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Fractions and decimals
8
CHAPTER
Specification reference: Ma2.2c, d, Ma2.3c, g
Chapter overview
Recognise a particular fraction
Express a given number as a fraction of another
Understand the meaning of the terms numerator and denominator
Be able to find equivalent fractions
Know how to simplify and order fractions
Know how to use decimal notation and order decimals
Know how to convert decimals to fractions and convert simple fractions to decimals
8.1 What is a fraction?
L
Demand
Grade
In this section …
L
GF
M
E
H
DC
By the end of this section students will:
Be able to recognise a fraction of a given shape.
Express a given number as a fraction of another.
PREPARING FOR THE TOPIC
Prior knowledge
Students should already: Be able to identify situations where fractions are used.
Checking prior knowledge
Non-ICT Starter 8.1
ICT Starter 8.1
Ask the class What fraction of the class are girls? What
fraction of the class have blond hair? Ask How would we
write this?
As a class find out the number of students who: Walk to
school; Own a pet; Have a sister. Ask students how you
would describe each as a fraction of the class? (You need
to know the total number of students in the class first.)
Write the fractions on the board.
Display ICT Starter 8.1 which shows a series of shapes
with simple fractions shaded. Students have 10 seconds
to estimate the shaded fraction before the answer
appears.
Click ‘Play’ to start, ‘Pause’ to stop. Use the arrows to
adjust the time. Use ‘Back’ and ‘Next’ to move back and
forth through the questions. ‘Restart’ returns the
program to the start.
Answers are displayed in both word form and fractional
notation. Fractions used are halves, thirds, quarters and,
in Q15, a sixth.
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Fractions and decimals
TEACHING THE TOPIC
Key vocabulary and phrases
Fraction
Numerator
Denominator
Non-ICT Main Activity 8.1
ICT Main Activity 8.1
Draw a circle and split it into seven equal parts. Shade 2
parts. Ask What fraction of the shape is shaded? What do
the terms numerator, denominator and fraction mean?
Draw a rectangle split into 9 equal parts. Ask
students to shade in 29 the rectangle. How many parts are
left unshaded?
In the starter you found out how many students walked
to school/owned a pet/have a sister as a fraction of the
whole class. Now find out the fraction who don’t walk
to school/don’t own a pet/do not have a sister.
Display ICT Main Activity 8.1 which is a simulation
showing a rectangle divided into two. Click ‘Hide decimal’,
‘Hide percentage’,‘Hide labels’. Click on either half of the
rectangle to shade it and ask What fraction of the rectangle
is shaded? (A half) How would we write this as a fraction?
On the right of the screen use the arrow buttons to input
what the students say. Click ‘Check’ to confirm.
Using the ‘Parts’ box in the bottom left of the screen,
use the arrow buttons to increase the number of
divisions in the rectangle. Click on the rectangle to
shade the desired number of parts. Ask students What
fraction of the shape is shaded?
Repeat with other fractions up to 24ths.
Now reverse this by clicking ‘Reset’ and entering a
fraction. Ask How many parts should we divide the
rectangle into? How many parts should we shade? Use
the ‘Parts’ box and click on the rectangle to enter what
the students say. Click ‘Check’ to confirm.
Click ‘Reset’ and click on the circle in the menu bar to
change the shape to a circle. Repeat the exercises above.
Stress that the denominator shows the number of equal parts the numerator is divided
by.
Emphasise that it doesn’t matter which segments of a shape are shaded to represent a
fraction. It is the number of parts that are shaded that is important.
Keep using the words numerator and denominator to help lower attaining students
become familiar with them.
TEACHER’S TIPS
Individual activity: Exercise 8A
Q1 to 10 are suitable for all and require students to recognise fractions of shapes.
Q11 requires Resource Sheet for Exercise 8A.
Q12 to 16 may be suitable for higher attainers only. Students write one quantity as a fraction of another.
Q17 and 18 involve Using and applying mathematics.
