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REV0902

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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.

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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. 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.

Table of Contents

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Curriculum Links ...................................................... ii Fractions .................................................................... 1 Parts of a whole ......................................................... 2 Parts of a set .............................................................. 3 Kinds of fractions (1) ................................................. 4 Kinds of fractions (2) ................................................. 5 Equivalent fractions (1)............................................. 6 Equivalent fractions (2)............................................. 7 Common denominator (1)......................................... 8 Common denominator (2)......................................... 9 Common denominator (3)....................................... 10 Common denominator (4)....................................... 11 Converting to hundredths (1) ................................. 12 Converting to hundredths (2) ................................. 13 Prim-Ed Publishing

Ordering fractions (1) .............................................. 14 Ordering fractions (2) .............................................. 15 Percentages (1) ........................................................ 16 Percentages (2) ........................................................ 17 Fractions as percentages (1) .................................. 18 Fractions as percentages (2) .................................. 19 Decimals and percentages ..................................... 20 Fractions, decimals and percentages ................... 21 Ordering decimals ................................................... 22 Adding decimals ..................................................... 23 Subtracting decimals .............................................. 24 Review (1) ................................................................ 25 Review (2) ................................................................ 26 Answers ............................................................. 27-29 i

Fractions

Curriculum Links 1st/2nd

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

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• • •

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

Prim-Ed Publishing

•

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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:

The dictionary tells us that fractions are: ‘a part of a whole number; a small part, piece or amount’. You have learnt that in mathematics fractions are: 1 1. equal parts of a whole number, e.g. 2 of a chocolate bar, or; 1 2. equal parts of a group of objects, e.g. 2 of a bag of marbles.

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Before the introduction of the decimal system children needed to learn a lot more about fractions, as this was the only way to show a part of a whole number. Today, the use of fractions is still very important. We use fractions to represent basic units with denominations to twelve.

Writing fractions is done differently to whole numbers. A fraction is made up of a numerator and a denominator.

2 3

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13 17 In the past, using fractions such as 32 and 64 to describe shares of objects or groups of objects were common. Today these fractions have been replaced by decimals and the calculations are often done with calculators or computers. numerator – tells us how many parts of the whole there are.

denominator – tells us how many parts are in the whole.

If the numerator is smaller than the denominator the fraction is called a proper fraction. If the numerator is larger than the denominator the fraction is called an improper fraction. If a fraction is accompanied by a whole number it is called a mixed number.

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1. On the back of this sheet, explain by using diagrams how a fraction can be part of a whole number as well as part of a group of objects.

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2. Why was the learning of fractions more complicated 50 years ago?

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3. Why are difficult calculations easier to do in today’s classrooms?

4. List three uses for fractions in today’s society.

5. Describe the three parts of a written fraction.

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1

Fractions

Parts of a whole

Name:

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

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1. Write the fraction represented by each of these diagrams.

2. Divide and shade these rectangles to show these fractions.

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3 10

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3. What fraction needs to be added to the following fractions to complete the equation?

= 1

2 3 +

= 1

7 10 +

= 1

25 100 +

= 1

5 8 +

= 1

1 4 +

= 1

13 32 +

= 1

3 10 +

= 1

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1 2 +

Prim-Ed Publishing

2

Fractions

Parts of a set

Name:

,, ,,

=

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

1 5

=

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

=

=

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

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1. Write the fraction that matches these diagrams.

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2. Draw and colour a set of objects that represents each of these fractions.

2 5

5 8

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11 12

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3 4

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

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

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3. Write the fraction and the decimal that describe these diagrams.

=

=

0.

=

=

0.

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

=

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=

0.

=

=

0.

=

=

0.

=

0.

,,, , ,, , ,, , ,, , ,,, ,, , ,, ,, , ,, , , ,, , ,, , ,, , ,, , ,,, ,,, ,, ,, , , , ,, , ,, , ,, , ,, , ,, , ,, , ,, ,, ,,, ,,,, ,,,, ,, ,, , =

3

Fractions

Kinds of fractions (1)

Name:

1 2 is a proper fraction, because itâ€™s denominator is larger than its numerator.

1 1 is a mixed number, because it is a mix of a whole number and a fraction. 2

3 is the same number, written as an improper fraction. 2 The numerator is larger than the denominator.

,,, ,, ,,, ,, ,,, ,,, ,, ,, ,,,,,,,, ,, =

7 5 7 5

5 5

=

2 5 2 5

,,,,,,,, ,, ,,,,,, ,, ,, ,,,,, ,, ,,, ,,, ,, 1 1

=

=

3 4

+

+

4 4 7 4

= =

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

+

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To change a mixed number to an improper fraction you convert the whole number to fraction form.

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To change an improper fraction to a mixed number you take out the whole numbers to leave a simple fraction.

