pl e Sa m g in ew Vi REV0902

2413窶的RE

Introduction Fractions, decimals and percentages all deal with 'a part of' something, whether it be 'part of a whole' or 'part of a group'. This area of mathematics has often caused problems for both teachers and pupils alike; this concern however, is unnecessary if the correct grounding is given and basic concepts are understood.

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This group of three copymasters provides an introduction to fractions, decimals and percentages. The activities provide a framework for the teacher and pupil to develop confidence and understanding in this often misunderstood area of mathematics. It is vital that repeated practical activities are provided so that a solid understanding of basic concepts is developed. Activities in this book should be repeated using concrete materials and a variety of different objects. Fractions, like all areas of mathematics, are an enjoyable topic if understanding exists.

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A language component has been provided through the inclusion of several pages of text and comprehension questions. This serves two main purposes: (i) to link mathematics directly to language; and

(ii) to provide pupils with a written description of what they are learning.

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Review pages are provided throughout the series and should be used to judge the progress of individual pupils.

Curriculum Links ............................................... ii Fractions and decimals ................................... 14 Centimetres and metres ................................. 15 Tenths and hundredths .................................. 16 Ordering decimals (1) ..................................... 17 Ordering decimals (2) ..................................... 18 Face, place and total value (1) ........................ 19 Face, place and total value (2) ........................ 20 Adding decimals (1) ........................................ 21 Adding decimals (2) ........................................ 22 Subtracting decimals (1) ................................. 23 Subtracting decimals (2) ................................. 24 Rounding to a whole number ......................... 25 Rounding to 1 decimal place .......................... 26 Answers ...................................................... 27-28

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Fractions ............................................................ 1 Part of a whole ................................................... 2 What fraction? (1) .............................................. 3 Parts of a group .................................................. 4 What fraction? (2) .............................................. 5 Equivalent fractions .......................................... 6 Ordering fractions ............................................. 7 Fraction review .................................................. 8 Decimal numbers (1) ......................................... 9 Decimal numbers (2) ....................................... 10 Decimal tenths ................................................ 11 Decimal hundredths (1) .................................. 12 Decimal hundredths (2) .................................. 13 Prim-Ed Publishing

i

Fractions

Strand Unit

Number

Counting/ numeration

count the number of objects in a set

Comparing/ ordering

compare equivalent and non-equivalent sets

Fractions

establish and identify halves and quarters of sets to 20

2-D shapes

• •

combine and partition 2-D shapes identify half and quarter of shapes

Symmetry

identify line symmetry in shapes and in the environment

Place value

explore and identify place value in decimal numbers to two places of decimals

Fractions

identify fractions and equivalent forms of fractions with denominators 2, 3, 4, 5, 6, 8, 9, 10 and 12 compare and order fractions with appropriate denominators and position on the number line calculate a fraction of a set using concrete materials solve and complete practical tasks and problems involving fractions

Shape/ space

3rd/4th

Content Objectives

Strand

Number

Sa m

• • •

Decimals

• •

identify lines of symmetry as horizontal, vertical or diagonal

Length

rename units of length using decimal or fraction form

Place value

• •

read, write and order whole numbers and decimals identify place value in whole numbers and decimals

Operations

add and subtract whole numbers and decimals without and with a calculator

Fractions

compare and order fractions and identify equivalent forms of fractions express improper fractions as mixed numbers and vice versa and position them on the number line add simple fractions and simple mixed numbers express tenths and hundredths in both fractional and decimal form

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Number

solve and complete practical tasks and problems involving 2-D shapes

Symmetry

• • • Decimals/ percentages

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in

2-D shapes

Measures 5th/6th

express tenths and hundredths as fractions and decimals identify place value of whole numbers and decimals to two places and write in expanded form order decimals on the number line add and subtract whole numbers and decimals up to two places solve problems involving decimals

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• • •

Shape/ space

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Class

• • •

use percentages and relate them to fractions and decimals compare and order fractions, decimals and percentages solve problems involving operations with whole numbers, fractions, decimals and simple percentages

ii

Fractions

Fractions

Name:

A fraction is something that you will learn more about in the next few years in mathematics. In dictionaries a fraction is described as: a part of a whole, a small part, piece or amount. Until now most of your work with numbers has been with whole numbers like 1, 2, 3, 4, 10, 100, and so on.

