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Year 8 Mathematics
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Fractions
Learning Intentions
• Learning Intentions
– Understand that fractions indicate that a whole is
divided into parts
– Understand the terms numerator and denominator
– Be able to compare and order fractions with different
denominators
– Be able to add simple fractions and mixed numbers
– Be able to subtract simple fractions and mixed
numbers
What is a Fraction
• A fraction is a quantity that has been divided
into parts
• For example: A Yorkie bar has seven chunks. If
you are given two then you have of the bar.
• The denominator indicate the number of parts
the bar has been divided into
• The numerator indicates the number of parts
that you have,
Equivalent Fractions
• Shade one fifth of each of the following
diagrams and then write the fraction.
Equivalent Fractions
• An equivalent fraction is a fraction written using
different numbers, but is the same size as the original.
• For example, we can write the fraction one fifth in a
number of different ways:
1 2
3
4
5
6





5 10 15 20 25 30
• All these fractions are the same if you multiply the
numerator and denominator by the same number.
Simplifying Fractions
• In the previous example the fraction can be
written in a number of ways.
• We should always try to write a fraction with
the smallest denominator.
• This is called simplifying the fraction.
• Simplify the following fractions:
8
18
24
32
2
14
12
60
Comparing Fractions
• Sometime we need to compare fractions to
find out which is the largest.
• To do this we need to change the fractions so
that they have the same denominator.
Comparing fractions
• Which fraction is the larger 3 or 7 ?
5
11
• To compare these fractions, we need to make
the denominators the same. We will make
them both 55.
• We multiply the numerator and denominator
of the first fraction by 11.
• We multiply the numerator and denominator
of the first fraction by 5.
33
35
or
• We now can compare the fractions! 55 55
Order! Order!
• To place fractions in order we need to express
them with the same denominator
• ASCENDING order places the fractions from
smallest to largest
• DESCENDING order places the fractions from
largest to smallest
Example
• Places the following fractions
in ascending order:
• The common denominator
(the LCM of the denominators)
is 20 so we need to express
all the fractions out of 20.
• Putting them in order gives:
• And putting them in
their original form:
3 1 7 17 3
5 2 10 20 4
12 10 14 17 15
20 20 20 20 20
10 12 14 15 17
20 20 20 20 20
1 3 7 3 17
2 5 10 4 20
Adding Fractions
• If you were given 3 chunks of Yorkie and your friend
was given 2, what fraction of the bar would you have?
3
2

• We need to calculate:
7
7
5
• The answer is
7
• We haven’t changed the number of chunks in the bar,
so the denominator stays the same.
• We have more chunks so the numerator increases.
Adding Fractions
• When adding fractions, we add the numerators and
keep the denominators the same.
• Add the following fractions
Subtracting Fractions
• If you were given 3 chunks of Yorkie and you eat
2, what fraction of the bar would you have?
3 2
• We need to calculate: 
7 7
1
• The answer is
7
• We haven’t changed the number of chunks in the
bar, so the denominator stays the same.
• We have less chunks so the numerator decreases.
Subtracting Fractions
• When subtracting fractions, we subtract the
numerators and keep the denominators the same.
• Subtract the following fractions
Different Denominators
• When adding fractions with different
denominators we need to change the
fractions into equivalent fractions with the
same denominator
• Add the following fractions
Mix it up
• What happens if you have three chunks of
Yorkie and your friend has five. How much do
you have now?
3
5

• We need to add
7
7
8
• Which gives
7
• This means that we have the 7 chunks making
one whole bar and one chunk left over!
• We write this as 1 1
7
It’s Improper
• The number 8 is called an IMPROPER fraction
7
because the numerator is larger than the
denominator.
1
• The number 1 is called a MIXED number
7
because it consists of a fraction and a whole
number.
• At the end of a sum, we always change
improper fractions into mixed numbers.
Improper Fractions
• Convert the following improper fractions into
mixed numbers:
Going backwards
• Sometimes we need to change mixed
numbers into improper fractions.
3
• For example, convert 2 into an improper
7
fraction.
• Let’s try drawing a diagram.
• Now divide the two wholes into sevenths,
3
17
2
•
=
7
7
Calculate:
• Convert each of the following fractions into
improper fractions:
Adding them up
• When adding mixed numbers we need to
change the numbers into improper fractions
first.
3
5
• Calculate 1  2
5
7
Take it Away
• When subtracting mixed numbers, we also
need to change mixed numbers into improper
fractions.
3
1
• Calculate: 3  1
7
5
Decimals
• Decimals are used for numbers less than 1.
• We extend our number system to the right.
Hundreds
Tens
units
tenths
hundredths
thousandths
3
2
1
5
9
7
Place Value
• Write the value of the 5 in each of the
following numbers:
– 35.327
– 432.456
– 3.578
– 267.435
Place Value
• Write each of the following numbers as
decimals
– One thousand two hundred and six tenths
– Three units and fifty tenths
– Forty and three hundred and two thousandths
– Four units and three fifths
– Seven hundred and sixteen fiftyths
Adding and Subtracting
• When adding and subtracting decimals the
decimal point must not move.
• Add or subtract the numbers in the columns
as normal
• Calculate the following:
 2.21 + 7.994
 13.65 + 7.0026
+ 0.6
Adding and Subtracting
• Calculate the following:
 13.334
– 6.4
 8 – 0.645
Multiplying by 10, 100, etc
• When multiplying by 10, 100, 1000, etc we
move the number to the left by the number of
zeros.
• Calculate:
– 0.36 x 1000
– 0.0054 x 100
– 4.506 x 10
Dividing by 10, 100, etc
• When dividing by 10, 100, 1000, etc we move
the number to the right by the number of
zeros.
• Calculate:
– 7.5 ÷ 1000
– 1.574 ÷ 100
– 0.0238 ÷ 10
Multiplying Decimals
• When multiplying decimals
– remove the decimal points
– multiply the numbers
– put the decimal point back
– there must be the same number of decimals in
the answer as there were in the question
Multiplying Decimals
• Calculate:
– 51.36 x 6
– 4.5 x 8.2
– 0.46 x 30.5
Dividing Decimals
• When dividing decimals
– Change the sum into an equivalent sum by
multiplying each number by 10, 100, 1000 so that
the divisor has no decimal places
– Use short or long division
– Do not move the decimal point
Dividing Decimals
• Calculate:
– 0.475 ÷ 5
– 142.5 ÷ 2.5
– 45.44 ÷ 0.32
Converting Fractions to Decimals
• To convert a fraction to a decimal we need to
use short or long division.
• Convert the following to decimals:
–
7
8
–
32
40
Converting Decimals to Fractions
• To convert a decimal to a fraction, write the
number as a fraction out of 10, 100, 1000, etc
• Convert the following decimals to fractions:
– 0.48
– 1.357