+

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

3 4

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Change these improper fractions to mixed numbers by colouring the diagrams.

6 4

=

+

5 2

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=

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

=

+

+

=

+

+

=

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

Change these mixed numbers to improper fractions by colouring the diagrams.

1

5 6

=

+

=

+

2

=

Prim-Ed Publishing

1 3

=

+

+

=

+

+

=

4

Fractions

Kinds of fractions (2)

Name:

Change these improper fractions to mixed numbers. 7 = 3

+

=

27 = 10

+

6 = 2

=

+

137 = 100

+

=

250 = 100

+

= 32 = 16

+

+

+

+

=

22 = 5

+

=

=

20 = 8

14 = 12

21 = 9

=

=

=

+

+

+

+

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=

+

=

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13 = 7

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7 = 5

1 13 =

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Change these mixed numbers to improper fractions.

+

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15 = 1 100 =

1 37 =

+

7 = 1 10

2 34 =

+

=

75 = 2 100

+

+

3 14 =

+

+

+

+

+

+

=

+

+

7 = 3 20

=

=

=

= 1 37 50

2 79 =

1 23 =

=

=

=

Prim-Ed Publishing

+

=

= 1 = 2 16

+

5

Fractions

Equivalent fractions (1)

Name:

,,, , ,, ,,, = ,, , ,,, ,, , ,,, ,2 ,, 1

Equivalent means â€˜equal in valueâ€™. Fractions can look different but be equivalent. For example:

2

4

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To make equivalent fractions follow this rule:

Multiply the fraction by one, in the form of a whole fraction, e.g. 4 . 4 Look at the following equivalent fractions and how they were made.

(x 2) = 2 = (x 2) = 4

1 4

(x 4) = 4 = (x 4) = 16

2 3

(x 3) = 6 = (x 3) = 9

3 5

(x 6) = 18 = (x 6) = 30

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To make more equivalent fractions for these examples, you can multiply the fraction by a different 1 2 3 4 whole fraction. For example, if you multiply 2 by the whole fractions 2 , 3 , 4 , etc. you get 2 3 4 the equivalent fractions 4 , 6 , 8 , etc.

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1 1. Write 5 equivalent fractions for 3 in the space provided below.

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3 2. Write 5 equivalent fractions for 4 in the space provided below.

2 3. Write 5 equivalent fractions for 5 in the space provided below.

Prim-Ed Publishing

6

Fractions

Equivalent fractions (2)

Name:

Write two equivalent fractions for each of these fractions.

2 3

=

=

6.

4 8

=

=

2.

7 10

=

=

7.

2 5

=

=

3.

15 100

=

=

8.

1 9

=

=

4.

3 5

=

=

9.

3 4

=

=

5.

3 8

=

=

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1.

10.

9 10

=

=

Which is the simplest way of writing one-half out of these equivalent fractions? 1 2

2 4

3 6

4 8

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1 The answer is of course 2 . This is the way to show one-half as a fraction. To simplify a fraction we find a number which will divide into both the numerator and the denominator evenly, leaving no remainder.

(รท 2) == 3 (รท 2) = 5

6 10

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6 For example, to simplify the fraction 10 , we divide the numerator and the denominator by 2:

So

3 6 is the simplified fraction for . 5 10

Simplify these fractions by dividing the numerator and the denominator by the same number.

1. 15 = 20

(divide both by

)

3. 15 18

2 = 10

(divide both by

)

4.

2.

Prim-Ed Publishing

7

=

(divide both by

)

5 = 10

(divide both by

)

Fractions

Common denominator (1)

Name:

To add and subtract fractions each fraction must have a common denominator â€“ they must be the same thing. This is just like adding objects. For example,

+

= 2 apples

4 apples

+

=

1 orange

2 apples

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2 apples

1 orange and 2 apples

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We can get an easy answer for the first equation but the second answer is the same as the fraction problem. To get an answer for the second equation we must find something that the orange and apples have in common. So what do apples and oranges have in common? Apples and oranges are both fruit! We can now reword the problem to read:

2 pieces of fruit

3 pieces of fruit

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1 piece of fruit

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We have found a common element.

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Find the common element in these problems: =

2. 3 boys + 3 girls

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1. 1 estate car + 2 hatchbacks

3. 2 daisies + 5 daffodils

=

4. 1 teddy bear + 1 action figure + 1 toy car

=

Write two problems of your own: 5.

=

6.