All of this work is done with whole numbers.

7+6 7-6 10 x 2 10 ÷ 2

= = = =

13 1 20 5

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You have learnt to add these numbers… You have learnt to subtract these numbers… You are starting to learn multiplying… and dividing…

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Working with fractions is when we start to work with a part or parts of a whole number. If you and a friend buy one chocolate bar you will need to share it. To do this you break the chocolate bar into two pieces. Now you both have one piece each.

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Each piece is one half of the chocolate bar. This is a fraction.

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1. How does the passage describe a fraction?

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2. How does your dictionary describe a fraction? Is it the same?

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3. Tell of some times when you have to divide things into parts or fractions.

4. What is the difference between a whole number and a fraction?

5. On the back of this page list 10 places or times where you may need to use fractions.

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1

Fractions

Part of a whole

Name:

A whole number can be divided into parts to become fractions. Each part must be equal in size.

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one whole

halves 2 equal parts

quarters 4 equal parts

fifths 5 equal parts

tenths 10 equal parts

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1. Colour the objects divided into halves red. Colour the objects divided into quarters blue. Colour the objects divided into fifths green. Colour the objects divided into tenths yellow.

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2. Divide these objects into halves using a blue pencil.

Can this be done in more than one way? Describe how and then illustrate with a green pencil.

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2

Fractions

What fraction? (1)

Name:

1 2

one half

three quarters

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one quarter

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one half

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Colour each shape to match the fraction. Write the fraction in number form. The first one is done for you.

one whole

two fifths

three tenths

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two quarters

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3

Fractions

Parts of a group

Name:

A fraction can be a part of an object or a group of objects.

We can find one half of a packet of sweets by dividing the sweets into two equal groups. Each group or share is called one half.

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g

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This is the same for other fractions as well.

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For example, we can find one half of a pizza by cutting the pizza into two equal parts.

Whole/Group

Halves

Fifths

Tenths

Divide into two equal parts/groups.

Divide into five equal parts/groups.

Divide into ten equal parts/groups.

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Write the fraction for these groups.

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one out of

or

three out of

or

two out of

or

three out of

or 4

Fractions

What fraction? (2)

Name:

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1. Write the fraction for each group of shapes below.

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2. Colour each group of shapes to match the fraction. Write the fraction in number form. The first one is done for you.

1 4

one out of five

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one out of four

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three out of five

seven out of ten

four out of ten

two out of four 5

Fractions

,, ,,  ,,         , , ,,, ,,  , ,,    ,  

Equivalent fractions

Name:

Equivalent means the same. Fractions that are equivalent are fractions that are equal. For example, 2 out of 5 is equivalent to 4 out of 10.

2 5

is equivalent to

4 10

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1. Write the fraction for each and say whether they are equivalent.

Equivalent

4

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2

Yes

No

Equivalent

Yes

No

Yes

No

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Equivalent

  , 

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2. Draw two equivalent fractions for each of the fractions below.

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1 2

1 4

3. Find an equivalent fraction for: (a) one out of three (b) one out of five Prim-Ed Publishing

6

Fractions

Ordering fractions

Name:

Fractions, like whole numbers can be ordered by their size. 1. Place these whole numbers in order from the smallest to the largest. 5

1

7

,

,

3 ,

9 ,

12 ,

15 ,

11 ,

two fifths

2 5

one half

1 2

two thirds

2 3

7 10

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seven tenths

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3 4

g

three quarters

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2. Divide and colour the boxes to show these fractions.

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3. Place the fractions in order from the smallest to largest.

