1. Vocabulary: fraction improper lowest common denominator
terminating decimal highest common factor
simplest numerator denominator
recurring percentage mixed numeral
order equivalent number line
vinculum ascending descending
proper round off

2. Main points covered in this unit:
Compare fractions using equivalence or number lines
Find the Highest common Factor (HCF) and Lowest Common Denominator Simplify fractions
Convert between fractions, decimals and percentages including improper fractions and mixed numbers
Complete the four operations with fractions and mixed numbers
Calculate fractions and decimals of quantities
Round off decimals
Express one quantity as a fraction of another
Order fractions, decimals and percentages

3. Ways to Represent a Fraction
How many ways can you think of to show the fraction 2 3 ? In your group, think of as many as you can and write them onto the fraction. Choose the four ways that you think show the fraction most clearly and write them in your book. Where does the word ‘fraction’ come from? 14th century - Latin fractio "a breaking," especially into pieces.

4. Fraction Wall
Use the fraction wall to complete the equivalence statements: equivalent to 1 2 ? equivalent to 3 4 ? equivalent to 2 3 ?

10. Definitions
A fraction gives one number as a part of another number. Another way to say this is a fraction is a part of a whole. PROPER FRACTION ~ numerator smaller than denominator eg 3 4 IMPROPER FRACTION ~ numerator larger than denominator eg 4 3 MIXED NUMERAL ~ whole number and a fraction part eg 5 1 3

13. Write as mixed numerals:
1. 9/4 = 2. 22/5 = 3. 16/3 =

14. 1. 3 2/5 =
2. 2 4/7 =
3. 4 2/3 =

19. What about these? A
1 2 B 1
1 4
1 4 A 1 B A
3 4 B 1

20. Adding and Subtracting Fractions
Adding fractions with the same denominator:
Subtracting fractions with the same denominator:

22. Adding Fractions with Different Denominators
OR use equivalent fractions (find them with the same denominator) e.g = = 19 20

23. Subtracting Fractions with Different Denominators
OR use equivalent fractions (find them with the same denominator)
e.g =
= 7 20

27. Multiplying Fractions

31. Dividing with Fractions

34. The easier way when dividing fractions is to use the RECIPROCAL of the second fraction, multiplying instead of dividing. You get the same answer as you would by dividing.

37. Place Value and Decimals
Using Decimals
Place Value and Decimals

46. Rounding off
Remember the ‘Rounding Coaster’? It works with decimals too. A ‘5’ or larger rounds up, a ‘4’ or lower rounds down. Round to 2 decimal places; = = = =

49. Adding and Subtracting Decimals
Make an estimate first
Line up decimal points so they are under each other
Fill empty places with zeroes to avoid confusion

51. Multiplying Decimals Estimate the answer first
Ignore decimal points and multiply the numbers
Count how many numbers after the decimal point in the question; answer must have the same number.

53. Powers of 10
To multiply by a power of 10, count the zeroes, then move the decimal place that many places to the right. If you need to, add extra zeroes. To divide by a power of 10, count the zeroes, then move the decimal place that many places to the left. If you need to, add extra zeroes.

55. Dividing Decimals
When dividing decimals, make sure you keep the decimal points aligned.
Add a zero if required to complete the division.

57. Finding a Fraction of a Quantity
Finding a fraction of a quantity is just like multiplying the fraction by the amount. For example, Find 1 4 of $8 means all of the following:

59. Calculator Practise

60. One quantity as a fraction of another
Make the measurement units the same
Write as a fraction – the first as the numerator, the second as the denominator
Simplify the fraction if necessary

62. Recurring Decimals
Recurring decimals go on forever. e.g means …… On your foldable, write 0 .1 , 0 .5 , , , 4. 1 , as fractions