Adult Numeracy Level 2

Working With FractionsDave Cross

Suffolk New College

At level 2 we need to be able to convert any fraction into its alternative format, this could be;-

• Proper• Improper• Mixed• Decimal• Percentage

Fractions at Level 2

Revision of fractions at Level 1

• A fraction shows a number as mixture of whole numbers (integers) and parts of a whole (fractions)

11-2

One and a Half =

=3-2

= 1.5

Or Three Halves

One whole and one half

• A proper fraction represents less than one whole

12

The top number (numerator) is lowerin value than the bottom number (denominator)

Revision of fractions at Level 1

• An improper fraction represents more than one whole

32

The top number (numerator) is higherin value than the bottom number (denominator)

Revision of fractions at Level 1

• To turn an improper fraction into a mixed fraction we need to find how many times we can get the denominator into the numerator, using division

32

So here we divide 3 by 2 giving one and a half

Thus 3/2 (improper) = 1 ½ (Mixed)

Revision of fractions at Level 1

Notice the meaning of the line that separates the Numerator and the Denominator = ‘Divided By’

32

If we divide the number above the line by the number below, this will give us the same number expressed as a decimal

1. 52 3. 10=

Revision of fractions at Level 1

Now Fractions at Level 2

Let’s use an example;If our class had 12 people in it,

then three more people joined• Q1 By what fraction has the

original class size increased?

3 out of 12 = 3/12We can simplify this fraction by dividing the top and bottom by their

common factor (here, three goes into 3 and 12, so we divide both by 3)

= ¼

Fractions at Level 2Let’s continue our example;If our class had 12 people in it, then three more

people joined

• Q2 Can you write the new class size as a fraction of the old class size?

1512

54

=

We can simplify this fraction by dividing the top and bottom by their common factor (here, three goes into 15 and 12, so we divide both by 3)

Fractions at Level 2If our class had 12 people in it, then three more people

joined• Q3 What is the new class size as a percentage of the

original class size?

1. 2 54 5. 10 20

In Q2 we found this answer as a simplified improper fraction = 5/4

Can you explain why 1.25 = 125% ?

Adding Fractions at Level 2

• Can you explain why 1.25 = 125% ?

Units Tenths Hundredths1x100% 2x10% 5x1%

1. 2 5Or 100/100 + 20/100 + 5/100 = 125/100

In words ‘one hundred and twenty five PER cent’

Remember- 1per cent is the same as one hundredth

Adding Fractions at Level 2

• Before we can add fractions together we must convert them into the same type of fraction (with the same denominator)

54

+28

712

+ = ?

Adding Fractions at Level 2

54

+28

712

+ =

Look at all three denominators 4, 8, and 12What is a common multiple (what numberdo they have in common?)?

3024

+6

241424

Adding Fractions at Level 2

• Now that we have expressed each fraction in a similar form we can add them all together then finally, we simplify them

3024

+6

241424

+ =

5024

=2512

=21

12