4. Place these two sets of fractions in order from smallest to largest.

2 10

1 3

3 6

3 4

9 10

1 5

1 2

1 4

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7

Fractions

Fraction review

Name:

Complete these fraction problems. 1. Divide this rectangle into quarters and colour three quarters of it.

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2. Divide these objects in halves. Use another colour to show other ways of dividing the objects into halves.

3. Colour each shape to match the fraction.

2 10

g

3 4

4. Write the fraction for these groups.

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5. Draw two equivalent fractions for this fraction. Write each fraction under the drawing.

=

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=

1 2

6. Write these fractions in order from smallest to largest.

1 2

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3 4

1 4

4 5

1 5

8

Fractions

Decimal numbers (1)

Name:

Cloze Activity â&#x20AC;&#x201C; Use these words to complete the passage below. conquered the depends

different comes invented

money symbols decimal

method using groups

on

(1)

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The decimal system is a

of

representing numbers in groups of ten. This system was (2)

in India around 300 BC by Hindus.

(3)

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India in the 700â&#x20AC;&#x2122;s, they learned of the Hindu numbering (4)

system. The Arabs created the

used today and spread this numbering system to other parts of the world. This is why

(5)

(6)

as Hindu-Arabic numbering, after

(7)

in

The word decimal

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develop it.

numbering is also known

two cultures which helped to

from the Latin word decem meaning ten. (8)

The decimal system represents numbers in (9)

numeral can be written by

of ten. Any

ten basic symbols, or digits 1, 2, 3, 4, (10)

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5, 6, 7, 8, 9, 0. The value of a digit

on its place in the (11)

numeral. For example the digit 5 means

things in

these numbers:

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111.15 111.51 115.11 151.11 511.11

The value of the 5 in this number is 5 hundredths or 0.05. The value of the 5 in this number is 5 tenths or 0.5. The value of the 5 in this number is 5 ones or 5. The value of the 5 in this number is 5 tens or 50. The value of the 5 in this number is 5 hundreds or 500.

A good real-life example of the decimal system is (13)

modern money systems are based Prim-Ed Publishing

9

(12)

. Many

the decimal system. Fractions

Decimal numbers (2)

Name:

1. Where was the decimal system invented?

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2. Why do you think that little is known of the early development of this system?

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3. Explain why the decimal system is sometimes known as the Hindu-Arabic system.

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4. What symbols form the basis of the decimal system?

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5. Show how the numeral six could be used to mean three different amounts in a number.

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6. Write ten different places where you have seen the decimal system used.

7. Why do you think a number system based on ten is so popular?

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10

Fractions

,,,,, ,,, ,,, , ,   , , ,        , , , ,     , ,  ,    ,  ,    ,     , ,  ,    ,  ,      , ,     , ,  ,    ,  ,      ,,,,,,,,  Decimal tenths

Name:

The following numbers have been written as decimals. Write them as fractions.

= 0.3 = = 0.5 =

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= 0.7 =

A tenth can also be written as a decimal. This is done like this:

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1 = 0.1 10

This means that a whole number has been divided into ten equal parts and the number after the decimal point is the number of parts you have. The following numbers have been written as fractions. Write the equivalent decimal number.

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6 = = 10

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7 = = 10

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8 = = 10 9 = = 10

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= 10 10 =

How did you write the last decimal number? Remember, ten tenths will make one whole number. How would you write this number?

=

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11

1

5 = 10 Fractions

, 

Decimal hundredths (1)

Name:

Write the following fraction as a decimal.

=

This number represents one part out of ten. Each tenth can be divided even further into another ten parts. These parts are called hundredths.

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If a whole number was divided into hundredths, it would look like this:

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=

1 whole

The hundredths are made up of 10 lots of tenths.

100 hundredths

g

=

10 tenths

in

100 hundredths

1.

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Colour these grids to match the fraction and then write the decimal. 2.

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13 100

59 100

0.

0.

3.

4.

75 100

7 100

0. Prim-Ed Publishing

0. 12

Fractions

  ,  ,  ,  , ,   , , ,, Decimal hundredths (2)

Name:

In the box below are one hundred patterned circles. Work out hundredths for each pattern and write your answer in the space provided.

