1 120
8= 140cm
4. 20 ÷ 10= 2 x 7 = 14 or 7
10 of 20 =
7×20
10×1 =
140
10= 14℃
London= 20℃ + 14 = 34℃ in New York
5. 36÷ 9= 4 x 7 = R28 or 7
9 of 36 =
7×36
9×1 =
252
9= R28
ACTIVITY 14
(a) 5
8 of 16 (b)
2
9 of 63 (c)
5
6 of 42
= 5
8 X 16 =
2
9 X 63 =
5
6 X 42
= 16 ÷ 8 X 5 = 63 ÷ 9 X 2 = 42 ÷ 6 X 5
= 10 = 14 = 35
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Page 36 of 43
Grade 6 Lesson
Common Fractions
(c) 7
8 of 144 (e )
2
5 of 70 (f)
2
7 of 35
= 7
8 X 144 =
2
5 X 70 =
2
7 X 35
= 144 ÷ 8 X 7 = 70 ÷ 5 X 2 = 35 ÷ 7 X 2
= 126 = 28 =10
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Page 37 of 43
Grade 6 Lesson
Common Fractions
DAY 7 MEMORANDUM CLASSWORK ACTIVITY 16:
1.
Number of people
who share (a) 2 3 4 5 6 7 8
Number of blocks
per person (b) 12 8 6 4 3
Fractions per person
(c)
1
2
1
3
1
42
1
6
1
8
Fractions written in
another way (e)
12
24
8
24
6
24
4
24
3
24
Note: Learners may use other equivalent fractions in the third and fourth rows.
(d) The numbers that can easily be shared are the factors of 24, i.e. 2, 3, 4, 6, 8 and 12.
2. (a) 24÷ 3= 8 x 1 = 8 or 1
3 of 24 =
1×24
3×1 =
24
3= 8 panels
(b) Day 1 + Day 2
1
3+
1
6
= 1+2
6 =
3
6 =
1
2
= 3
6=
(c) Day 3
1
4+
1
8
= 2+1
8
= 3
8
(d) Three (3) panels
(e) Day 1 and 2 painted: + Day 3 painted:
1
2 +
3
8
= 4+3
8
= 7
8
Remaining wall panels : 8
8 -
7
8 =
1
8 (
1
8 of 24= 24 ÷ 8 = 3 panels )
3. Six (6) children
4. 41
3= 4 +
1
3
41
3 x 9 children = 4 x 9 =36;
1
3 x 9 = 3; 36 + 3 = 39 sausages
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Page 38 of 43
Grade 6 Lesson
Common Fractions
DAY 7: MEMORANDUM HOMEWORK ACTIVITY 17: 1 (a) Note that the question asks what fraction of houses don’t have running water.
Township A: 450
600 Township B:
160
240
(b) 450
600 =
45
60 =
3
4 and
160
240 =
16
24 =
2
3
The situation in Township B is best, because 2
3 <
3
4.
Two thirds being less than three quarters means that, relative to the total number of people
living in each township, more people are provided with water in Township B than in
Township A.
2 (a) Orange A: 7 + Orange B: 8 + Orange B: 11 = 26 wedges
(b)11 players in a cricket team
= 26
11 = 2
5
11
11 players x 2 wedges =22
Each player received a minimum of 2 wedges
(c) 26 – 22 already shared = 4 wedges left
4 tops players would receive an extra wedge each, bringing their total to 3 each.
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Page 39 of 43
Grade 6 Lesson
Common Fractions
DAY 8: MEMORANDUM: CLASSWORK ACTIVITY 17
1.
2.
3. (a) 45% (b) 70% (c) 3% (d) 95% (e) 20% (f) 250%
4. (a) 40% (b) 70% (c) 75% (d) 250% (e) 65% (f) 122%
(g) 56% (h) 120%
Square Fraction Decimal
Fraction Percentage
A 50
100 0,5 50%
B 1
100 0,01 1%
C 25
100 0,25 25%
D 83
100 0,83 83%
Square Fraction Decimal
Fraction Percentage
A 50
100 0,5 50%
B 99
100 0,99 99%
C 75
100 0,75 75%
D 17
100 0,17 17%
CLASSWORK ACTIVITY 18
1. (a) 12,3 (b) 1,23 (c) 12,34 (d) 12,34
2. a) 0,23 (b) 2,34 (c) 2,3 (d) 35,23 (e) 40,06 (f) 0,05
HOMEWORK ACTIVITY 19
3. a) 0,56 (b) 13 (c) 127 (d) 0,47 (e) 2,37 (f) 0,03
(g) 5
4. (a) 10 (b) 150 (c) 3,8 (d) 1,6 (e) 10
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Page 40 of 43
Grade 6 Lesson
Common Fractions
DAY 9 Activity 20
(d) 6% of 65
Step 1: Find 10 % of 65
We can say 65 ÷ 10 = 6,5
Step 2: Find 1% of 65
If 10% of 65 = 6,5 then 1% of 65 = 0,65 ( or 6,5 ÷ 10)
