Skills With Numbers

Fractions

FRACTIONS

7 16

Creating a Fraction Cake is cut into 4 equal parts

4

a Cake

Creating a Fraction One of the equal parts is removed.

1 4

3 How How much much of has the cake beenremains? removed?

Creating a Fraction • First find how many equal parts a whole has been divided into. • This is the value that goes on the bottom (denominator) of the fraction. • The value of interest, what you have, is placed on the top of the fraction.

Creating a Fraction How many are there? This is the bottom value.

16

Creating a Fraction Fill in the top number to state what fraction of the total number remains.

16

Creating a Fraction Fill in the top number to state what fraction of the total number remains.

16

Creating a Fraction Fill in the top number to state what fraction of the total number remains.

16

Creating a Fraction Fill in the top number to state what fraction of the total number remains.

16

Creating a Fraction Did you get these answers? 12 16

7 16

8 16

5 16

You are now able to write fractions. Try the next problem.

Creating a Fraction A set of coloured dots will appear. This represents a small section of a TV screen. The colours used are: Blue

Green

Cyan

Magenta

Red

Creating a Fraction Write each colour as a fraction of the total.

Answer will appear in 1 minute

Creating a Fraction Solutions

4 Blue 20 7 Red 20

5 Green 20 Cyan

Magenta

2 20

2 20

Creating a Fraction â&#x20AC;˘ You can create a fraction from almost anything. The process is always the same. â&#x20AC;˘ By keeping the fraction in the original form you know what the practical situation consists of. For example, there were 20 dots and 4 of them were blue.

Creating a Fraction • Keeping the original form is also useful in probability. • It is often necessary to write a fraction in its simplest equivalent form. • Writing a “simpler” equivalent fraction has more meaning in many cases.

Simplest Form Letâ&#x20AC;&#x2122;s revisit the TV dots problem and write those fractions in a simpler form â&#x20AC;&#x201C; where possible.

4 Blue 20 How do we reduce this fraction to its simplest form?

Simplest Form The first thing to try is to see if the top number will divide into the bottom number without any remainder.

4 Blue 20

20 รท 4 = 5

4

It works! 1

20

5

Simplest form

Simplest Form Challenge. For the other fractions found from the TV dot pattern, find which of these can be written in their simplest form using the same method. Check your answers with your tutor

Simplest Form This is the second stage of your learning. If you need further knowledge of working with fractions then continue. You have covered the first basics of how to simplify a fraction. We will now progress onto the other methods of finding this for each fraction.

Simplest Form The first method tried was division. If this does not work then we progress to the other methods. The next process is to find the largest number possible that will divide into both numbers in the fraction. Note: not everyone is good at this particular process but you should try it first.

Simplest Form Take the fraction:

6 10

6 will not divide into 10 (try it) Descend from 6 and try dividing each fraction number by each value as you go through them. That is, try 5, then 4, then 3 and so onâ&#x20AC;Śâ&#x20AC;Ś

Simplest Form Does 5 divide into both numbers? no

5

6 10

yes

no

6

no

10

Try 4 yes

6

no

10

Try 3

Simplest Form So far nothing has worked. We have still to try 2. Both numbers yes 6 can be divided 2 yes by 2 10

3 10 รท 2 = 5 6 รท2=

This is the simplest form

Simplest Form We now need to practice this process. We will look at one more example and then you can practice on some other fractions. Remember to try the first method before reducing the dividing value.

Simplest Form Reduce this fraction to its simplest form.

12 30 12 does not divide into 30 11, 10, 9, 8, and 7 do not divide into both 6 works

12 รท 6 = 30 รท 6 =

2 5

Simplest form

Simplest Form Time to test yourself to see if you are making progress. Try the fractions below remembering to try method 1 first.

3

4

2

6

9

18

26

20

7

16

14

5

54

72

36

75

Screen will change in 1 minute

How Did You Do? â&#x20AC;˘ Show your solutions to your tutor. â&#x20AC;˘ If you are still not sure about simplifying then repeat the work covered.

Simplest Form Some of you may have found it took a little while to find the value that divides into both fraction numbers. If you found this a bit off-putting then try this final method. This involves reducing the size of the fraction one step at time.

Simplest Form A) For the fraction below the bottom number cannot be divided by the top number.

24 78 Both numbers are even, so they will divide by 2. This gives:

12 39

Simplest Form 12 39

One odd number so 2 will not work again.

Now try dividing both numbers by 3, then 4 etc. 3 works!

This gives

4 13

Nothing else will divide into 4 and 13, so this is the simplest form.