=

Prim-Ed Publishing

8

Fractions

Common denominator (2)

Name:

To find common denominators in fractions we must find a number that all the denominators will divide evenly into. For example, look at the fractions 1 and 1 . 2 3 The denominators for these fractions are 2 and 3. A number that 2 and 3 will divide into evenly is 6. We can express both of these fractions as sixths, and so give them both a common denominator. This is how it is done:

(x 3) = = 3 (x 3) 6

To change the denominator in 1 from 2 to 6 we multiply the 2 3 fraction by . 3

1 3

(x 2) = = 2 (x 2) 6

To change the denominator in 1 from 3 to 6 we multiply the 3 2 fraction by . 2

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1 2

Once we express 1 and 1 as fractions with common denominators, we can add them: 2 3

,, ,, , ,, , , ,, ,, ,, ,,,, ,, , ,,, ,, , ,, , ,,, ,, 1 2

1 3

3 6

=

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=

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2 6

5 6

=

1 1 2 , 4

Lowest common denominator =

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Find a common denominator for these fraction pairs.

6.

1 1 5 , 10 Lowest common denominator =

1 1 2 , 5

Lowest common denominator =

7.

1 1 2 , 8

Lowest common denominator =

1 1 3. 3 , 8

Lowest common denominator =

8.

1 1 3, 4

Lowest common denominator =

1 1 4. 3 , 6

Lowest common denominator =

9.

1 1 9, 5

Lowest common denominator =

1 1 4 , 6

Lowest common denominator =

10.

1 1 9, 4

Lowest common denominator =

2.

5.

Prim-Ed Publishing

9

Fractions

Common denominator (3)

Name:

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Many fraction pairs have more than one common denominator. 1 1 For example, for the fraction pair of 2 and 4 , the common denominators are 4, 8, 12, 16, 20, etc. In this case, 4 is known as the lowest common denominator. That is, it is the lowest number which is divisible by the denominators 2 and 4, without leaving a remainder: 1 For the fraction 4 , 4 รท 2 = 2 with no remainder. 1 For the fraction 2 , 2 รท 2 = 1 with no remainder. Find the lowest common denominator for the fraction pairs below, and two other common denominators as well. 1.

1 1 2 , 4

Lowest common denominator =

2.

1 1 5 , 10

Lowest common denominator =

Other common denominators =

,

3.

1 1 2 , 5

Lowest common denominator =

Other common denominators =

,

4.

1 1 2 , 8

Lowest common denominator =

Other common denominators =

,

1 1 5. 10 , 20

Lowest common denominator =

Other common denominators =

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Other common denominators =

,

Find the lowest common denominator for these fraction pairs. Lowest common denominator =

1 1 7. 5 , 10

Lowest common denominator =

1 1 2 , 10

Lowest common denominator =

1 1 8. 2 , 8

Lowest common denominator =

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1 1 1. 3 , 7

1 1 3. 6 , 9

Lowest common denominator =

1 1 9. 3 , 4

Lowest common denominator =

1 1 4 , 5

Lowest common denominator =

1 1 10. 9 , 5

Lowest common denominator =

1 25 5. 25 , 100 Lowest common denominator =

1 1 11. 8 , 9

Lowest common denominator =

4.

6.

1 1 2 , 9

Prim-Ed Publishing

Lowest common denominator =

2 21 12. 5 , 25 Lowest common denominator =

10

Fractions

Common denominator (4)

Name:

When you have found a common denominator for a fraction pair, you can add them together. 1 1 For example, take the fraction pair 3 and 4 . The common denominator for these two fractions is 12. Therefore, 1 + 1 = 4 + 3 3 4 12 12

7 12

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=

1.

2 1 3 , 4

______ + ______ = ______ + ______

Lowest common denominator =

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2 1 5 , 2

= ______ ______ + ______ = ______ + ______

Lowest common denominator =

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3.

= ______ ______ + ______ = ______ + ______

Lowest common denominator =

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17 1 4. 25 , 5

= ______

______ + ______ = ______ + ______

Lowest common denominator =

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2.

1 1 4 , 5

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Find the lowest common denominator for these fraction pairs and then use it to add the fractions.

= ______

This is Harder! Find the common denominator for these groups of fractions and add them on the back of this sheet. 1 1 1 2 , 4 , 3

Common denominator =

4.

1 3 1 4 , 8 , 2

Common denominator =

1 1 1 2. 5 , 10 , 3

Common denominator =

1 1 1 5. 3 , 6 , 9

Common denominator =

Common denominator =

6.

1.

3.

1 1 1 2 , 10 , 20

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11

2 21 1 5 , 25 , 20 Common denominator = Fractions

Converting to hundredths (1)

Name:

A way to express fractions as decimals is to convert them to hundredths. Complete the diagrams below to convert the fraction on the left into a decimal number (out of 100).

=

1 4

=

2.

3.

4.

,,, ,,,

=

=

=

100

=

=

100

=

100

in

1 10

=

=

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1 5

,,,,, ,,,,,

=

100

=

0.

=

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1 2

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

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1.

=

0.

=

0.

=

0.

2 4

=

100

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Write these fractions as hundredths and decimals.