TOPIC SUMMARY
Key questions
1 In the fraction 38, what do you call the number on the top? (numerator) What do you call the number on the
bottom? (denominator)
2 There are 15 cars in a car park. 4 of the cars are red. What fraction of the cars is not red? (1115)
8.2 Equivalent fractions
L
Demand
Grade
66
In this section …
L
GF
M
E
H
DC
By the end of this section students will:
Know how to obtain equivalent fractions.
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8.2 Equivalent fractions
PREPARING FOR THE TOPIC
Prior knowledge
Students should already: Be able to multiply and divide by whole numbers.
Checking prior knowledge
Non-ICT Starter 8.2
How many times the size of 4 is 8?
How many times the size of 8 is 4?
Repeat with other numbers for a mental warm up.
TEACHING THE TOPIC
Key vocabulary and phrases
Equivalent fractions
Non-ICT Main Activity 8.2
ICT Main Activity 8.2
If possible, take a disk of card, a cake or pie into the
class. Cut the disk or cake in half and cut one half in half
again. Ask What fraction of the disk do we now have?
(One half and two quarters.) Ask What do you notice
about the two quarters compared to the one half? (That
two quarters are the same size as a half.) Cut one
quarter into eighths and ask students questions so they
notice two eighths make a quarter.
Draw a circle on the board and split it into four. Shade
three parts. Draw another circle split into eight and
shade six parts. What do you notice about the two
circles? (Same amount is shaded.) Conclude that 34 68
Repeat with 23 46 and point out that in each case the
numerator and denominator have been multiplied by
the same amount.
As a class complete the following fractions so they are
equivalent to the first fraction.
Display ICT Main Activity 8.2 which is a simulation
showing an unshaded square divided into 2 parts. Click
on one part to shade it.
● 2 ?
3 9
● 1 ?
6 18
● 7 ?
8 16
● 3 ?
7 28
● 2 ?
5 15
● 1 ?
9 54
● 9 ?
10 100
● 5 ?
16 32
1
● 0
?
11 55
TEACHER’S TIPS
Understand how to write equivalent fractions.
Click the on-screen lock to fix this as the starting
fraction, and fix the shaded area.
What fraction of the square has been shaded?
Use the arrows to increase the number of columns from
1 to 2. The shading remains unchanged, but a vertical
line divides the shape. The shape is now divided into 4
pieces.
What has happened to the shape?
Is any more or less of the shape shaded?
How many parts is the shape now divided into?
How many parts are now shaded?
What fraction of the shape is shaded?
Input the equivalent fraction into the empty fraction to
the right of the equals sign. The left-most input box is
for units, the next tens, the next hundreds.
Click ‘Check’ to check.
Now use the arrows to increase the number of columns
from 2 to 3. The shape is now divided into 6 parts.
Question as above.
The maximum number of divisions is 10 by 10.
Use show labels to remind students which is the
numerator and which is the denominator.
ICT Main Activity 8.3, ‘Writing fractions in their simplest
form’ can be taught directly from this, by selecting
‘Simplest Form’ mode.
When writing equivalent fractions, stress that students must multiply both numerator and
denominator by the same whole number.
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Fractions and decimals
Individual activity: Exercise 4B
Non-calculator exercise
Q1 to 15 students must fill in a missing number to produce two equivalent fractions.
Q16 to 21 students must use their understanding of equivalent fractions to shade a given fraction of a diagram. A
resource sheet is available for this.
TOPIC SUMMARY
Key questions
1 Tell me three fractions that are equivalent to 12. (24, 36, 48…)
2* Would you be able to write down all the fractions that are equivalent to 12? (No, there is an infinite number
of equivalent fractions.)
8.3 Simplifying fractions
L
Demand
Grade
In this section …
L
GF
M
E
H
DC
By the end of this section students will:
Be able to simplify fractions.
PREPARING FOR THE TOPIC
Prior knowledge
Students should already: Be able to find a common factor of two numbers.
Checking prior knowledge
Non-ICT Starter 8.3
Ask students to write down the factors of 12 and the factors of 18. Which are the common factors? Which is the
highest common factor? Repeat this with other whole numbers.
