Using 9ths. Stg 5/E6
props & rats
Name: ______________________
Ninths show us whole things or sets of things split into 9 equal parts. It’s kind
their thing. They are a little harder to draw in a circle because you can’t halve
and halve again like even fractions, but they have their own charms. Let’s get
chummy with unit and non-unit ninths – colour the fraction shown:
1
9
6
9
4
9
8
9
7
9
5
9
3
9
Some things we know: We know our 9 times tables. There are 9 ninths in one whole or set. The bottom number of the
fractions (the denominator) tells us it’s been chopped up 9 times.
But, what if we had more than one whole or set? How many ninths would there be then? Try figuring out how many
ninths are in these cheeky little numbers below.
How many 9ths are in these sets of ninths? (9 segments in each ball – check if you like)
(2 x 9) = ___
(3 x 9) = ___
(5 x 9) = ___
(4 x 9) = ___
Then, without the pictures:
1.
2.
3.
4.
5.
6.
7.
8.
9.
There are ____ ninths in 7 (9 x 7)
There are ____ ninths in 6 (9 x 6)
There are ____ ninths in 9 (9 x 9)
There are ____ ninths in 8 (9 x 8)
There are ____ ninths in 11 (9 x 11)
There are ____ ninths in 10 (9 x 10)
There are ____ ninths in 12 (9 x 12)
There are ____ ninths in 20 (9 x 20)
There are ____ ninths in 1/3 (1/3 x 9)
Only about one ninth of the mass of an
iceberg is visible above the water.
Nearly all its bulk remains hidden
beneath the surface.
Dave Moran 2015
Using 9ths.
Stg 6
props & rats
Name: _________________________
We’ve learned that chopping things into fractions is much the same as dividing. This is good news for us
because dividing by 9 is what all the cool kids are doing. Let’s go over some non-unit fractions to start with
th
For example: We know that 36 ÷ 9 = 4. So then we can easily say that 1/9 of 36 is also 4. – It’s the same
th
thing, only written down differently. What if the numerator is bigger? Like 4/9 of 36? Well, we are still
chopping up 36 into 9 parts, but we are talking about more of the parts than just one.
So if 1/9 of 36 = 4 …
4/9 of 32 = (4 x 4) = 16
1/9 of 36
Let’s try a few for ourselves then (watch out for improper fractions) :
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
1/9 of 27 = ___
1/9 of 36 = ___
1/9 of 63 = ___
1/9 of 54 = ___
1/9 of 18 = ___
1/9 of 27 = ___
1/9 of 90 = ___
1/9 of 72 = ___
1/9 of 45 = ___
1/9 of 81 = ___
1/9 of 45 = ___
1/9 of 18 = ___
1/9 of 90 = ___
1/9 of 63 = ___
1/9 of 54 = ___
so
so
so
so
so
so
so
so
so
so
so
so
so
so
so
5/9 of 27 = (5 x ____ ) = ____
6/9 of 36 = (6 x ____ ) = ____
8/9 of 63 = (8 x ____ ) = ____
7/9 of 54 = (7 x ____ ) = ____
6/9 of 18 = (6 x ____ ) = ____
3/9 of 27 = (3 x ____ ) = ____
5/9 of 90 = (5 x ____ ) = ____
3/9 of 72 = (3 x ____ ) = ____
4/9 of 36
4/9 of 45 = (4 x ____ ) = ____
8/9 of 81 = (8 x ____ ) = ____
9/9 of 45 = (9 x ____ ) = ____ (What the…?)
11/9 of 18 = (11 x ____ ) = ____ (OK, - crazy!)
13/9 of 90 = (13 x ____ ) = ____ (Oh! Now I see)
11/9 of 63 = (11 x ____ ) = ____
10/9 of 54 = (10 x ____ ) = ____
By now you’ll have noticed that some of the fractions end up with bigger numerators than denominators called ‘improper’ fractions. What is a ‘proper’ fraction? That’s when we write any sets that can be made
complete into whole numbers. Take 9/9ths - when you have the full set, it’s the same as saying you have 1
whole thing. So 9/9 = 1. That means we can simplify improper fractions to show wholes as well. E.g 11/9 is
the same as 1 and 2/9, or 1 2/9 (9/9 + 2/9)
Write in the proper (mixed) fractions below:
12/9 = (9/9 + 3/9) = ____ 15/9 = (9/9 + 6/9) = ____ 17/9 = (9/9 + 8/9) = ____
19/9 = (9/9 + 9/9 + 1/9) = ____
24/9 = (9/9 + 9/9 + 6/9) = ____
21/9 = ____
16/9 = ____
36/9 = ____
30/9 = ____
32/9 = ____
29/9 = ____
41/9 = ____
49/9 = ____
23/9 = ____
27/9 = ____
46/9 = ____
25/9 = ____
Dave Moran 2015
Using 9ths.
Stg E7
props & rats
Name: _________________________
We know a little bit about ninths already, but is it possible to turn fractions like this into decimal numbers?
Well, of course it is – decimals are just another way of dividing things into smaller parts – all we need to do is
convert it using our standard division form. The denominator becomes our devisor. E.g.
0.4 4 rec.
4 4
9 4.0
0
4
9
The maths here is that 9 can’t easily go into 4, so we lay out some
‘place holders’ – zeros - in the decimals. Then we can use our
ordinary division to figure how many 9s you can fit into 40 tenths
and so on.
You’ll have noticed that the answer seems really simple – just a whole load of 4s! – Yes, it is, and they go on
forever too because the remainder is always the same, something we call ‘recurring’. In fact any ninth will have
the same effect – so we can predict the decimal without having to work it out each time!
Have a go at these, to 3 decimal places:
2/9 = 0. 2___
1/9 = 0. ____
5/9 = 0. ____
6/9 = 0. ____
8/9 = ______
4/9 = ______
3/9 = ______
7/9 = ______
Man, how easy was that? What else can we do with this information? By turning a fraction into a decimal, we
can then quickly turn it into a percentage. ( ‘Percentage’ % is a proportion ‘out of 100’). So, once we have the
decimal number, all we do is multiply it by 100.
E.g 4/9 = 0.444 (recurring)
Then 0.444 x 100 = 44.4 %
(same digits, 100 x bigger)
Tip 1: we just shift our place values along twice – there are 2 zeroes in 100
Tip 2: 100% = 1.00
So have a go at turning these ninth fractions into percentages:
7/9 = 0. _____ x 100 = ___. _ %
5/9 = 0. _____ x 100 = ___. _ %
2/9 = 0. _____ x 100 = ___. _ %
8/9 = 0. _____ x 100 = ___. _ %
What if I get a test score like 43 out of 90? Can we figure the percentage for that? – Most certainly! In this case,
it’s easiest to divide by 10 first, so you only have to divide by 9, rather than 90.
43
90
=
4.3
9.0
7 7rec.
= 0.4
4 7 7
= 47.7 %
9 4.3 0 0
Ok, fair enough, it is reasonably complicated,
but you can do it if you take it step by step.
Let’s try a few, see how it goes:
a. 56/90 ÷ 10 = _._/__ = 9 5.6 0 0 x 100 = ___.__ %
Wow! Marathon effort.
b. 85/90 ÷ 10 = _._/__ = 9 ______ x 100 = ___.__ %
c. 73/90 ÷ 10 = _._/__ = _ 7.3 0 0
x 100 = ___.__ %
Beethoven's 9th and final symphony was composed in 1824 when he was completely deaf. The words to
the 9th Symphony come from the poem "Ode to Joy" from 1785.
Dave Moran 2015