7 10

=

2 3. 10

=

3 10

=

2.

4.

Prim-Ed Publishing

100

100 100

=

0.

5.

4 5

=

=

0.

6.

2 5

=

=

0.

6 7. 10

=

=

0.

8.

3 4

=

12

100 100

100 100

=

0.

=

0.

=

0.

=

0.

Fractions

Converting to hundredths (2)

Name:

To convert a fraction to hundredths we follow the same rule as equivalent fractions. We multiply the fraction by the whole fraction which gives a denominator of 100. 1 2 50 to a fraction out of 100 we multiply it by the whole fraction : 50

For example, to convert the fraction

1 (xx 50) = = 50 2 (x 50) 100 1 50 becomes , which is 0.5 as a decimal. 2 100

Convert these fractions into decimals.

1 5

=

1 3. 20

=

4.

15 20 =

100 100

100

=

1 6. 25

=

0.

=

0.

=

0.

17 7. 25

=

=

0.

8.

8 10

=

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2.

100

6 5. 20

=

g

=

in

1 1. 10

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Therefore,

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whole fraction

100 100 100

100

=

0.

=

0.

=

0.

=

0.

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Convert these decimals back into fractions. Simplify the fractions wherever possible.

1. 0.95 =

2. 0.6

=

3. 0.75 =

100 100

100

.

4. 0.33 = Prim-Ed Publishing

100

= ______

5. 0.9

=

= ______

6. 0.2

=

= ______

7. 0.02 =

= ______

8. 0.85 = 13

100 100

100 100

= ______

= ______

= ______

= ______ Fractions

Ordering fractions (1)

Name:

Look at the example below to see how fractions are ordered from smallest to largest.

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

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

3 10

2

7 10

110

5

110

9 10

1 10

3 10

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1 10

Ordered from smallest to largest

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Unordered

7 10

9 10

2

110

5

110

Colour these fractions on the diagram and then order them from smallest to largest:

Ordered from smallest to largest

1 4

1 3

1 5

1 8

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1 2

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Unordered

1 10

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Place these fractions in ascending order (from smallest to largest), by first expressing them with a common denominator.

1.

1 2 1 3 , 5 , 2

2.

1 3 3 4 , 2 , 8

common denominator

in ascending order

3 2 15 3. 10 , 5 , 100 4.

7 65 3 5 , 10 , 100

Prim-Ed Publishing

14

Fractions

Ordering fractions (2)

Name:

Simplify these fractions. The first has been done for you.

15 60 50 75 25 20 100 , 100 , 100 , 100 , 100 , 100 3 20

1.

1 + 2 = 5 5

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Add these fractions together and order the answers. 2.

1 + 1 = 6 2

+

=

1 + 1 = 3 4

+

=

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1 + 1 = 4 4

ew 2 + 1 = 6 5

=

2 + 3 10 5

=

+

=

1 + 2 = 3 3

=

5 + 1 = 12 6

+

=

=

=

2 + 1 = 4 5

+

=

=

1 + 1 = 2 4

+

=

3 + 1 = 8 4

+

=

1 + 1 = 8 2

+

3 + 7 = 16 8

+

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+

+

=

4.

=

Answers in order from smallest to largest:

Prim-Ed Publishing

=

1 + 1 = 5 3

+

5 + 25 = 100 100

1 + 1 10 9

Answers in order from smallest to largest:

in

Answers in order from smallest to largest:

3.

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Now order the simplified fractions in order from smallest to largest.

Answers in order from smallest to largest:

15

Fractions

Percentages (1)

Name:

Per cent, adv. 1. in every hundred. 2. percentage. 3. one part in every hundred. Percentage, n. 1. rate or proportion per cent. 2. proportion (Taken from The Oxford Dictionary of Current English 1992, New Edn., Oxford University Press, New York)

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7%

g

hin

t clo

INT

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In Advertising

ST

T

S TES MATH

BAN K

75%

ON TT CO ON % YL 75 % N 25

20FF

T CO AST

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Percentages play an important part in our life. It is common to see proportions shown as percentages. For example: In Banking On clothing labels

On tests

2 76 Percentage means hundreds. Therefore 2% is 100 or 0.02. Likewise 76% is 100 or 0.76. MATHS TEST # 1

MATHS TEST # 2

14 / 20 75%

21 / 31 75%

MATHS TEST # 1

MATHS TEST # 2

14 / 20 70%

21 / 31 68%

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Percentages are also easy to compare. For example, in two maths tests, John scored the marks shown on the right. Which of these is the better result? It is difficult to tell just by looking at these marks.

But if we express both of these marks as percentages it is easier to compare them with one another.

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So John did better in the first maths test.