Ask students to write down fractions that are equivalent to a half.
Which of the fractions equal to a half has the lowest numerator and denominator?
TEACHING THE TOPIC
Key vocabulary and phrases
Simplify
Simplest form
Cancelling
Lowest terms
Non-ICT Main Activity 8.3
ICT Main Activity 8.3
Draw a circle on the board, divide it into 6 equal parts
and shade in two parts. Ask
What fraction of the shape is shaded? Rub out 3 alternate
divisions and ask the same question. Write 2/6 and 1/3
on the board and show how this relates to dividing both
the numerator and the denominator by 2 (the same
whole number).
Now as a class simplify some of the following fractions.
Use the highest common factor of the numerator and
denominator.
2
●
10
● 3
18
● 4
16
continued Display ICT Main Activity 8.3 which is a simulation
showing an unshaded square divided into 12 parts
(3 rows and 4 columns), with the shaded fraction shown.
The program is in ‘Simplest Form’ mode.
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Understand how to write fractions in their simplest
form
Click the right-most 6 parts of the square, so the end 2
columns are shaded.
Click the ‘lock’ to fix this as the starting fraction, and fix
the shaded area.
What fraction of the square has been shaded?
Use the arrows to decrease the number of rows from 3
to 2. The shading remains unchanged, but the shape is
now divided into 8 pieces.
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8.4 Ordering fractions
Non-ICT Main Activity 8.3 (contd)
12
0
●
280
● 5
15
● 9
54
7
6
●
100
1
6
●
32
7
5
●
550
● 6
8
3
● 3
44
1
6
●
44
7
7
●
122
● A shop sells 20 sheets of silver wrapping paper, 12
sheets of blue, 6 red and 2 pink; what fraction of
the total sheets sold is each colour?
● Tony discovers that only 6 out of his 10 pens work;
what fraction is this in its simplest form?
ICT Main Activity 8.3 (contd)
What has happened to the shape?
Is any more or less of the shape shaded?
How many parts is the shape now divided into?
How many parts are now shaded?
What fraction of the shape is shaded?
Reduce the fraction further by removing further rows
and columns until the simplest form of the fraction is
found.
Input the simplest form of the fraction into the empty
fraction to the right of the equals sign. The left-most
input box is for units, the next tens, the next hundreds.
Click ‘Check’ to check to return a tick or cross.
Click ‘Reset’ and repeat with a variety of different
fractions.
In Example 6, emphasise that either method can be used and that, in the first method, it
does not matter whether the numerator and denominator are divided by 2 or 3 first.
In the exam, students should always write down the original fraction first before
attempting to simplify. This will ensure that if an error is made in the simplification
process, then a mark will still be gained for a correct original fraction.
TEACHER’S TIPS
Individual activity: Exercise 8C
Q1 to 10 can be completed using knowledge of tables up to the 10 times-table.
Q11 to 15 require more demanding simplification of fractions.
Q16 to 20 students write fractions in their simplest forms.
Q21 to 25 are in context. Students write one quantity as a fraction of another quantity, in its simplest form.
TOPIC SUMMARY
Key questions
1 Simplify the fraction 182. (23)
50
00
10 0
1
2* Kelly says that 1
200 simplifies to 100, Martin says that 200 simplifies to 2. Who is correct and why? (They are
both correct but Martin has fully simplified the fraction.)
8.4 Ordering fractions
L and M In this section …
Demand
Grade
L
GF
M
E
H
DC
By the end of this section students will:
Know how to order fractions by writing each fraction with a common
denominator.
PREPARING FOR THE TOPIC
Prior knowledge
Students should already: Be able to order whole numbers.
Be able to find the lowest common multiple (LCM) of two, three or four numbers.
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Checking prior knowledge
Non-ICT Starter 8.4
ICT Starter 8.4
Ask students to draw two 3 by 3 grids and in one grid
colour 2 squares and in the other grid colour 8. Ask
students which grid has the smallest fraction of shaded
squares. Ask students to write down all the other
fractions between these two as they colour in more
squares one by one.
