Stg 5 x/÷
Divide by 9.
Name: __________________________
Let’s try chopping things up into 9 equal groups. So let’s have a look at some numbers: Say you had 27
jellybeans to share out with your group of 9 people. First share them fairly one at a time – how many beans
would they end up with each?
OK, they’re in sets – so what does the maths look like for this? 27 ÷ 9
= ___
Try another one. Ben had 9 goldfish. He wanted to treat them with a fishy nibble, and had 36 left in the
packet. Just use ticks or dots to mark the count for each nibble.
What numbers can we use to
Show the sharing:
36 ÷ 9 = ___
Good going. Let’s try another. Nick had 45 marbles to share out equally in his group of 9 (including himself).
How many did they have each?
So, what does the maths look like for this?
45 ÷ 9 = ___
What if we took a large number and just counted the sets of 9 we find. It sounds quite hard, but it’s not too
bad really, because 9 is very nearly 10 – and we all know 10s are easy. One might even say “easy-as Bro”. See
the 18 seeds in a line below. How many sets of 9 can you make?
18 ÷ 9 = ____
54 Sapphires
54 ÷ 9 = ____
63 Jaffas
63 ÷ 9 = ____
81Knots
81 ÷ 9 = ____
Maths inquiry - If you had 4 apples and 5 oranges in one hand and 2 apples and 7 oranges in the
other, what would you have?
A: Very large hands.
Dave Moran 2015
Stg E6 x/÷
Divide by 9.
Name: _________________________
The Nines are the world’s most awesome set of times-tables. They have all sorts of tricks up their sleeves. As
always, the best way to get comfy with the 9x table is to memorise the facts so they are ready for instant
recall. Along the way though, there are some handy signposts E.g. If a number is a multiple of 9, it’s digits will
add up to 9 or a multiple of 9 (99; 9 + 9 = 18, 108; 1 + 0 + 8 = 9, 72; 7 + 2 and so on.)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
9 x 6 = ___
9 x 4 = ___
9 x 10 = ___
9 x 9 = ___
9 x 5 = ___
9 x 7 = ___
9 x 11 = ___
9 x 3 = ___
9 x 8 = ___
9 x 12 = ___
So __ ÷ 9 = 6
So __ ÷ 9 = 4
So __ ÷ 9 = 10
So __ ÷ 9 = 9
So __ ÷ 9 = 5
So __ ÷ 9 = 7
So __ ÷ 9 = 11
So __ ÷ 9 = 3
So __ ÷ 9 = 8
So __ ÷ 9 = 12
and
and
and
___ ÷ 6 = 9
___ ÷ 4 = 9
___ ÷ 10 = 9
and
and
and
and
and
and
___ ÷ 5 = 9
___ ÷ 7 = 9
___ ÷ 11 = 9
___ ÷ 3 = 9
___ ÷ 8 = 9
___ ÷ 12 = 9
‘On cloud nine’ means happy, euphoric or `high'.
The phrase came into use in the 1950s from a term
used by the US Weather Bureau. For the
meteorologists Cloud Nine is cumulo-nimbus cloud
at a height of 10 km, which is high even by the
standard of clouds.
E.g. What is 18 ÷ 9? We know that 2 x 9 = 18, so using the ‘family’ we know 18 ÷ 9 = 2
Try these ones to build up your division basic facts:
Now the time has come for us to practice some basic facts (go on, you’ll LOVE it):
81 ÷ 9 = ___
63 ÷ 9 = ___
27 ÷ 9 = ___
36 ÷ 9 = ___
45÷ 9 = ___
18 ÷ 9 = ___
72 ÷ 9 = ___
90 ÷ 9 = ___
54 ÷ 9 = ___
108 ÷ 9 = ___
We can use a combination of our basic facts and place value to figure out some of the very large or very small
divided-by problems. E.g. We know that 9 x 2 = 18 and then 18 ÷ 9 = 2. So then 180 ÷ 9 = 20 and 1.8 ÷ 9 = 0.2
With decimal numbers, watch out that you shift the place value enough times. Say if you get 1.8 ÷ 0.9, the
value will shift twice and you’ll end up with a whole number again: 1.8 ÷ 0.9 = 2 (there are two 0.9s in 1.8)
1.
2.
3.
4.
5.
6.
7.
8.
9.