Questions

On a separate piece of paper, answer these questions about percentages. 1. In your own words describe what is meant by a percentage. 2. Is a percentage harder or easier to use than a fraction? Provide an example to illustrate your answer. 3. List ten uses of percentages in every day life. 4. Do you think that percentages will play a greater or lesser part in your life as you grow older? Explain your answer. Prim-Ed Publishing

16

Fractions

Percentages (2)

Name:

A percentage is a fraction of hundredths represented in another form. For example, 20 is a fraction. 20% is the same number represented in a different way. 100 Shade these grids to show the fraction and then write the percentage. 5.

30 = 100

=

95 100 =

%

6.

=

=

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2.

7 100 =

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1.

5 100 =

%

=

%

%

7.

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3.

75 100 =

%

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4.

35 100 =

=

18 100 =

=

%

8.

99 100 =

%

=

%

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In a class mental arithmetic test these were the marks out of 100. Express them as a percentage. 1.

77 = 100

%

6.

63 = 100

%

2.

85 = 100

%

7.

55 = 100

%

3.

94 = 100

%

8.

80 = 100

%

4.

75 = 100

%

9.

70 = 100

%

%

10.

60 100 =

%

98 5. 100 = Prim-Ed Publishing

17

Fractions

Fractions as percentages (1)

Name:

To convert a fraction into a percentage we must represent the fraction with a denominator of 100. To do this we follow a simple procedure. We multiply the fraction by 100 and divide the resulting numerator by the denominator. Follow the examples below:

1 2

x 100 = 100 = 50

= 50%

1 4

x 100 = 100 = 25

= 25%

2 5

x 100 = 200 = 40

= 40%

1

2

4

5

1

Sa m

1

1

pl e

1

1

Now convert these fractions to percentages using this method. 3 4

x

=

=

2.

3 5

x

=

=

3.

7 x 10

=

=

in =

ew

4. 15 x 20

=

=

=

=

=

=

=

6. 17 x 25

=

=

=

Vi

%

=

5. 45 x 50

7.

1 4

x

=

=

=

8.

4 5

x

=

=

=

9.

4 x 10

=

=

=

10.

9 x 10

=

=

=

Prim-Ed Publishing

%

g

1.

%

%

%

%

%

%

%

% 18

Fractions

Fractions as percentages (2)

Name:

More difficult fractions can be converted to a percentage using a calculator. 14 For example, 31 can be calculated by using these steps:

1.

Press 1

2.

Press the รท

3.

Press 3

4.

Press the % button if your calculator has one. This should give an answer of 45.16%, rounded to two decimal places.

4

to enter the numerator into the calculator.

1

to enter the denominator.

Sa m

If your calculator does not have a % button, then you can do the following:

pl e

button.

(a) Press the = button. This should give an answer of 0.45612... (b) Press the x button, and enter 1

0

0

.

g

(c) Press the = button, to give you the percentage, 45.16 rounded to two decimal places.

4 9

ew

1.

in

Using this method and your calculator, convert the fractions below to percentages. Give your answer rounded off to two decimal places.

13.

3 7

2 3

5 14. 21

4 3. 13

7 9. 11

7 15. 12

21 4. 32

46 10. 54

11 16. 19

23 5. 30

18 11. 26

44 17. 60

12 6. 13

1 12. 13

1 18. 99

Vi

6 2. 19

13 7. 17

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8.

19

Fractions

Decimals and percentages

Name:

1. 0.6

6. 0.95

2. 0.4

7. 0.01

3. 0.56

8. 0.39

4. 0.07

9. 0.7

5. 0.25

10. 0.63

Write the following percentages as decimals. 6. 15%

Sa m

1. 75%

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Write the following decimals as percentages.

2. 60%

7. 98%

3. 65%

8. 7%

4. 1%

9. 50%

10. 41%

g

5. 67%

The following are a studentâ€™s test results as fractions. Show each grade as a %.

19 20

ew

Spelling

%

in

Fraction

Fraction

%

Mathematics

45 50

% %

Comprehension

8 10

%

Health

21 25

Science

4 5

%

Social Studies

72 10

Vi

%

1

%

The following are a studentâ€™s test results expressed as a percentage. Find the numerator for each fraction which gives this percentage. %

Spelling

90%

Comprehension

60%

Science

75%

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Fraction

10 5 20

%

Mathematics

84%

Health

74%

Social Studies

75%

20

Fraction

25 50 40 Fractions

Fractions, decimals and percentages

Name:

Write the following diagrams as fractions, decimals and percentages. %

g

Sa m

pl e

Decimal

ew

in

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

Fraction

Match the fraction, decimal and percentage.

Vi

Fraction

3 4

1 2

7 8

17 20 7 12 3 8 1 3 2 5 Prim-Ed Publishing

Decimal (round to 2 d.p.) . 0.583

Percentage (round to 1 d.p.)