How can we compare the sizes of fractions with different
denominators e.g. 23 with 35?
Display 1 or Starter 8.4 which shows a series of fractions
to be simplified. The students will have 10 seconds to
simplify the fraction before the answer appears.
Click ‘Play’ to start, and ‘Pause’ to stop. If required, use
the arrows to adjust the time. ‘Back’ and ‘Next’ can be
used to move backwards and forwards through the
questions. ‘Restart’ returns the program to the start.
Q9 to 15 involve more complex divisors, or may require
more than 1 step.
TEACHING THE TOPIC
Key vocabulary and phrases
Order fractions
Common denominator
Non-ICT Main Activity 8.4
Ask students Which is larger 34 or 172? Draw two 3 by 4 rectangles that have 12 squares inside. Ask students How would
we colour in 34 of this rectangle? Get students to write 34 as the equivalent fraction 192 to do this. For the other
rectangle ask How many squares should I shade to colour in 172 of the rectangle? Compare rectangles to see that 34 is
larger than 172. What did we do to the fraction 34 to compare it to 172? (Wrote it with the same denominator.)
Ask students to put these sets of fractions in order by using a common denominator:
1
7
3
4
8
8
1
5
13
24
8
24
1
3
5
9
7
10
9
11
4
6
2
7
5
35
44
100
4
88
1
9
5
18
7
8
3
4
2
8
12
16
2
14
5
7
2
5
12
20
6
15
7
10
How can you quickly tell if a fraction is more than a half or more than one?
Ensure that students realise that choosing the lowest common multiple of the
denominators means that the arithmetic needed will be easier.
TEACHER’S TIP
Individual activity: Exercise 8D
Q1 to 8 students order two or three fractions.
Q9 and 10 are more demanding, as students have to order four or five fractions.
Q11 and 12 involve Using and applying mathematics.
TOPIC SUMMARY
Key questions
1 Put these fractions in order 69 29 89 49. (29 49 69 89)
2 What is the smallest number (or lowest common multiple) that 2, 3, 4 and 6 all divide into exactly? (12)
3 Put 152 14 23 56 in order, starting with the smallest fraction. (14 152 23 56)
4* Which fraction is larger 190 or 1290? (1290 as 210 is smaller than 110)
8.5 Improper fractions and mixed numbers
M
Demand
Grade
70
In this section …
L
GF
M
E
H
DC
By the end of this section students will:
Be able to change a mixed number to an improper fraction, and vice versa.
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8.5 Improper fractions and mixed numbers
PREPARING FOR THE TOPIC
Prior knowledge
Students should already: Understand what fractions are.
Checking prior knowledge
Non-ICT Starter 8.5
How many halves are there in a whole?
1 whole 2 halves 22.
Ask students to write similar statements for thirds, quarters, fifths, sixths etc.
Test students with the following key questions:
How many quarters are there in 34 ?
How many quarters are there in one whole? In two wholes?
How many sixths are there in a whole one? In three whole ones?
TEACHING THE TOPIC
Key vocabulary and phrases
Improper fraction
Mixed number
Non-ICT Main Activity 8.5
Draw a rectangle on the board and ask How many quarters in a whole? Write 44 on the board and divide the rectangle
into 4.
What does 94 mean? (There are nine quarters.)
Draw the diagram below and ask How else can we write the fraction 94? (94 214)
What is the name of a fraction where the numerator is bigger than the denominator? (improper)
What is the name given to a number with a whole number part and a fractional part? (mixed number)
In the following examples ask students to find the equivalent improper fraction or mixed number and to illustrate
the example with a diagram:
b 73
c 143
d 165
e 152
f 323
g 225
h 134
i 335
a 95
Which do you think is easier to understand – an improper fraction or a mixed number? (Think about 3 23 and 131.)
Remind students, how many thirds there are in a whole, in two wholes, and so on.
Diagrams, such as those used in Examples 12 and 13 on page 154, can help visual learners.
Stick to quarters, thirds and halves initially.