=

100

= 0.

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=

out of 100

=

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=

100

= =

g

= 0.

out of 100

100

= =

out of 100

= 0. out of 100

100

= 0.

in

Complete the equations and colour the grid for the fractions given below. Yellow = 5 out of 100

= 0.

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=

100

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Green = 17 out of 100 =

Red

= 0.

= 63 out of 100

=

Blue

100

100

= 0.

= 15 out of 100 =

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100

= 0.

13

Fractions

Fractions and decimals

Name:

1. Colour these fractions and write them as decimals.

45 100

76 100

34 100

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12 100

2. Write these fractions as decimals. (i)

twenty seven hundredths

(ii)

nine hundredths

(iii) seventy five hundredths

g

(iv) one hundredth

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3. Colour the grids to match these decimals. (Numbers to the left of the decimal point are whole numbers. Numbers to the right of the decimal point are decimal fractions.)

1.27

0.03

1.85

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0.75

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14

Fractions

Centimetres and metres

Name:

One hundred centimetres equal one metre. Any measurement less than a hundred centimetres is a fraction, or part of, one metre. These measurements can be written in decimal form. 1. Write these centimetre measurements as metres in decimal form. For example 156 cm = 1 metre and 56 cm = 1.56 m. (v)

175 cm

95 cm

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(i)

(vi) 345 cm

(iii) 215 cm

(vii) 10 cm

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(ii) 105 cm

(iv) 176 cm

(viii) 271 cm

2. The following are the measurements taken of children in Year 4 at Milby Primary School. Convert the measurements to metres and order them from smallest to largest. Height in centimetres

John

154 cm

Height in metres

Order

in

g

Name

165 cm

Chris

134 cm

Martin

125 cm

Andrea

143 cm

Richard

121 cm

Michelle

149 cm

Mark

137 cm

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ew

Mary

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15

Fractions

Tenths and hundredths

Name:

To divide a whole number into tenths we need ten equal parts. This can be done like this:

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Each one of these tenths can be written as a fraction and a decimal.

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= 1 = 0.1 10 Each tenth can be divided again into a further ten equal parts. Each tenth divided into a further ten will give us one hundred parts, or hundredths.

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Each one of these hundredths can be written as a fraction and a decimal.

in

= 1 = 0.01 100

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Write these fractions as decimals.

2 = 10

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1.

6.

5 = 10

2.

24 = 100

7.

147 = 100

3.

9 = 10

8.

201 = 100

4.

65 = 100

9.

7 = 10

5.

7 = 100

10.

8 = 10

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16

Fractions

Ordering decimals (1)

Name:

, ,, ,, , ,, , ,, , ,, , ,, , ,, , ,, , , ,, ,, ,,, ,, ,, ,, ,,, ,, ,,,, ,

,, , ,, ,, , ,, , ,, , ,,, , ,, ,,, ,, ,,,

1. Write the following decimals and place in order from smallest to largest.

,

,,, ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,,, ,, , ,, , ,, , ,, , ,, , ,,,, ,,, ,, ,,, ,, , ,, , ,, , ,, , ,,, , ,, , ,, , ,, , ,, , ,,, , ,, , ,, , ,, , ,, , ,,, , ,, , ,, , ,, , ,, , ,,,,, ,,, ,,, ,

,

,

,, , ,, , ,, ,, , ,, , ,, ,, , ,, ,, , ,, , ,, , ,, ,, , ,, , ,, , ,, , ,, , ,, ,, , , ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, ,, , ,, , ,, ,, , ,, ,, , ,, , ,, , ,, ,, , ,, , ,, , ,, , ,, , ,, ,, , , ,, , ,, , ,, , ,, , ,, ,,,, ,,

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,

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2. Write the following decimals and place them in order from smallest to largest.