Then 6% = 0,65 x 6 =3,9
(e) 20% of 300
If 10% x 300 =300 ÷ 10 =30
Then 20% = 30 x 2= 60
(f) 12 % of 450
If 10% x 450 =450 ÷ 10 =45; 1% x 450 = 4,5 (45 ÷ 10)
2 % =4,5 x 2 =9
Then 45 + 9 = 54
(g) 25% of 244
25 % = 1
4 then
1
4 of 244= 244÷ 4= 61
(h) 3% of 60
10% of 60 = 6; then 1%= 0,6 (6 ÷ 10)
3% = 0,6 x 3= 1,8
(i) 14% of R 150
10% of 150 = 15; then 1%= 1,5 (15 ÷ 10)
4% = 1,5 x 4= 6
Then 15 + 6= R 21
CLASSWORK ACTIVITY 21
1. 25% of R 120
25 % = 1
4 then
1
4 of 120= 120 ÷ 4= 30
R 120- R 30 = R 90
2. Ms. Jones Mr McNeil
15 out of 100 =15
100 = 15% 3 out of 20 =
3 × 5
20 ×5 =
15
100 = 15%
Of 15 + 3 learners = 18 out of 120 learners = 18
120 ×
100
1 = 15%
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Page 41 of 43
Grade 6 Lesson
Common Fractions
3. Team A= 19 out of 20 = 19 × 5
20 ×5 =
95
100 = 95%
Team B= 7
8
100 ÷ 8 = 12,5; then 7
8 = 12,5 x 7 = 87,5%
Team A has a higher win percentage
4. (a) 6 out of 10 = 6
10
(b) 6
10=
6 × 10
10 ×10=
60
100= 60%
( c) 100% - 60% = 40%
5. 21 out of 30 =21
30=
21 ÷3
30÷3 =
7
10=
7 × 10
10 ×10=
70
100= 70%
6. 120 of 800 =120
800=
120 ÷8
800÷8 =
15
100= 15%
HOMEWORK ACTIVITY 22
1. (a) Travel : R 6 + R 12 =R 18 = 18
50=
18× 2
50 ×2=
36
100= 36%
(b) Food: R 3 + R 8 + R 13= R 24 = 24
50=
24× 2
50 ×2=
24
100= 48%
2. 78% = 78
100 =
78
100 ×
150
1 = 117 marks
3. 20% of R 850
20% = 1
5 then
1
5 of R850= 850 ÷ 5 = R170
Discount: R850 - R170 = R680
4. 30% = 30
100 =
30
100 ×
46
1 = 13,8 ( rounded up to 14 learners)
OF
30% of 46
10% of 46 = 4,6;
Then 30%= 4,6 x 3 (6 ÷ 10)
= 13, 8 (rounded up to 14 learners)
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Page 42 of 43
Grade 6 Lesson
Common Fractions
DAY 10 Revision
CLASSWORK ACTIVITY 23
3.
(a) 3
15 or
1
5 (b)
3
7 (c)
3
12 or
1
4
4.
(a) 2
3 <
4
5 (b)
2
3 >
1
2 (c)
7
14 =
9
18
(d) 4
5 >
7
10 >
3
6 (e) 75% <
4
5 (f)
2
5 = 40%
5. a) 3
5 b)
1
5 c)
3
10 d)
4
25 e)
70
100 f)
23
50
6. There 7 players in a netball team. Wants to give of an orange.
The oranges will be shared equally and will be divided in two. She will need 7 oranges
5.
60
30 30
10 10 10 10 10 10
5 5 5 5 5 5 5 5 5 5 5 5
6.
(a) 1
2 metre >
1
10 metre (b)
1
5 metre <
5
10 metre
7.
(b) 2
3 +
4
15 (b)
4
16 +
3
8 (c)
4
9 +
3
9 -
1
9
= 2 × 5
3 × 5 +
4
15 =
4
16 +
3 × 2
8 × 2 =
6
9
= 10
15 +
4
15 =
14
15 =
4
16+
6
16=
10
16
(e) 2
12 +
4
6 (e)
1
6 +
1
3 +
3
12 (f) 4
4
9 + 6
1
3 + 5
3
18
= 2
12 +
4 ×2
6 ×2 =
1 ×2
6 ×2 +
1×4
3 ×4 +
3
12 =15
4 ×2
9 ×2 +
1 ×6
3 ×6 +
3
18
= 2
12 +
8
12 =
2
12 +
4
12 +
3
12 =15
8
18 +
6
18 +
3
18
= 10
12 =
9
12 = 15
17
18
GET DIRECTORATE
Page 43 of 43
Grade 6 Lesson
Common Fractions
(h) 62
14 + 3
1
2 - 3
5
14
= 92
14 +
1 ×7
2 ×7 - 3
5
14
= 92
14 +
7
14 - 3
5
14
= 9 9
14 - 3
5
14
= 6 4
14= 6
2
7
8. (a) 2
3 of 21 (b)
4
9 of 81 (c)
2
6 of 42
= 2×21
3×1 or 21 ÷ 3 x 2 =
4×81
9 × 1 or 81 ÷ 9 x 4 =
2×42
6 × 1 or 42 ÷ 6 x 2
= 42
3 or = 7 x 2 =
324
9 or = 9 x 4 =
84
6 or = 7 x 2
= 14 = 36 = 14
9. (a) R400 – ( 20 % of R400) (b) R120 – ( 20 % of R120)
= R400 – (20
100 ×
400
1) = R120 – (
20
100 ×
120
1)
= R400 – R80 = R120 – R24
= R320 = R96
(c) R150 – (20% of R150) (d) R60 – (20% of R60)
= R150 – (20
100 ×
150
1) = R60 – (
20
100 ×
60
1)
= R150 – R30 = R60 - R12
= R120 = R48
(e) R70 – (20% of R70) (f) R1 250 – (20% of R1 250)
= R70 - (20
100 ×
70
1) = R1 250 - (
20
100 ×
1250
1)
= R70 – R14 = R1 250 – R250
= R56 = R1 000