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Introduction Fractions, decimals and percentages all deal with 'a part of' something, whether percentages all dealThis with 'a partofof'mathematics something, whether it be 'part of a it beFractions, 'part of decimals a whole'and or 'part of a group'. area has often caused whole' or 'part of a group'. This area of mathematics has often caused problems for both teachers problems for both teachers and pupils alike; this concern however, is unnecessary if and pupils alike; this concern however, is unnecessary if the correct grounding is given and basic the correct concepts are grounding understood. is given and basic concepts are understood. This group of three copymasters an introduction to fractions, decimals This group of three copymasters providesprovides an introduction to fractions, decimals and percentages. The provide framework provide for the teacher and pupil to develop and activities percentages. Thea activities a framework for the teacherconfidence and pupiland to understanding in this often misunderstood area of mathematics. develop confidence and understanding in this often misunderstood area of It is vital that repeated practical activities are provided so that a solid understanding of basic mathematics.

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concepts is developed. Activities in this book should be repeated using concrete materials and a It isof vital that repeated practical activities are provided that atopic solidif variety different objects. Fractions, like all areas of mathematics, are anso enjoyable understanding of basic concepts is developed. Activities in this book should be understanding exists.

repeated usingcomponent concretehas materials and a variety different Fractions, likeand all A language been provided throughof the inclusionobjects. of several pages of text areas of mathematics, enjoyable topic if understanding exists. comprehension questions.are Thisan serves two main purposes:

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(i) to link mathematics directly to language; and A language component has been provided through the inclusion of several pages (ii) to provide pupils with a written description of what they are learning.

of text and comprehension questions. This serves two main purposes:

Review pages are provided throughout the series and should be used to judge the progress of (i) to linkpupils. mathematics directly to language; and individual

(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 The school fete .................................................. 1 Sharing with a friend ........................................ 2 Sharing with two friends .................................. 3 Sharing with three friends ................................ 4 Sharing ............................................................... 5 Equal parts ......................................................... 6 Halves ................................................................. 7 Quarters ............................................................. 8 Thirds ................................................................. 9 Halves, quarters and thirds ............................ 10 Parts of a group ................................................ 11 Sharing a group (1) .......................................... 12 Sharing a group (2) .......................................... 13 Prim-Ed Publishing

Fraction review (1) .......................................... 14 Fractions .......................................................... 15 Fifths ................................................................. 16 Tenths ............................................................... 17 Sharing fifths and tenths ................................ 18 Shade the fraction ........................................... 19 The same share (1) .......................................... 20 The same share (2) .......................................... 21 The same fraction ........................................... 22 Sharing problems ............................................ 23 Writing fractions (1) ........................................ 24 Writing fractions (2) ........................................ 25 Fraction review (2) .......................................... 26 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

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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

The school fete

Name:

Saturday was the school fete. Everyone in Lindsayâ€™s class was very excited. They were looking forward to the games that would be played. The cake stall and the ice-cream stall were going to be the best places to be.

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On the day of the fete Lindsay and her friend Joanne played many games and won a lot of prizes which they put into a large paper bag. At the end of the day they were very tired and very happy.

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They had a problem. The girls had forgotten who had won which prizes in their bag. They didnâ€™t want to argue, so they decided to share the prizes evenly. That way each girl had the same number of prizes from the fete. Do you think this was the best way to solve the problem?

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1. Why was the class of children excited?

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2. Which were the most popular stalls at the school fete?

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3. How can you tell that the girls did well at the games they tried?

4. What did they do with their prizes?

5. What problem did this cause?

6. How did they solve this problem?

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Fractions

Sharing with a friend

Name:

You and your friend spent Saturday afternoon at the school fete with your parents. Show how you would share these items with your friend. Colour your share red.

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Colour your friendâ€™s share blue.

A bag of marbles

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Cake

A bag of sweets

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Hot dog

Write about times you have shared things with your family or friends.

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Fractions

Sharing with two friends

Name:

If you had two friends at the school fete, show how you would share the items. Colour your share red. Colour one friendâ€™s share blue.

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Colour one friendâ€™s share green.

A bag of marbles

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Cake

A bag of sweets

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Hot dog

Is it harder or easier to share things with two friends or one friend? Why?

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Fractions

Sharing with three friends Name: If you had three friends at the school fete, show how you would share the items. Colour your share red. Colour one friend’s share blue. Colour one friend’s share green.

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Colour one friend’s share yellow.

A bag of marbles

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Cake

Hot dog

A bag of sweets

Explain why you divided up the items this way.