TEACHER’S TIPS
Individual activity: Exercise 8E
Q1 and 2 give practice in changing mixed numbers to improper fractions.
Q3 and 4 give practice in changing improper fractions to mixed numbers.
TOPIC SUMMARY
Key questions
1 Change 114 to an improper fraction. (54)
3 Change 154 to a mixed number. (245)
2 How many thirds are there in 123? (5)
4 Change five halves to a mixed number. (212)
8.6 Reading and writing decimals
8.7 Understanding place value
L
Demand
Grade
In these sections …
L
GF
M
E
H
DC
By the end of this section students will:
Be able to use decimal notation.
Know how to read a decimal shown on a scale (tenths only).
Understand the place value of decimals.
Be able to read decimals from scales – extend to hundredths and thousandths.
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Fractions and decimals
PREPARING FOR THE TOPIC
Prior knowledge
Students should already: Be able to read whole numbers on a scale.
Checking prior knowledge
Non-ICT Starter 8.6–8.7
Draw a number line on the board with marks every two from 30 to 50 but only labelled every ten. Point to some of
the tick marks (labelled and unlabelled) and ask What number is this?
TEACHING THE TOPIC
Key vocabulary and phrases
Tenths
Decimal point
Place value
Tenths
Centimetres
Hundredths
Millimetres
Thousandths
Non-ICT Main Activity 8.6–8.7
ICT Main Activity 8.6–8.7
Ask students to write down the length of the following
items: pen; textbook; locker key or other key; thumb nail.
Ask If lengths aren’t exactly a whole number of
centimetres, how do we write the measurement? Discuss
tenths of a centimetre or millimetres with the class.
Ask students to measure to the nearest millimetre a
variety of objects round the room e.g. clock face
diameter, doorframe width, window depth and give their
answers in centimetres.
Why is it helpful to have parts of a centimetre?
Begin with the first paragraph of Non-ICT Main Activity
8.6–8.7, left.
Ask students to consider £23.75 and £647.39. How
many £10 notes would each amount have? How many
pound coins would be necessary to make up each
amount?
How many tenths and hundredths of a pound are in the
figure? (i.e. How many 10 p pieces and pennies would
be needed?) Relate each of these to the position that
the digit has in relation to the decimal point.
At appropriate points, stop the animation and ask or
discuss:
The column headings in the decimal place value table.
Where would you place each digit of the numbers
displayed in the table?
What is the value of 2 in each number?
What is the 1 in 32.1? 134.24?
What is the value of 4 in 563.432?
What are the values of the 4s in 4.724?
Write the headings Thousands, Hundreds, Tens, Units,
‘Decimal point’, Tenths, Hundredths, Thousandths on the
board. Write up the following numbers and ask the class
where each digit should be placed in the table: 8734.23;
2.404; 614.549; 1701; 4329.75; 10.99; 120.649
Display ICT Main Activity 8.7 which is an animation
showing how a place value diagram is used to represent
decimals, and the values of digits in different positions
on the diagram.
Click ‘Play’ to start, ‘Pause’ to stop. ‘Restart’ returns the
animation to the start. Use the ‘Playback control’ for
manual operation.
Draw a number line from 4.3 to 4.5, labelled at each
tenth with marks at every hundredth (i.e. marks at 4.31,
4.32 etc, but no labels). Ask students where an arrow
should be placed to indicate the position of the
following numbers: 4.45, 4.47, 4.31, 4.39.
TEACHER’S TIP
An arrow pointing to, for example 2.79, is often misread as 2.81. Warn students to take
care with readings near labelled marks on a scale.
Individual activity: Exercise 8F
Q1 to 12 students must write down the decimals shown on a variety of scales.
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8.8 Ordering decimals
Individual activity: Exercise 8G
Q1 students use a place value table to write the value of a digit in different numbers.
Q2 and 3 students write the value of digits in different numbers without referring to a place value table.
Q4 students read decimals on scales.