,

3. Place the following decimals in order from smallest to largest. 0.09

in

0.1

ew

,

0.21

,

0.8 ,

0.11 ,

4. Place the following decimals in order from smallest to largest.

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0.61 ,

0.09

0.27

,

0.55 ,

5. Colour 0.4 on this grid.

0.11 , Colour 0.04 on this grid.

How many times bigger is 0.4 than 0.04? Prim-Ed Publishing

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Fractions

Ordering decimals (2)

Name:

,, , ,, , ,, , ,, ,, , ,, , ,, ,, , ,, ,,, ,, ,,, , ,, ,,, ,, , ,, ,

,, , ,, ,, , ,,

1. Write the following decimals and place in order from smallest to largest.

,

,

,

,,, ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, ,, ,, , ,, , ,, ,, , ,, , ,, ,, , ,, ,, , ,, , ,, , ,, ,,, ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, ,, , , ,, , ,, , ,, , ,, , ,, ,, , , ,, , ,, , ,, , ,, , ,, , ,,, ,, , ,, , ,, , ,, , ,, ,, ,, , ,, , ,, ,, , ,, , ,, ,, , ,, ,, , ,, , ,, , ,, ,,, ,, , ,, , ,, , ,, , ,, , ,, ,, , , ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, , ,, ,, , , ,, , ,, , ,, , ,, , ,, , ,,,, ,,, ,,, ,,, ,,, ,,,,, ,,,,, ,,, , ,

,

g

,

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2. Write the following decimals and place them in order from smallest to largest.

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3. Write the larger number of each pair.

(iii) 0.45 and 0.5

(ii) 0.23 and 0.32

(iv) 0.78 and 0.87

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(i) 0.3 and 0.03

4. Which is the larger number, one tenth or one hundredth?

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5. Write the order for these decimals from smallest to largest. 0.34

0.4

0.56

0.75

0.57

0.43

0.04

0.3

,

,

,

,

,

,

,

.

6. Measure the height of five of your friends and order them in size. Record your answers in decimal form in the space provided below. Friend Height (m) Prim-Ed Publishing

18

Fractions

Face, place and total value (1)

Name:

Each number in the decimal system has a face, place and total value.

Sa m

Place Value The place value is the value of the place where the number appears. For example, in the number 156… the number 1 has a place value of hundreds; the number 5 has a place value of tens; and the number 6 has a place value of ones.

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Face Value The face value is always the number as it appears. For example, in the number 156… the number 1 has a face value of 1; the number 5 has a face value of 5; and the number 6 has a face value of 6.

Total Value The total value is the face value times the place value. For example, in the number 156… the number 1 has a total value of one hundred (100); the number 5 has a total value of five tens (50); and the number 6 has a total value of six ones (6).

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in

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Decimal fractions have the same face value but different place values to whole numbers as their value is measured in tenths and hundredths. For example, in the number 1.56… the number 1 has a place value of 1; the number 5 has a place value of 5 tenths; and the number 6 has a place value of 6 hundredths. Complete the place value chart for these numbers.

Hundreds

Tens

Ones

Tenths

Hundredths

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1.5

7.56

12.6 7.98 15.56 243.87 Prim-Ed Publishing

19

Fractions

Face, place and total value (2)

Name:

1. Write these decimals from their description. (i) A face value of 6. A place value of tenths. (ii) A face value of 9. A place value of tenths. (iii) A face value of 4. A place value of tenths. (iv) A face value of 6. A place value of hundredths. (vi) The six has a place value of tenths. The one has a place value of hundredths.

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(vii) The 5 has a place value of tenths. The 7 has a place value of hundredths.

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(v) A face value of 9. A place value of hundredths.

(viii) The 1 has a place value of tens. The 0 has a place value of ones. The 7 has a place value of tenths. The 9 has a place value of hundredths.