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Fractions

Sharing

Name:

Cathy and Simon were very good friends and always played together at lunchtime. They played basketball and football all of the time.

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In summer, Cathy bought a bag of 20 marbles and she brought them to school to play with Simon at lunchtime. Simon enjoyed playing marbles so much, he soon bought his own bag of 20 marbles.

One day the children were happily playing a game of marbles when a bully came along and told them that he was going to take their marbles.

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The children quickly put all of the marbles in Cathy’s bag, which was the closest, and ran home to Simon’s house. They were happy that they had escaped from the bully and still had their marbles. But they now had a big problem, all of their marbles were in the one bag!

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1. What sports did the children play before they learned marbles?

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2. Why do you think summer is a good time to play marbles?

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3. What was the childrens’ big problem?

4. What was the cause of the childrens’ big problem?

5. Can you think of a way to solve the childrens’ problem?

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Fractions

Equal parts

Name:

To share fairly, each part must be the same size as the other parts. In other words, the parts must be equal.

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Colour the groups which have been shared fairly blue. Colour the groups which have not been shared fairly red.

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Draw a picture of ten pencils shared equally with one other friend.

Draw a picture of twelve sweets shared equally with two other friends.

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Fractions

Halves

Name:

When you share something into two equal parts, each part is called one half.

one half

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Use a line to share these objects into halves. Colour one half blue.

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one half

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Colour the objects below that are shared into halves blue. Colour the objects that are not shared into halves red.

When do you have to share things in halves?

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Fractions

Quarters

Name:

When you share something into four equal parts, each part is called one quarter.

one quarter

one quarter

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Use lines to share these objects into quarters. Colour one quarter.

one quarter

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one quarter

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Colour the objects that are shared into quarters blue. Colour the objects that are not shared into quarters red.

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Fractions

Thirds

Name:

When you share something into three equal parts, each part is called one third.

one third

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Use lines to share these objects into thirds. Colour one third.

one third

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one third

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Colour the objects that are shared into thirds blue. Colour the objects that are not shared into thirds red.

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Fractions

Halves, quarters and thirds

Name:

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Colour the objects shared into halves yellow. Colour the objects shared into quarters green. Colour the objects shared into thirds brown. Colour any other objects red.

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Which is the easiest? Sharing into halves, quarters or thirds? Why do you think so?

Which is the hardest, sharing into halves, quarters or thirds? Why do you think so?

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Fractions

Parts of a group

Name:

Ben

Amanda

Sue

John

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1. How many children are in this group?

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Ben, Amanda, John and Sue are all eight years old. Ben has blue eyes, blonde hair and is tall. John has green eyes, black hair and is short. Amanda has blue eyes, brown hair and is short. Sue has brown eyes, blonde hair and is tall.

Fill in this information about the group of children. out of four have blue eyes.

3.

out of four have blonde hair.

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2.

5.

out of four have green eyes. out of four have black hair.

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6.

out of four are tall.

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7.

out of four are short.

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Fill in this information about your class. 8. How many children are there in your class? 9. How many are girls? 10. How many are boys? 11.

out of

are girls.

12.

out of

are boys.

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Fractions

Sharing a group (1)

Name:

One block out of two is shaded.

One out of two Two blocks out of three are shaded.

Two out of three

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Write the share that is shaded.

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Draw the boxes to match these sentences. Colour the right number of boxes to match the sentence.

one out of two

two out of four

one out of three

two out of five

four out of four

one out of four

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Fractions

Sharing a group (2)

Name:

Match the sentence to the object. one out of two

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three out of four

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one out of four

one out of three

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three out of three

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two out of three

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Write the sharing sentence to match the drawing.

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Fractions

Fraction review (1)

Name:

1. Share the sweets with one friend by colouring.

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3. Draw boxes and colour two out of four.

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2. Share the marbles with two friends by colouring.

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4. Draw boxes and colour one out of three.

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5. Write the word sentence for these fractions.

6. Mary, John and Susan collected 15 football cards which they shared. How many cards would each person get?

My mark for this test was out of Prim-Ed Publishing

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. Fractions

Fractions

Name:

When we share things it can be done in two ways.

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The first way is where we share one object, like a cake, among a group of people. Each person gets one share of the cake. This share can also be called a fraction. Draw lines to show how you would share this cake among four people.

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The second way is where we share a group of objects, like a bag of sweets, among a group of people. Each person gets one share of the sweets. This share is also called a fraction. Show how you would share these mints among three people.

A fraction is a part of something or a part of a group of things.

