Mathematics GRADE 6

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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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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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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


(c) 3

10 +

7


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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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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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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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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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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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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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


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


4 (A) in

half AND


4 (B) in

quarters


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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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


4 (A) in

half AND


4 (B) in

quarters


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


4 (A) in

half AND


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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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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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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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?


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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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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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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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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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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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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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?


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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Grade 6 Lesson

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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


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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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


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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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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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


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


We can say 65 ÷ 10 = 6,5


If 10% of 65 = 6,5 then 1% of 65 = 0,65 ( or 6,5 ÷ 10)

Then 6% = 0,65 x 6 =3,9


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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Grade 6 Lesson

Common Fractions


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?


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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Grade 6 Lesson

Common Fractions

DAY 10 Revision


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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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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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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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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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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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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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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Grade 6 Lesson

Common Fractions


(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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Grade 6 Lesson

Common Fractions

DAY 4 & 5 MEMORANDUM


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


(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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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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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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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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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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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%


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%


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%


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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Grade 6 Lesson

Common Fractions

DAY 9 Activity 20

(d) 6% of 65


We can say 65 ÷ 10 = 6,5


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


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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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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Grade 6 Lesson

Common Fractions

DAY 10 Revision


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

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

Mathematics GRADE 6

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Transcript of Mathematics GRADE 6