1.
Year 8 Maths Home Learning - Fractions Unit 8
In this unit you will learn about:
- ‘Ordering Fractions’ and determining which fractions are more or less than ½ – 8.1
- ‘Adding and Subtracting Fractions’ and finding common denominators – 8.2
- ‘Multiplying Fractions’ by both whole numbers and other fractions - 8.3
- ‘Dividing Fractions’ by whole numbers and fractions, using reciprocals – 8.4
- Converting Mixed Numbers to Improper Fractions – 8.5
- Using all four operations, ‘Calculating with Mixed Numbers’ – 8.5
8.1 Ordering Fractions
Let’s have a look at some of the Key Terms we will need:
Denominator (the bottom number in the fraction)
Numerator (the top number in the fraction)
When ordering or comparing fractions, it can be helpful to start comparing
each fraction to ½.
! # !
Q 1) Write these fractions in order, smallest first: , ,
" $ %
! #
Step One: Compare each fraction to ½ to see if they are bigger or smaller ----- " is equal, $ is
!
bigger because half of 8 is 4 and 5 is bigger than 4; % is smaller because half of 4 is 2 and 1
is smaller than 2
! ! #
Step Two: Now, see if that is enough to put them in order ----- in this case it is:
% " $
! " &
Q 2) Write these fractions in order, smallest first: - ,- ,-
" # '
Step One: This time we are working with negatives, so we will compare each fraction to - ½
to see if they are bigger or smaller
"
Step Two: - # seems smaller because half of 5 is 2.5 and 2 is smaller than this – however
!
because it is negative it is important to remember that it is LESS NEGATIVE than - " so it
&
is actually MORE POSITIVE, or bigger; - '
seems bigger because half of 9 is 4.5 and 7 is
bigger than this – however because it is negative it is actually MORE NEGATIVE which
means it is actually SMALLER than – ½
& ! "
Step Three: Order them - - -
' " #
2.
8.1 Continued
Fractions with the same denominator, have a common denominator.
! # &
For example , , have a common denominator of 12.
!" !" !"
If we need to compare fractions with different denominators (and we can't use the method
of comparing to 1/2) then we have to find a common denominator.
To find a common denominator of two (or more) numbers, It Is the lowest common
multiple (LCM), the smallest number that Is In the times tables of both numbers.
Q 1) What is the lowest common multiple (LCM) of 4, 5 and 10?
Step One: List the first few multiples (times tables) of each number
4, 8, 12, 16, 20, 24, 28 5, 10,15, 20, 25, 30 10, 20, 30, 40, 50
Step Two: Find the numbers that are the same in each list ----- easy to see that 20 is it!
Step Three: If you have more than one number that is the same, it’s always the SMALLEST
number that you want to choose
! " &
i) What is the common denominator of , , ?
% # !(
Step One: Find the LCM, as we did in the previous question –---- we know it’s 20
Step Two: Change all the fractions so that they have a denominator or 20
Calculate that 4 x ? = 20 ----- we know that it’s 5, so you multiply the numerator by 5 as well
Calculate 5 x ? = 20 ----- we know that it’s 4, so you multiply the numerator of 2 by 4 for 8
Calculate 10 x ? = 20 ----- we know that it’s 2, so you multiply 7 by 2 to get 14
! # " $ & !%
= = =
% "( # "( !( "(
ii) Put the above fractions in order, starting with the smallest.
Now that all the denominators are the same, it’s just a matter of ordering the numerators
# $ !% ! " &
SO final answer with original fractions:
"( "( "( % # !(
Now have a go at 8.1 Ordering Fractions Worksheet J
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