Simplest Form You should now practice reducing fractions. Try some paper-based problems to test your knowledge. Show your solutions to your tutor for feedback.

Find a Fraction of a Value It is often the case that a value is split into parts. We often need to find a fraction of a value and this is dealt with next. An example of this might be: I need to find

2 3

of ÂŁ7.50

Find a Fraction of a Value Now you are aware of what we will be working on. We will look at various examples of this and show how to reach the solution. You can then practice this process on some problems provided.

Find a Fraction of a Value We will keep it simple at first. What is

3 4

of 20?

3 ร 20 รท 4 = 15 Always divide by the bottom number. Always multiply by the top number. When you see of this means multiply.

Find a Fraction of a Value More examples What is

1 3

of 144?

1 ร 144 รท 3 = 48

Find a Fraction of a Value More examples What is

2 5

of 225?

2 ร 225 รท 5 = 90

Find a Fraction of a Value More examples What is

3 7

of 63?

3 ร 63 รท 7 = 27

Find a Fraction of a Value More examples What is

5 12

of 60?

5 ร 60 รท 12 = 25

Find a Fraction of a Value Try the problems below. I need to find:

2 5 5 32

of 100

3 8

of 96

of 3520

11 12

of 384

Page will change in 1 minute

Find a Fraction of a Value • How did you do? • If you are not sure about your solutions repeat this section or speak to your tutor. • If you need to learn more on fractions then let’s take the next step.

Fraction of a Fraction You may require to find a fraction of a fraction. Confused? Example Half of a group of people were female, and of those two thirds were over 21 years old.

Fraction of a Fraction Here we have two fractions.

1 2

and

2 3

What I want to do is find what fraction of Half of a group of people were female, and the group is female and over 21. of those two thirds were over 21 years old. Rather than have two fractions I will change this problem into one fraction.

Fraction of a Fraction Half of a group of people were female, and of those two thirds were over 21 years old. We want to find

2 3 2 3 2 3

of × × ×

1 2 1 2 1 2

2 6

Fraction of a Fraction Half of a group of people were female, and of those two thirds were over 21 years old. We now know that this is represented by one fraction for the whole group.

2 6

1 3

So, this is one third of the group. If we know the group size we can find one third of this amount.

Fraction of a Fraction Example Members of a bowling club were asked to vote on increasing the annual fees. Of the 150 members four fifths voted, and from the members that voted three quarters voted yes. How many of the total membership voted to increase the fees?

Fraction of a Fraction We need to find

3 4

×

4 5

3 4

of the

=

12 20

4 5 =

that voted.

3 5

Fraction of total membership voting yes.

150 × 3 ÷ 5 = 90

members voting yes

We could have cancelled the 4’s before multiplying. This is something worth doing before multiplying as it can greatly reduce the complexity of any problem.

Fraction of a Fraction Try the following problems putting the answer in simplest form where applicable.

2 5 5 8

×

1 4

3 4

×

3 5

6 15

×

3 5

×

5 10

(answers will appear in 1 minute)

If you are unsure of any answers see your tutor.

Fraction of a Fraction Solutions

1 10

9 20

3 8

1 5

Fraction of a Fraction Solve the following practical problems. 1. An orchard supplies apples to a supermarket chain. Three quarters of the orchard apples meet the criteria and of this eight-ninths are sold to the public. How much of the orchard fruit is sold to the public? 2. A car dealer states that a new car will be worth threequarters of its value after the first year and two-thirds of its subsequent value over the following two years. What fraction of the new price will the car be worth after the three years? If unsure of solutions check with your tutor

Need to Know More? â&#x20AC;˘ If you need to learn more on fractions then you should go on and complete this presentation. â&#x20AC;˘ We will cover problems where you will require to: divide fractions, add fractions, and subtract fractions.

Comparing Fractions There may be times where you will need to compare fractions and express the answer in fraction form.

To understand where this type of situation may arise letâ&#x20AC;&#x2122;s look at a basic problem.

Comparing Fractions

Here we have two identical pizza each divided into eight equal parts. One eighths of the left-hand pizza is removed and three eighths of the right-hand pizza is removed.

Comparing Fractions How does the missing fraction of the right-hand pizza compare to the missing fraction of the left-hand pizza? When we compare values we divide to find the relationship. For example, how does 20 compare to 5? 20 รท 5 = 4 So we have:

20 is 4 times larger than 5.

3 8

รท

1 8

Comparing Fractions You may have realised that 3/8 is 3 times 1/8 and this is the solution we will arrive at (3). In many cases the answer is not obvious so we must learn the process that will provide the answer. The fraction that you will be dividing by is inverted (turned upside-down) and then the fractions are multiplied.