0.75

87.5%

0.375

40%

0.4

85%

0.5

33.3%

0.85

37.5%

. 0.333

50%

0.875

58.3%

21

75%

Fractions

Ordering decimals

Name:

Draw a box around the largest decimal in each group. Draw a circle around the smallest decimal in each group.

0.75

0.62

0.51

0.09

2.

0.1

0.09

0.14

0.2

3.

0.95

0.8

0.76

0.08

4.

0.42

0.95

0.59

5.

1.75

0.95

1.9

pl e

1.

0.24

Sa m

1.19

Fill the missing decimals in these sequences.

1. 0.6, 0.7, 0.8,

, 1.0

3. 0.25, 0.30,

, 0.40

4. 0.91, 0.93, 0.95,

g

2. 0.56, 0.57, 0.58, 0.59,

in

, 0.99

Order these decimal fractions and percentages from smallest to largest.

1

3

Vi

ew

1. 4 , 0.5 , 100% , 4

Is 75% bigger 7 than ? 10 7

1

2. 0.2 , 10 , 75% , 0.9 , 10 , 5%

1

3

3. 15% , 2 , 0.65 , 4 , 95% , 0.25

Prim-Ed Publishing

22

Fractions

Adding decimals

Name:

The simple rule when adding decimals is to always keep the decimal points in line.

1.75

For example,

+ 0.64 2.39

1.7

1.

3.45

2.

0.72

+ 2.6

+ 1.94

6.07 1.9

6.75

+ 7.94

7.24

6.

7.34

5.67

1.94

9.34 + 7.89

4.34

+ 5.65

in

+ 6.8

3.07

g

5.

1.46

3.

Sa m

1.9

4.

pl e

Complete these decimal additions.

ew

Set the following decimal additions out below and calculate the answers. 2. 7.04 + 1.9 + 5.95 + 2.3

3. 7.64 + 9.1 + 9.43 + 5.03

4. 7.64 + 55 + 1.95 + 6.95

Vi

1. 1.9 + 0.7 + 6.9 + 4.2

1.

Prim-Ed Publishing

2.

3.

23

4.

Fractions

Subtracting decimals

Name:

The rule for subtracting decimals is the same as adding. It is very important to keep the decimal

1.75

point in line. For example,

– 0.78 0.97 Complete these decimal subtractions.

– 0.72

6.07

5.

– 3.9

– 2.87

6.55

4.75

0.94

– 1.34

– 0.2

ew

in

– 1.98

– 5.1

9.

g

8.

6.24

6.

– 5.34

3.22

7.

3.1

3.

Sa m

– 1.7

4.

2.45

2.

pl e

1.9

1.

0.5

10.

Vi

– 0.03

11.

11.70

1.25

12.

– 7.34

– 0.25

Set the following decimal subtractions out below and calculate the answers. 1. 1.8 – 0.75

1.

Prim-Ed Publishing

2. 23 – 1.95

3. 0.9 – 0.15

2.

3.

24

4. 2.1 – 0.24 4.

Fractions

Review (1)

Name:

1. Complete these equations. (a)

1 + 2

= 1

(b)

25 + 100

= 1

(c)

3 + 10

= 1

(d)

2 + 3

= 1

115 = 100

(c)

35 = 16

+

=

+

+

=

(b)

37 = 10

(d)

5 = 3

+

+

+

+

=

+

+

Sa m

(a)

pl e

2. Change these improper fractions to mixed numbers.

out of 4

=

out of 4

3. Change these mixed numbers to improper fractions. (a)

1 1 = 4

(c)

2 7 = 9

+

=

+

=

3 3 = 4

(d)

1 3 = 7

g

+

(b)

+

=

+

=

out of 4

2 3

(c)

5 8

ew

(a)

in

4. Write two equivalent fractions for each of these fractions. (b)

2 5

(d)

3 4

out of 4

5. Find the lowest common denominator for these fraction pairs.

1 1 , 7 3

(b)

1 1 , 3 4

1 1 4 , 5

(d)

1 1 5 , 10

Vi

(a)

(c)

out of 4

6. Find the lowest common denominator for these fraction pairs and use it to add them together. (a)

1 , 1 4 3

1 + 1 = 4 3

+

=

(b)

2 , 3 3 4

2 + 3 = 3 4

+

=

(c)

2 , 1 5 2

2 + 1 = 5 2

+

=

Prim-Ed Publishing

25

=

out of 6

Fractions

Review (2)

Name:

7. Express these fractions as percentages. (a)

3 4

(b)

7 10

(c)

16 20

(d)

17 25

out of 4

(a)

5 9

(b)

7 11

(c)

21 32

(d)

11 19

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8. Use a calculator to express these fractions as percentages.