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The very important part about a fraction is that it is an equal part. This is because when we share, it is very important that all shares are the same, or equal. Colour the objects which have been shared into fractions.

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Fractions

Fifths

Name:

When we share an object into five equal parts, each part is called one fifth.

one fifth

one fifth

one fifth

one fifth

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one fifth

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Use lines to share these objects into fifths and colour one fifth.

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Colour the objects that are shared into fifths blue. Colour the objects that are not shared into fifths red.

Was this harder than other sharing activities? Why/why not?

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Fractions

Tenths

Name:

When we share an object into ten equal parts, each part is called one tenth.

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one one one one one one one one one one tenth tenth tenth tenth tenth tenth tenth tenth tenth tenth

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Use lines to share these objects into tenths and colour one tenth.

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Colour the objects that are shared into tenths blue. Colour the objects that are not shared into tenths red.

Was this harder than other sharing activities? Why/why not?

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Fractions

Sharing fifths and tenths

Name:

Two blocks out of five are shaded.

2 out of 5 Eight blocks out of ten are shaded.

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8 out of 10 Complete these number sentences.

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out of out of

out of

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out of

out of

Shade the boxes to match the sentences.

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7 out of 10 2 out of 5

3 out of 10 4 out of 5 5 out of 10 5 out of 5 Prim-Ed Publishing

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Fractions

Shade the fraction

Name:

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Colour one half of each shape.

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Colour one third of each shape.

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Colour one fifth of each shape.

Colour one tenth of each shape.

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Fractions

The same share (1)

Name:

As we are finding out, fractions are equal shares of an object or a group of objects. Some fractions can be the same. How can this be?

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If a chocolate bar was shared between two people they would get one share out of two. Draw this share on the chocolate bar.

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If a chocolate bar was shared among four people each person would get one share out of four. Draw this share on the chocolate bar.

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If one of the four people gave you their share you would now have two out of the four shares. Draw this on the chocolate bar.

Now look back at your first chocolate bar. Is there any difference in the piece of chocolate that you will get? This is because one share out of two is the same as two shares out of four. Prim-Ed Publishing

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Fractions

The same share (2)

Name: Draw lines to share this cake equally among four people.

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Draw lines to share this cake equally between two people.

Shade one share of the first cake. Shade two shares of the second cake. Which shaded share would you like to have?

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Draw lines to share this chocolate bar equally between two people.

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Draw lines to share this chocolate bar equally among four people.

Shade one share of the first chocolate bar. Shade two shares of the second chocolate bar. Which shaded share would you like to have?

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Fractions

The same fraction

Name:

Follow the instructions and place a tick next to any of the shares below that are the same size. Shade one share out of two.

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Shade two shares out of three. Shade two shares out of four.

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Shade seven shares out ten. Shade three shares out of four. Shade five shares out of ten.

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Circle the sets below that are divided into shares of the same size.

Can you draw any other shares that are the same size?

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Fractions

Sharing problems

Name:

Answer the following sharing problems. Draw a picture of the problem if it will help you. 1. If I shared ten marbles between two children, how many marbles would they each have?

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2. If I shared twelve marbles among three children, how many marbles would they each have?

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out of

out of

out of

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3. If I shared twenty sweets between two children, how many sweets would they each have?

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4. There were ten basketballs and five basketball teams. How many balls did each team have for training? out of

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5. There were twelve football cards and four children. How many cards does each child get? out of 6. A farmer had twelve horseshoes to put on his horses. If he had three horses, how many shoes did each one get? out of

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Fractions

Writing fractions (1)

Name:

Colour one share of two. How many parts are shaded?

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How many parts altogether?

You have just written the sharing as a fraction!

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1 The fraction is written as â€” . 2 This means that we have one of the two shares. We use a line to show a fraction.

The number above the line is called the numerator and tells us how many shares we have.

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The number below the line is called the denominator and tells us how many shares there are altogether.

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Finish writing these fractions.

=

=

= Prim-Ed Publishing

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2 10 24

=

3

=

2

=

3 Fractions

Writing fractions (2)

Name:

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Write the correct fraction for these drawings.

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3 4 2 3 5 8 1 6

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Shade the boxes to show these fractions.

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Fractions

Fraction Review (2)

Name:

1. Shade three shares out of five. 2. Shade six shares out of ten. Write the word sentence for these fractions. 3.

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out of

4.

2 5

6. Shade the box.

1 3

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5. Shade the box.

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out of

7. Write the fraction for

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8. Write the fraction for

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My mark for this test was out of .

Written as a fraction this is

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Fractions