Letâ&#x20AC;&#x2122;s try it.

Comparing Fractions 3 8

รท

3 8

1 ร 8

1 8

Remember this process

=

24 8

=

3

Comparing Fractions Comparing fractions (dividing) process The fraction you are dividing by, is INVERTED and then the fractions are: MULTIPLIED X X X X

X

X

X

X

Comparing Fractions Example Jennifer and John each had to shift 100 bags of compost. Jennifer shifted John shifted

3 5

3 4

of the bags

of the bags

How does the amount Jennifer shifted compare to the amount John shifted?

Comparing Fractions We are comparing Jennifer’s amount to John’s so we divide Jennifer’s by John’s

3 3 ÷ 4 5 3 3 × 4 5

Now implement the process

15 = 12

=

5 4

This tells us that – for every 4 bags John shifted Jennifer shifted 5 bags

Comparing Fractions Exercise

2 5

Find the following in the simplest form.

÷

1 4

3 8

÷

2 4

Irena sold 65 out of 100 raffle tickets and Paula 80 out of 100 raffle tickets. Simplify each fraction then compare Paula’s sales to Irena’s From a plate of sausage rolls, Richard ate one quarter and Jim ate five sixteenths of the sausage rolls. Compare Jim’s amount to Richards Slide will change in 1 minute

Adding & Subtracting Fractions Adding and subtracting is one of the first things we learn to do. Unfortunately, when dealing with fractions it is not so straightforward. We will deal first with fractions with the same denominator, these being quite straightforward, then with those with different denominators, these being more difficult.

Adding & Subtracting Fractions Fractions with the same denominator Before showing examples with fractions, think about adding two whole numbers Take 3 + 5

the answer is obviously 8

This can be written as shown below

3 1

+

5 1

=

8 1

Adding & Subtracting Fractions 3 1

+

5 1

=

8 1

The important thing to note here is that we simply added the top values in the â&#x20AC;&#x153;fractionâ&#x20AC;? but did nothing with the denominator. If the denominator is the same value then you only add, or subtract the top values.

Adding & Subtracting Fractions Examples

3 10

+

4 10

7 8

_

5 8

=

7 10

7 16

=

2 8

13 20

+

_

1 16 2 20

=

8 16

=

11 20

Adding & Subtracting Fractions Try the following problems

3 5

+

1 5

15 16

_

7 16

=

3 32

=

13 27

Screen will change in 20 seconds

+

_

11 32

=

8 27

=

Adding & Subtracting Fractions Fractions with different denominators We cannot add or subtract fractions unless the denominator is the same. This means we must change the denominator of one or more of the fractions before we can add or subtract. Same as 1/2

Simple example

1 4

+

1 2

=

1 4

+

2 4

=

3 4

Adding & Subtracting Fractions In some cases it is quite straightforward to make the denominators the same, as in the previous example. However, it is often the case that it is a bit more difficult to change one fraction to match another. To avoid having to cover the range of methods to achieve this I will stick to one method that always works when adding/subtracting two fractions. Note, this method often leaves you with the task of having to state the answer in the simplest form.

Adding & Subtracting Fractions Method â&#x20AC;&#x201C; cross multiplication Multiply opposite top value by denominator of the other fraction. Multiply the two denominators together. Example

10 21 2 + 3 = 7 5 35

=

31 35

Adding & Subtracting Fractions Method â&#x20AC;&#x201C; cross multiplication Example 2

24 33 6 + 3 = 11 4 44

=

57 44

Adding & Subtracting Fractions Method â&#x20AC;&#x201C; cross multiplication Example 3

15 6 1 5 6 3 18

=

=

9 18

=

1 2

Adding & Subtracting Fractions Try the following problems

3 4

+

2 5

5 6

_

3 4

=

3 32

=

3 8

+

_

1 2

=

1 3

=

Screen will change in 1 minute. If you have problems with the above questions see your tutor.

What to do Now This presentation is designed to provide you with the basics of working with fractions. If you were able to complete the problems in this presentation without too much difficulty then you will be able to go on and improve your ability with fractions.

If you wish to further your knowledge of fractions and their application speak to one of the numeracy tutors. Your tutor will know what the resources are for you and your needs.

Other Similar Presentations There are 3 other presentations that are available to you that use the same method of presentation.

1 Percentages 2 Working with Money 3 Ratios

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FRACTIONS powerpoint LOOP

Fractions Skills With Numbers 7 16 FRACTIONS 4 Creating a Fraction 1 How much has been removed? How much of the cake remains? Creating a Fra...