TOPIC SUMMARY
Key questions
1 Use your ruler to measure the length of your pen or pencil. Ask your neighbour to check your measurement.
2 What is the value of 7 in (a) 27 (b) 758 (c) 0.72 (d) 0.007. (7, 700, 7 tenths, 7 thousandths.)
8.8 Ordering decimals
L and M In this section …
Demand
Grade
L
GF
M
E
H
DC
By the end of this section students will:
Be able to put decimals in order by using place value.
PREPARING FOR THE TOPIC
Prior knowledge
Students should already: Understand the place value of decimals.
Know how to order whole numbers.
Checking prior knowledge
Non-ICT Starter 8.8
ICT Starter 8.8
Ask students
What is the smallest decimal we can make with the digits
3, 0, and 9?
Discuss the place value of each of the digits. Repeat with
other numbers and vary the number of decimal places
you will allow.
Display ICT Starter 8.8 which shows sets of numbers to
order from smallest to largest. Students have 10 seconds
to order the values from smallest to largest before the
answer appears.
Click ‘Play’ to start, ‘Pause’ to stop. Use the arrows to
adjust the time. Use ‘Back’ and ‘Next’ to move back and
forth through the questions. ‘Restart’ returns the
program to the start.
Questions require students to order between 3 and 5
numbers. Questions 10 to 15 involve large numbers.
TEACHING THE TOPIC
Key vocabulary and phrases
There is no new vocabulary for this section. Use the vocabulary for 8.6–8.7.
Non-ICT Main Activity 8.8
ICT Main Activity 8.8
Ask students to put the following numbers in order,
using a table of tens, units, tenths, hundredths and
thousandths if necessary.
● 1.2, 0.6, 0.9
● 4.33, 4.34, 4.333, 4.3
● 18.9, 18.75, 18.958, 18.98, 18.58
● 0.46, 0.045, 0.446, 0.041, 0.4
● 7.01, 7.003, 7.009, 7.019, 7.19
● 63.4, 64.339, 64.8, 64.09, 64.89
Here are some questions in context that you might like
to do as a class:
● Who is taller, Ash at 1.6 m tall or Pete at 1.58 m tall?
● Sam is shopping around to get the new book by his
favourite author as cheaply as possible. He has found
books with the following prices: £9.99, £9.25, £7.97,
£8.50, £8.90, £9.00. Put the prices in order from the
cheapest to the most expensive.
Display ICT Main Activity 8.8 which is an animation
showing the process of ordering decimals using a place
value diagram. The values 45.5, 5.45, 4.55, 4.45 and 4.44
are ordered.
Click ‘Play’ to start, ‘Pause’ to stop. ‘Restart’ returns the
animation to the start. Use ‘Playback control’ for manual
operation.
What is the value of the 5 in 45.4?
What is the value of the 4 in 5.45?
How does the place value diagram help us to see that
45.4 is the largest number?
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Fractions and decimals
It is important to stress that, for example, 4.56 is read as ‘four point five six’ and not ‘four
point fifty six’. Saying decimals wrongly can lead to students’ thinking that, for example,
4.5 is smaller than 4.23 because 5 is smaller than 23.
Encourage students to put in missing zeros, as in Example 16, when ordering and
comparing decimals.
TEACHER’S TIPS
Individual activity: Exercise 8H
Q1 and 2 students use place value tables to write decimals in order.
Q3 to 12 students order decimals given in lists.
Q13 and 14 students order decimals given in contexts.
TOPIC SUMMARY
Key questions
1 Put these decimals in order 6.7, 6.77, 6.06, 6.67, 6.6 (6.06, 6.6, 6.67, 6.7, 6.77)
2 Which is bigger, 3.5 or 3.19? Why? (3.5, because 5 tenths is more than 1 tenth.)
8.9 Converting decimals to fractions
8.10 Converting fractions to decimals
By the end of this section students will:
Be able to convert decimals to fractions by using place value.
Be able to convert fractions to decimals.
L and M In this section …
Demand
Grade
L
GF
M
E
H
DC
PREPARING FOR THE TOPIC
Prior knowledge
Students should already: Know and understand place value of decimals.