2. Write the place, face and total value for the underlined number.

12.76

(ii)

246.78

seven

tenths

Total Value

0.7

ew

in

(i)

Place Value

g

Face Value

1.95

(iv)

16.54

(v)

7.08

(vi)

17.98

(vii)

1.56

(viii)

76.76

Vi

(iii)

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20

Fractions

Name:

1. Add the following decimals by colouring and then writing the answer. 0.3

0.2 =

+

=

+

0.6

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0.3

0.7 =

+

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0.5

2. Add the following decimals by colouring and then writing the answer.

0.2

g

0.07

=

0.16

in

+

0.6

ew

+

0.56

Vi

0.35

=

+

=

3. Add these decimals. (i) 0.7 + 0.2 =

(v) 0.13 + 0.25 =

(ii) 0.2 + 0.5 =

(vi) 0.77 + 0.28 =

(iii) 0.3 + 0.7 =

(vii) 0.25 + 0.75 =

(iv) 0.4 + 0.8 =

(viii) 0.95 + 0.15 =

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21

Fractions

Name:

0.5

,,,,, ,,,,, ,,,,,

+

0.26

,,, ,,, ,, ,,, ,, ,,, ,, ,,, ,,, ,,

=

0.4

,,,,, ,,,,, ,,,,,

+

,,, , ,, , ,, , ,, , ,,, ,, ,,, ,,, ,,

=

0.67

+

0.2

=

+

0.3

=

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0.95

in

g

Sa m

0.37

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1. Add the following decimals by colouring and then writing the answer.

2. Add these decimals. (i) 0.7 + 0.12 =

(v) 0.13 + 0.5 =

(ii) 0.12 + 0.5 =

(vi) 0.7 + 0.28 =

(iii) 0.33 + 0.7 =

(vii) 0.5 + 0.75 =

(iv) 0.24 + 0.18 =

(viii) 0.9 + 0.15 =

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22

Fractions

Subtracting decimals (1)

Name:

1. Subtract the following decimals by colouring and then writing the answer. 0.9

0.7 –

0.5 –

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0.5

=

=

0.9

Sa m

1.6 –

=

2. Subtract the following decimals by colouring and then writing the answer.

0.23

0.75

ew

0.81

=

in

g

0.38

=

Vi

1.4

0.65 –

=

3. Subtract these decimals. (i) 0.52 – 0.3 =

(v) 0.6 – 0.22 =

(ii) 0.79 – 0.28 =

(vi) 0.5 – 0.12 =

(iii) 0.75 – 0.7 =

(vii) 0.7 – 0.36 =

(iv) 0.34 – 0.18 =

(viii) 0.9 – 0.15 =

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23

Fractions

Subtracting decimals (2)

Name:

0.26

=

0.4

0.37

=

0.70

0.55

Sa m

0.88

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1. Subtract the following decimals by colouring and then writing the answer.

in

g

=

0.55

=

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ew

1.28

2. Subtract these decimals. (i) 0.8 – 0.12 =

(v) 1.13 – 0.5

=

(ii) 0.12 – 0.05 =

(vi) 2.7 – 1.28 =

(iii) 0.33 – 0.1 =

(vii) 0.5 – 0.49 =

(iv) 0.84 – 0.18 =

(viii) 0.95 – 0.57 =

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24

Fractions

Rounding to a whole number

Name:

Rounding decimal numbers is where the number is rounded to the decimal place or whole number that is required. For example, rounding 1.7 to the nearest whole number gives a choice of rounding up to 2 or down to 1. Look at the number line below.

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Which whole number (1 or 2) is 1.7 closest to?

1.8

1.9

2

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1

1. Place these numbers on a number line and round to the nearest whole number.

(iii)

3.2

(iv)

2.9

(v)

3.6

1.2

1

1.1

1.2

3

3.1

3.2

2

2.1

2.2

(vi)

1.5

1.3

3

1

3.1

1.1

1.4

1.5

1.6

1.7

Sa m

1.3

1.1

1.8

1.9

2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

g

(ii)

1

in

1.6

ew

(i)

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Vi

What problems did you have with part (vi)? How did you solve these?

