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

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

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.

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

Signpost p 318 Q1-10

Signpost p 322 Q1-4

Signpost p 322 Q6-7

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

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

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

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

Adding Fractions with Different Denominators OR use equivalent fractions (find them with the same denominator) e.g. 7 10 + 1 4 = 14 20 + 5 20 = 19 20

Subtracting Fractions with Different Denominators OR use equivalent fractions (find them with the same denominator) e.g. 3 5 - 1 4 = 12 20 - 5 20 = 7 20

Multiplying Fractions

Dividing with Fractions

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.

Place Value and Decimals Using Decimals Place Value and Decimals

Rounding off The ‘Rounding Coaster’ works with decimals too. A ‘5’ or larger rounds up, a ‘4’ or lower rounds down. Round to 2 decimal places; 3.348 = 9.163 = 10. 6555 = 0.001 =

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

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.

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.

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

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:

Calculator Practise

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

Recurring Decimals Recurring decimals go on forever. e.g. 0 .3 means 0.333333……