? ? ?
? ? ?
this is called
Partitive Division
this is called
Quotative Division
?
?
Partitive Division Quotative Division
Let’s try something harder.
Phrasing it as a Quotative Division problem:
And indeed
Hold on, don’t invert and multiply just yet.
Emma had 1/3 of an apple.
She divided it evenly
between 1/6 of a friend.
How many apples did each friend get?
1
3
1
6
What is
divided by
?
What does
1
3
1
6
divided by
“ ”
MEAN?
How big is each part?
How many times does 6 go into 18?
3
4
1
8
What is
3
4
1
8
÷
=
6
1
3
1
6
So what is
divided by
?
÷
?
Ours is not to reason why
Just invert and multiply
Let’s consider it as a
problem
In other words
Since is exactly as large as
, the answer is
twice
2
1
0
Quotative Division
1
6
1
6
How many times does fit into
?
1
6
1
3
How many times does
fit into ?
1
8
3
4
1
3
That’s quite simple.
(you’ll get the same result by
inverting and multiplying)
1
3
Paris divided evenly 18 apples between 6 of her friends
How many apples did each friend get?
There are two ways to think about division
Going back to the basics...
Another Perspective
We know we need to divide into 6 parts, the only question is -
In other words
Quentin bags his 18 apples, putting 6 in each bag.
How many bags will Quentin need?
To Summarize
How big is
each part?
How many
parts?
Many interpretations
So we have two dierent problems that are both expressed as
“18 ÷ 6=?”. Assigning dierent meanings to the same expression is
common in Math.
Think about 5+3 — it could mean that Paris had $5 and got $3 more.
It could also mean that Quentin got on an elevator on the fih floor
and rode it up three more floors.
How many
TWO
1
8
1
4
fit into
?
How many
THREE
1
4
3
4
fit into
?
1
8
1
8
1
4
1
4
1
4
SO OVERALL
There are
SIX
1
8
3
4
in
1
8
1
8
1
8
1
8
1
8
1
8
Teach math like a mathematician
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