Cancelling Fractions
12
84
Cancel these fractions to their lowest terms
20
45
27
42
5
45
40
90
16
96
120
600
1
Which of these fractions is the odd man out?
1
3
2
6
12
36
30
48
60
96
15
32
5
8
102
404
22
77
12
42
7
17
2
7
2
Converting fractions to decimals
Which fractions do you know the decimal equivalent of?
Terminating decimals
Recurring Decimals
Investigate fractions with a denominator of 7.
Investigate fractions with a denominator of 9.
Try to find a rule for fractions which terminate.
Test it out on the fractions:
3
Can this recurring decimal be expressed as a fraction?
0.678678678678...
0.454545454545....
3.153153153....
page 454
4
Show that 0.696969..= 23/33
5
Ordering fractions
There are two main ways to order fractions:
• if you can use a calculator, change them to decimals.
• use equivalent fractions to compare.
Put these fractions in order of size, starting with the smallest:
5
1) 6
3
10
2
3
2) 1, 2, 1, 2
4 5 6 7
1
2
no calculator
no calculator
3) 5, 3, 4, 3
8 7 9 10
4) 7, 4, 6, 5
11 15 12 7
1, 2, 5,
6 9 12
7
15
6
Finding a fraction of an amount.
5 of 88
8
means find one eighth, then find 5 of those
work out:
3 of 35
7
4
5 of 45
2 of 36
9 7
Andrew ate a quarter of a pizza, Adrian ate a third of the pizza. How much was left for Matthew?
Thea, Bella and Hannah shared a bar of chocolate.
Thea had 3 tenths, Bella had one sixth so how much did Hannah have?
8
Adding and subtracting fractions with whole numbers
2
1
+ 5
4
6
2
1 ­ 5
4
6
3
1 ­ 2
7
9
9
Multiplying Fractions
This is the easiest of all the fraction questions.
Multiply the numerators together.
Multiply the denominators together.
That's it!
2 x 5 = 10
3 7 21
If you have a whole number, change it to an improper fraction:
2
1 x 3 =
3
4
A fraction trick: when multiplying fractions, cancel where you can and you will save yourself work.
For example : page 29
10
Dividing by a fraction
This is easy if you can remember the rule:
Turn the second fraction upside down and multiply!
C5 ­ C9 all parts
Fractions divided by fractions
3÷1
4 2
2÷7
9 10
page 286
11
Find 3 fractions that have a sum of 1, but all have different denominators.
12
Solve:
Homework: convert these decimals to fractions:
0.56 0.605
0.45 3.7826
13
Solving problems with fractions.
1. A cake is divided up between 3 people.
Adrian has two fifths, Sean has two sevenths and Ben has the rest.
a﴿ How much does Ben get?
b﴿ Who has the biggest piece?
c﴿ If Christian gave half his piece to Kieran how much would they each get?
2. A bag of smarties is shared between 4 people.
Aisling has one fifth, Orla has one fifteenth, Rebecca has one third and Alice has 60 sweets.
How many sweets did they have?
3. A school day of 6 hours is divided into modules of three­quarters of an hour. How many modules are there in a day?
4. ﴾extension﴿ The Egyptians used fractions but only those with a numerator of one ﴾called unit fractions﴿. They would not repeat a fraction in working.
How might they have made 5 ?
8
What about 7 ?
12
14
5
of a school day is spent in lessons.
6
What percentage of the day is spent in lessons? 72% of students like sport.
What fraction of the students like sport?
15
Work out:
5
6
7
10
3
30
3
4
2
3
60
1
2
2
5
4
15
9
20
16
understand equivalent fractions, simplifying a fraction by cancelling all common factors
order fractions by rewriting them with a common denominator
calculate a given fraction of a given quantity, expressing the answer as a fraction
express a given number as a fraction of another
add and subtract fractions by writing them with a common denominator
perform short division to convert a simple fraction to a decimal
addition, subtraction, multiplication and division of mixed numbers
multiply and divide a given fraction by an integer, by a unit fraction and by a general fraction
distinguish between fractions with denominators that have only prime factors of 2 and 5 ﴾which are represented by terminating decimals﴿, and other fractions ﴾which are represented by recurring decimals﴿
convert a recurring decimal to a fraction
multiply and divide a given fraction by an integer, by a unit fraction and by a general fraction
convert simple fractions of a whole to percentages of the whole and vice versa
use efficient methods to calculate with fractions, including cancelling common factors before carrying out the calculation,
recognising that, in many cases, only a fraction can express the exact answer
17