Checking prior knowledge
Non-ICT Starter 8.9–8.10
Tell students that Shaun has run 200 m in 23.46 s but to get into the county heats he needs to run a tenth of a
second faster. Ask the students to write down what time Shaun is aiming for. Compare this time with the previous
time and write down what one tenth is in decimals.
Write down seven tenths and three hundredths as decimals.
TEACHING THE TOPIC
Key vocabulary and phrases
Recurring decimal
Non-ICT Main Activity 8.9–8.10
Identify the place value of each of the digits in the following numbers and ask How would we write this number as a
fraction?
0.1, 0.04, 0.45, 0, 2.5, 14.2, 1.5, 0.99, 0.606, 5.677, 10.1
When is it easier/quicker to write numbers as fractions?
As a class convert the following fractions to decimals by first writing them as fractions with a denominator of 10 or 100.
1
10
2
5
7
10
17
25
1
100
8
20
9
90
7
5
20
80
20
40
13
100
As a class convert the following fractions into decimals using a calculator.
1
3
7
9
2
3
5
11
19
28
79
124
1
7
7
16
3
9
(The fractions in the table at the beginning of Section 8.10 have been used in this activity. Students should learn
these conversions.)
How can we show a decimal is recurring?
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Answers to chapter review questions
When changing fractions into recurring decimals, the calculator does not always show
enough digits to convince students that there is a recurring pattern. Use a spreadsheet to
display more digits than a calculator. Example 22c could be demonstrated using a
spreadsheet to show the recurring pattern more clearly.
TEACHER’S TIPS
Individual activity: Exercise 8I
Q1 students write decimals shown in a place value table as fractions.
Q2 to 10 students write decimals less than 1 as fractions.
Q11 to 15 students write decimal numbers greater than 1 as mixed numbers.
Individual activity: Exercise 8J
Q1 students convert fractions involving tenths, hundredths or thousandths to decimals.
Q2 students use equivalent fractions to convert fractions to decimals.
Q3 students should know the decimal equivalents of these fractions.
Q4 students use short division to convert fractions to decimals.
Q5 and 6 students use a calculator to convert fractions to decimals. The fractions in Q6 convert to recurring decimals.
TOPIC SUMMARY
Key questions
1 Change the following to fractions (a) 0.9 (b) 0.07 (c) 0.003 (190,
2* Change 5.13 to a mixed number. (511030)
3 Give the decimal equivalent of the following fractions
(c) 110 (d) 12 (0.25, 0.3333…, 0.1, 0.5)
(a) 14 (b) 13
4 Using your calculators, change the following fractions into decimals
3
(a) 78 (b) 59
16 (0.875, 0.555…, 0.1875)
7
100,
3
1000)
Answers to chapter review questions
1 a
2
5
10
24 12
b
8
1
24 3
c
12
3
16 4
12
3
20 5
3
4
3 a
b Shade 16 squares
4
7
35
60 12
5 a
c
4
12
5
15
9
45
10 50
b
d
6
3
16
8
5
20
8 32
6 a Shade 4 squares
7 a
1
4
b
1
3
c
b
1
4
3
12
d
3
4
8 a A(3.63), B(3.69), C(3.76)
b 1.2
c 0.9
d
3
8
9 a
b
c
d
6 units
6 tenths
6 thousandths
6 hundredths
16 Amanda
17 0.25, 0.5, 0.52, 2.2, 2.5
18
7
12
2
3
5
6
10 20.4, 20.34, 20.04, 19.96, 19.9
19
1
3
4
11
3
8
11 a 0.7
d 0.067
20 a
7
20
21 a
b
c
d
e
0.575
.
0.83
0.6875
..
0.36.
0.07
22 a
8
3
12
45
9
100 20
13
28
7
1000 250
14
2
3
3
5
b 0.09
e 0.4
c 0.43
f 0.35
as 10 squares shaded
only 9 squares shaded
2
5
1
2
b 0.375
b
44
5
15 0.875
75