9. Complete this table. Decimal

1 4 0.7

Percentage

Sa m

Fraction

out of 4

20%

g

2 25

out of 8

in

10. Order these groups of numbers from smallest to largest.

1 3 , 0.5 , 95% , 4 4

(a)

2 0.3 , 10 , 0.95 , 75% , 5%

ew (b)

out of 2

11. Complete these decimal additions.

1.6 1.5 + 2.6

(b)

Vi

(a)

2.45 0.92 + 1.98

(c)

5.76 1.01 + 3.87 out of 3

12. Complete these decimal subtractions. (a)

1.7 – 1.2

(b)

8.4 – 1.94

(c)

0.95 – 0.4 out of 3

My score for this test was Prim-Ed Publishing

50

or

as a decimal or 26

% Fractions

Answers (1) Common denominator (2)............... page 9

Parts of a whole ................................. page 2 1. 1 , 2 , 3 , 7 , 3 , 3 2 3 5 10 4 8 1 1 3 75 19 7 3 3 3. , , , 2 3 10 100 32 , 10 8 4

1. 4 5. 12 9. 45

2. 10 6. 10 10. 36

3. 24 7. 8

4. 6 8. 12

Common denominator (3)............. page 10

Parts of a set ....................................... page 3 35 77 52 1. 3 , 2 3 100 , 100 , 100 4 3. 3 = 0.3 , 6 = 0.6 25 = 0.25 , 9 = 0.09 10 100 10 10 78 = 0.78 99 = 0.99 , 100 100

1. 21 5. 100 9. 12

Kinds of fractions (1) ........................ page 4

2. 10

3. 10

4. 8

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1. 4 5. 20

2. 10 6. 18

3. 18 7. 10

4. 20 8. 8

10. 45

11. 72

12. 25

Common denominator (4)............. page 11 1 5 4 9 1 1. LCD = 20, 4 + 5 = 20 + 20 = 20 2 1 8 3 11 2. LCD = 12, 3 + 4 = 12 + 12 = 12 2 1 9 4 5 3. LCD = 10, 5 + 2 = 10 + 10 = 10 5 22 17 17 1 4. LCD = 25, 25 + 5 = 25 + 25 = 25

Sa m

Improper to mixed 4 2 2 1 1 2 2 = 4 + 4 =1 4 ,= 2 + 2 + 2 =2 2 Mixed to improper 6 5 11 3 3 1 7 = 6 + 6 = 6 ,= 3 + 3 + 3 = 3

Kinds of fractions (2) ........................ page 5

ew

in

g

Improper to mixed 2 1 1 5 ,2 3 ,3 7 37 50 2 10 , 1 100 , 2 100 6 2 1 7 ,2,4 5 4 2 3 2 8 , 1 12 , 2 9 Mixed to improper 4 17 11 3 , 10 , 4 115 275 13 100 , 100 , 4 10 33 67 7 , 16 , 20 87 25 5 50 , 9 , 3

1. 12 5. 18

2. 30 6. 100

3. 20

Converting to hundredths (1) ...... page 12 1. 50, 0.5 3. 20, 0.2

2. 25, 0.25 4. 10, 0.1

1. 2. 3. 4.

5. 6. 7. 8.

50, 0.5 70, 0.7 20, 0.2 30, 0.3

80, 0.8 40, 0.4 60, 0.6 75, 0.75

Vi

Converting to hundredths (2) ...... page 13 1. 10, 0.1 2. 20, 0.2 3. 5, 0.05

5. 30, 0.3 6. 4, 0.04 7. 68, 0.68

Equivalent fractions (2) ................... page 7

4. 75, 0.75

8. 80, 0.8

Simplify these fractionsâ€Ś

19 1. 95, 20 6 2. 60, 10 3 3. 75, 4 1 4. 33, 3

9 5. 90, 10 1 6. 20, 5 1 7. 2, 50 17 8. 85, 20

1. 3 (5) 4

2. 1 (2) 5

3.

5 (3) 6

4.

1 (5) 2

Common denominator (1)............... page 8 1. 3 cars 3. 7 flowers

Prim-Ed Publishing

2. 4.

4. 8

6 children 3 toys

27

Fractions

Answers (2) Ordering fractions (1) .................... page 14 1 1 1 1 1 1 10 , 8 , 5 , 4 , 3 , 2

Spelling = 95% Mathematics = 90% Comprehension = 80% Health = 84% Science = 80% Social Studies = 75%

10 12 15 30 , 30 , 30 4 6 3 8 , 8 , 8 15 30 40 100 , 100 , 100 60 65 70 100 , 100 , 100

9 Spelling = 10

3 Comprehension = 5 15 Science = 20

Fractions, decimals and percentages .. page 21 10 100 = 0.1 = 10% 95 100 = 0.95 = 95% 70 100 = 0.7 = 70% 15 100 = 0.15 = 15% 75 100 = 0.75 = 75%

2 , 3 4 , 5 5 , 8 13 , 20

7 1 , 12 , 2 11 , 1 , 12 13 3 , 16 , 10 3 7 , 4 , 8

1 2 19 90 3 10 8 15

7 , 12 4 , 5 17 , 30 13 , 20

3 , 5 11 , 12 5 , 8 3 , 4

2 , 3

,1 13 , 16 7 , 8

g

3 5 19 2. 90 3. 17 30 4. 8 15

1.

