Vocabulary: fraction improper terminating decimal
simplest numerator recurring percentage
order equivalent vinculum ascending
proper round off lowest common denominator
highest common factor denominator mixed numeral
number line descending
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 ? 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 ? equivalent to ?
equivalent to ? 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
IMPROPER FRACTION ~ MIXED NUMERAL ~
numerator larger than denominator whole number and a fraction part
eg
eg 5 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. + = + =
Subtracting Fractions with Different Denominators
OR use equivalent fractions (find them with the same denominator) e.g. - = =
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. 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 of $8 means all of the following:
Calculator Practise
One quantity as a fraction of another 1. 2.
3. 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 means 0.333333