2. Round these decimals to the nearest whole number. (i)

1.3

(iv) 2.34 Prim-Ed Publishing

(ii) 1.6

(iii) 3.4

(v) 3.89

(vi) 1.55 25

Fractions

Rounding to 1 decimal place

Name:

Rounding to one decimal point is where a decimal number in hundredths is rounded back to tenths. For example, rounding 1.76 to one decimal place means that the decimal can be rounded back to 1.7 or up to 1.8. Look at the number line below.

1.71

1.72

1.73

1.74

1.75

Which is 1.76 closest to?

1.76

1.77

1.78

1.79

1.8

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1.7

1. Place these numbers on a number line and round to one decimal place.

(iv) 2.93

1.23

1.1

1.11

1.12

1.13

1.14

1.15

1.16

3.4

3.41

3.42

3.43

3.44

3.45

2.9

2.91

2.92

2.93

2.94

1.0

1.01

ew

(v) 1.03

1.22

(vi) 2.65

2.6

2.61

1.24

1.25

1.26

1.27

1.28

1.29

1.3

1.17

1.18

1.19

1.2

3.46

3.47

3.48

3.49

3.5

2.95

2.96

2.97

2.98

2.99

3.0

Sa m

(iii) 3.49

1.21

g

(ii) 1.17

1.2

in

(i) 1.26

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.1

2.62

2.63

2.64

2.65

2.66

2.67

2.68

2.69

2.7

Vi

What problems did you have with part (vi)? How did you solve these?

2. Round these decimals to the nearest tenth. (i)

1.36

(ii) 1.67

(iii) 3.49

(iv) 2.34

(v) 3.89

(vi) 1.55

Prim-Ed Publishing

26

Fractions

Answers (1) Parts of a group ................................. page 4 1 one out of four or 4 3 three out of five or 5 2 two out of four or 4 3 three out of ten or 10

Decimals numbers (1) ...................... page 9 1. 4. 7. 10. 13.

conquered the using money

pl e

Sa m

2 3 4 , 6 , etc. 1 2 4 , 8 , etc.

Decimal tenths ................................. page 11 3 7 5 10 , 10 , 10 0.6 , 0.7 , 0.8 , 0.9 , 1 1.5

in

g

Decimal hundredths (1) ................. page 12

3. (a) two out of six, etc. (b) two out of ten, etc.

ew

Ordering fractions ............................ page 7 1. 1, 3, 5, 7, 9, 11, 12, 15

2 1 2 7 3 5 , 2 , 3 , 10 , 4

Vi

1 3 3 2 4. 10 , 3 , 6 , 4 1 1 9 1 5 , 4 , 2 , 10

Fraction Review ................................ page 8 4 3 4. 10 , 8 5.

2 3 , 4 6 , etc.

6.

1 1 4 3 1 5 , 4 , 2 , 4 , 5

Prim-Ed Publishing

invented 3. decimal 6. groups 9. different 12.

1. India 2. Because it happened a long time ago. 3. Because the Hindus and Arabs were involved in developing the system. 4. 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 5. 116, 161, 611 etc.

Equivalent Fractions ....................... page 6 1 2 yes 1. 2 4 1 5 yes 2 10 2 1 no 4 5

3.

2. 5. 8. 11.

Decimals numbers (2) .................... page 10

What fraction? (2) .............................. page 5 1 3 1. 4 10 2 3 5 4

2.

method symbols comes depends on

27

1.0.13

2. 0.59

3. 0.75

4. 0.07

Decimal hundredths (2) ................. page 13 13 crosshatch = 13 out of 100 = 100 = 0.13 31 clear = 31 out of 100 = 100 = 0.31 30 dark grey = 30 out of 100 = 100 = 0.3 26 light grey = 26 out of 100 = 100 = 0.26 5 yellow = 5 of 100 = 100 = 0.05 17 green = 17 out of 100 = 100 = 0.17 63 red = 63 out of 100 = 100 = 0.63 15 blue = 15 out of 100 = 100 = 0.15

Fractions

Centimetres and metres ............... page 15

2. (ii) (iii) (iv) (v) (vi) (vii) (viii)