Sa m

Ordering fractions (2) .................... page 15 1 1 3 3 3 1 20 , 5 , 2 , 4 , 4 , 5

1 1 3 3 3 1 20 , 5 , 4 , 2 , 5 , 4

in

Percentages (2) ................................ page 17 2. 7% 6. 5%

3. 75% 7. 18%

4. 35% 8. 99%

1. 77% 5. 98% 9. 70%

2. 85% 6. 63% 10. 60%

3. 94% 7. 55%

4. 75% 8. 80%

ew

1. 30% 5. 95%

Vi

3. 70% 7. 25%

3 4 7 8 7 12 1 3

1 2 17 20 3 8 2 5

= 0.75 = 75%

= 0.875 = 87.5% . = 0.583 = 58.3% . = 0.333 = 33.3%

= 0.5 = 50% = 0.85 = 85% = 0.375 = 37.5% = 0.4 = 40%

Ordering decimals .......................... page 22 1. 2. 3. 4. 5.

Fractions as percentages (1) ........ page 18 1. 75% 2. 60% 5. 90% 6. 68% 9. 40% 10. 90%

21 Mathematics = 25 37 Health = 50 30 Social Studies = 40

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1. 10 , 12 , 15 30 30 30 2. 6 , 4 , 3 8 8 8 3. 30 , 40 , 15 100 100 100 4. 60 , 70 , 65 100 100 100

Decimals and percentages (cont.) .... page 20

4. 75% 8. 80%

largest = 0.75 largest = 0.2 largest = 0.95 largest = 0.95 largest = 1.9

1. 0.9

smallest = 0.09 smallest = 0.09 smallest = 0.08 smallest = 0.24 smallest = 0.95

2. 0.60

3. 0.35

1 3 4 , 0.5 , 4 , 100%

Fractions as percentages (2) ........ page 19

1.

1. 4. 7. 10. 13. 16.

7 1 2. 5% , 10 , 0.2 , 10 , 75% , 0.9

44.44% 65.62% 76.47% 85.19% 42.86% 57.89%

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2. 5. 8. 11. 14. 17.

31.58% 76.67% 66.67% 69.23% 23.81% 73.33%

3. 6. 9. 12. 15. 18.

30.77% 92.31% 63.64% 7.69% 58.33% 1.01%

4. 0.97

1 3 3. 15% , 0.25 , 2 , 0.65 , 4 , 95%

28

Fractions

Answers (3) 1. 6.2 5. 21.68

2. 6.11 6. 30.14

3. 12.47

4. 19.11

1. 13.7

2. 17.19

3. 31.2

4. 71.54

Subtracting decimals ..................... page 24 1. 0.2 5. 1.21

2. 1.73 6. 1.14

3. 0.23 7. 1.24

9. 0.74

10. 0.47

11. 4.36

1. 1.05

2. 21.05

4. 2.17 8. 3.41

10.

12. 1

3. 0.75

4. 1.86

3.

(a) (c)

21 20

(b)

70%

0.2

20%

0.08 8% 1 3 , 0.5, 4 4 , 95%

2 5%, 10 , 0.3 , 75% , 0.95

11.

(a) 5.7

(b) 5.35

(c) 10.64

12.

(a) 0.5

(b) 6.46

(c) 0.55

Sa m

(d)

7 3 10 2 1 3

0.7

15 4 10 7

(d) (b) (d)

12 10

3 7 4 12, = 12 + 12 = 12 8 9 17 5 12, = 12 + 12 = 12 = 1 12 9 4 5 10, = 10 + 10 = 10

ew

5.

(c)

5 4 25 9

(a)

(b)

25%

g

(c)

15 1 100 3 2 16

0.25

in

(a)

(a) (b)

Review (1) .......................................... page 25 1 75 1. (a) (b) 100 2 7 1 (c) 10 (d) 3 2.

1 4 7 10 1 5 2 25

pl e

9.

Adding decimals ............................. page 23

6.

(a)

(b)

Vi

(c)

Review (2) .......................................... page 26 7.

(a) (c)

75% 80%

(b) (d)

70% 68%

8.

(a) (c)

55.6% 65.6%

(b) (d)

63.6% 57.9%

Prim-Ed Publishing

29

Fractions