? ? ?

? ? ?

this is c alled

P artitive Division

this is c alled

Quot ative Division

?

?

Partitive Division Quotative Division

L et’ s tr y some thing harder .

Phr asing it as a Quot ativ e Division problem:

And indeed

Hold on, don’t invert and multiply just ye t.

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 e ach p art ?

How many times does 6 g o int o 18?

3

4

1

8

What is

3

4

1

8

÷

=

6

1

3

1

6

So what is

divided by

?

÷

?

Ours is not t o r eason why

Just invert and multiply

L et’ s c onsider it as a

problem

In other wor ds

Sinc e is ex actly as larg e as

, the answer is

twic e

2

1

0

Quotative Division

1

6

1

6

How many times does fit into

?

1

6

1

3

How many times does

fit int o ?

1

8

3

4

1

3

That’ s quit e simple.

(you’ll g et the same r esult by

inverting and multiplying)

1

3

P aris divided evenly 18 apples betw een 6 of her friends

Ho w many apples did each friend g e t ?

There ar e two w ays to think about division

Going b ack to the b asics...

Another P er spective

We know we need t o divide int o 6 parts, the only question is -

In other wor ds

Quentin b ags his 18 apples, putting 6 in e ach bag.

Ho w many bags will Quentin need?

T o Summariz e

How big is

e ach p art ?

How many

p arts?

Many int erpre t ations

So we have two di erent pr oblems that are both e xpressed as

“18 ÷ 6=? ” . Assigning di erent me anings to the same expr ession is

c ommon in Math.

Think about 5+3 — it c ould me an that P aris had $5 and g ot $3 mor e.

It c ould also me an that Quentin got on an elev ator on the fih floor

and rode it up thr ee more floor s.

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 O VER ALL

There ar e

SIX

1

8

3

4

in

1

8

1

8

1

8

1

8

1

8

1

8

T e ach math lik e a mathematician

matific.c om