1. (i) 1.75 (ii) 1.05 (iii) 2.15 (iv) 1.76

Adding decimals (1) ....................... page 21

Fractions and Decimals ................ page 14 1. 0.12, 0.45, 0.76, 0.34

Tenths and hundredths ................. page 16 3. 0.9 7. 1.47

4. 0.65 8. 2.01

Adding decimals (2) ....................... page 22

Sa m

2. 0.24 6. 0.5 10. 0.80

1. 0.76, 0.77, 0.87, 1.25 2. (i) 0.82 (ii) 0.62 (iii) 1.03 (iv) 0.42 (v) 0.63 (vi) 0.98 (vii) 1.25 (viii) 1.05

Ordering decimals (1) .................... page 17

Subtracting decimals (1) ............... page 23

g

1. 0.6, 0.8, 0.2, 0.9 In order: 0.2, 0.6, 0.8, 0.9 2. 0.99, 0.06, 0.54, 0.45 In order: 0.06, 0.45, 0.54, 0.99 3. 0.09, 0.1, 0.11, 0.21, 0.8 4. 0.09, 0.11, 0.27, 0.55, 0.61 5. 0.4 is ten times bigger than 0.04.

in

Ordering decimals (2) .................... page 18 1. 0.8, 0.5, 0.2, 0.3 In order: 0.2, 0.3, 0.5, 0.8 2. 0.23, 0.32, 0.87, 0.78 In order: 0.23, 0.32, 0.78, 0.87 3. (i) 0.3 (ii) 0.32 (iii) 0.5 (iv) 0.87 4. one tenth 5. 0.04, 0.3, 0.34, 0.4, 0.43, 0.56, 0.57, 0.75

ew

Vi tens

ones

0 0 0 0 0 2

0 0 1 0 1 4

1 7 2 7 5 3

5 5 6 9 5 8

Subtracting decimals (2) ............... page 24 1. 0.62, 0.03, 0.15, 0.73 2. (i) 0.68 (ii) 0.07 (iii) 0.23 (iv) 0.66 (v) 0.63 (vi) 1.42 (vii) 0.01 (viii) 0.38

1. (i) (v) 2. (i) (v)

2 4 1 4

(ii) (vi) (ii) (vi)

1 2 2 2

(iii) 3

(iv) 3

(iii) 3

(iv) 2

Rounding to 1 decimal place ....... page 26

tenths hundredths

• • • • • •

1. 0.2, 0, 0.7 2. 0.15, 0.06, 0.75 3. (i) 0.22 (ii) 0.51 (iii) 0.05 (iv) 0.16 (v) 0.38 (vi) 0.38 (vii) 0.34 (viii) 0.75

Rounding to whole number ......... page 25

Face, place and total value (1)..... page 19 hundreds

40 0.05 6 0 0.08 0.5 70

1. 0.5, 0.8, 1.3 2. 0.27, 0.76, 0.91 3. (i) 0.9 (ii) 0.7 (iii) 1.0 (iv) 1.2 (v) 0.38 (vi) 1.05 (vii) 1 (viii) 1.1

(v) 0.95 (vi) 3.45 (vii) 0.10 (viii) 2.71

1. 0.2 5. 0.07 9. 0.70

tens hundredths ones tenths hundredths tenths tens

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2. (i) 0.27 (ii) 0.09 (iii) 0.75 (iv) 0.01

four five six zero eight five seven

0 6 0 8 6 7

1. (i) (v) 2. (i) (v)

1.3 1.0 1.4 3.9

(ii) (vi) (ii) (vi)

1.2 2.6 1.7 1.6

(iii) 3.5

(iv) 2.9

(iii) 3.5

(iv) 2.3

Face, place and total value (2)..... page 20 1. (i) 0.6 (ii) 0.9 (iii) 0.4 (iv) 0.06 (v) 0.09 (vi) 0.61 (vii) 0.57 (viii) 10.79

Prim-Ed Publishing

28

Fractions

2413 Fractions - Middle