63 ÷ 9 = ____
45 ÷ 9 = ____
36 ÷ 9 = ____
27 ÷ 9 = ____
54 ÷ 9 = ____
81 ÷ 9 = ____
72 ÷ 9 = ____
18 ÷ 9 = ____
108 ÷ 9 = ____
630 ÷ 9 = _____
450 ÷ 9 = _____
360 ÷ 9 = _____
2.7 ÷ 9 = ____
540 ÷ 9 = _____
810 ÷ 9 = _____
7.2 ÷ 9 = _____
180 ÷ 9 = _____
10.8 ÷ 9 = ____
6.3 ÷ 9 = ____
4.5 ÷ 9 = ____
3.6 ÷ 9 = ____
270 ÷ 9 = _____
5.4 ÷ 9 = ____
8.1 ÷ 9 = ____
720 ÷ 9 = _____
1.8 ÷ 9 = ____
10.8 ÷ 0.9 = ____
6300 ÷ 9 = _______
450000 ÷ 9 = _______
3.6 ÷ 0.9 = _______
2700 ÷ 9 = _______
5.4 ÷ 0.9 = _______
81000 ÷ 9 = _______
7.2 ÷ 0.9 = _______
1800 ÷ 9 = _______
1080 ÷ 9 = _______
Dave Moran 2015
Stg 6/E7 x/÷
Name: _________________________
Dividing with a remainder: E.g 24 ÷ 9 = ?? 24 isn’t a multiple of 9, but we know that 18 ÷ 9 = 2, and that
27 ÷ 9 = 3. We just choose the one that fits inside 24 (18), then take away 18 from 24 (24 – 18 = 6)
So 24 ÷ 9 = 2 r6 … That’s 2 times with a remainder of 6 (Which can also be called 6/9). Let’s try:
i. 11 ÷ 9 = __ r __
ii. 84 ÷ 9 = __ r __
iii. 40 ÷ 9 = __ r __
iv. 66 ÷ 9 = __ r __
v. 51 ÷ 9 = __ r __
vi. 113 ÷ 9 = __ r __
vii. 75 ÷ 9 = __ r __
viii. 29 ÷ 9 = __ r __
ix. 21 ÷ 9 = __ r __
A 9 sided shape is
called a nonagon.
Divide by 9.
So how do we solve longer problems like 576 ÷ 9 = ?? The answer (as you know by now) is to split
it into smaller, easier bits! Hopefully you have had some practice with other times-tables using
this old fashioned standard form of fast long division but here’s how we do it:
64
9 5 736
1. Look at numbers that can be divided by 9, starting on the left. The ‘5’ in the 100s
column is too small, so go to ‘57’. (it’s actually 57 tens BTW)
2. 57 ÷ 9 = 6 r3 (57-54=3) Put the ‘6’ above on the answer line
3. Put the r3 in the 1s column on the left of the 6. to make ‘36’
4. 36 ÷ 9 = 4. Put the ‘4’ in the 1s place on the answer line – all done! Answer: 64
OK, your turn: don’t forget to stick in the remainder at the end if it needs it!
a. 9 5 6 9
b. 9 3 1 5
c. 9 7 2 1
d. 9 4 7 6
e. 9 7 8 4 2
f. 9 9 5 7 5
g. 9 7 4 8 7
h. 9 1 0 7 1
i. 9 8 3 6 8
j. 9 8 3 4 8
k. 9 1 8 7 6
l. 9 5 6 2 5
m. 9 8 6 5 7
n. 9 2 7 4 8
o. 9 1 0 9 6
p. 9 8 1 0 7
OK here’s a thought: If you divide 1 by 9 you get 0.11111 recurring. So it should be easy to convert the
remainder in a divide-by-nine problem into decimals. Supposing we just round it to 2 decimal places, we can
say if the remainder is 3, we can just go 0.33 – couldn’t be easier! Have a try at these ones:
q. 9 6 7.5 6
r. 9 4 5. 2 3
s. 9 5 2. 6 2
t. 9 2. 0 4 1
u. 9 2 3 1. 7
v. 9 3. 6 7 5
w. 9 6 4. 7 7
x. 9 8 7 3. 1
Dave Moran 2015
Stg 7 x/÷
Divide by 9.
Name: _________________________
Maths investigation time! If you’re on this page, you are clearly some kind of smarty-pants.
That’s good, because it’ll come in handy for this next thing: What if you are dividing by
multiples of 9 (or multiples of any number for that matter)? Suddenly things get interesting! Like that time you emptied a box of cockroaches into Aunt Hazel’s handbag.
Say we had 8208 ÷ 18? The standard form would look like this:
18 8 2 0 8
(Write it out in your own book – what am I, a stationery shop?)
What are the ways you could attack this? (Assuming you don’t wimp out and use a calculator of course). As it
often is, the key is to break the problem down into smaller parts. Try these strategies, see if you get any joy:
1. Halve both numbers first – If I simplify them in the same way, the quotient should be
the same – Give it a go, see what happens! (Half, because 2 x 9 =18)
2. Use the standard fast way you already know, but round the 18 up to 20. E.g. 4 20s fit in
82, so you’ll also get 4 18s in. You’ll then have 2 x 4 to add to the remainder. (4 x 2) + 2
… Whoops, I may have said too much!
3. Evaluate: Which one was easier for you? If you’re working with a buddy, compare notes
– did you get the same answer? Which method is quicker?
OK, now try some of these:
18 2 2 1 4
18 1 4 2 0 2
18 6 4 2 6
18 2 8 6.2
Alright, the question then becomes, can we do something similar with bigger multiples? Have a play about
with these ones: (There’s a fair amount of computation to do on these – take your time, double check, look
for familiar patterns, use as much space in your maths books as you need, watch that place value!)
27 6 9 6 6
36 1 2 8 5 2
54 7 9 3 8
45 7 1 5.5
Still too easy? Have a crack at some of these where the divisor is a prime number (This is just mean, sorry)
17 3 2 1 4
19 1 5 9 2
23 7 4 3 6
13 5 8 6 7
Helpful Hinty McHintiness:
https://www.youtube.com/watch?v=7cBRXayBNr4
Tecmath videos
https://www.youtube.com/watch?v=HdU_rf7eMTI
Math Antics – how to divide with 2 digit divisors
What are the 10 kinds of people in the world?
Those who know binary and those who don't.
Dave Moran 2015