Multiplying fractions mentally. Mostly, we multiply fractions in writing. However, in some cases we...

Multiplying fractions mentallyMultiplying fractions mentally

Mostly, we multiply fractions in writing.Mostly, we multiply fractions in writing.

However, in some cases we can multiply them However, in some cases we can multiply them

mentally.mentally.

It can be useful to know how to think in such cases.It can be useful to know how to think in such cases.

Let’s investigate it...Let’s investigate it...

1st Calculate:

a) 3 × =12__ 3 times half of something = 1

12__

=12__ +

12__ +

12__ =

32__ = 1

12__

1st Calculate:

a) 3 × =12__

b) × 3 =12__

We are interested not only about result,but also how to imagine what happens in this example!

3 times half of something = 112__

1st Calculate:

a) 3 × =12__

b) × 3 =12__

Let’s remember:

3 × 3 =

2 × 3 =

1 × 3 =

triple three = 9

?double three = 6

?single three = 3

× 3 =12__

Continue the sequence!

half three = 112__

half three = 112__

3 times half of something = 112__

1st Calculate:

a) 3 × =12__

b) × 3 =12__

3 times half of something = 112__

half three = 112__

1st Calculate:

a) 3 × =12__

b) × 3 =12__

3 times half of something = 112__

half three = 112__

1st Calculate:

a) 3 × =12__

b) × 3 =12__

= of 3 =12__ 1

12__

First number tells ushow many times to take second number.

If the first number is fraction,then imagine "of" instead of "times"!

REMEMBER IT!

3 times half of something = 112__

half three = 112__

1st Calculate:

c) × 6 =12__ half of 6 = 3

1st Calculate:

c) × 6 =12__

d) 6 × =12__ 6 times half of something = 3

=62__ =

12__ +

12__ =+

12__ +

12__ +

12__+

12__ 3

half of 6 = 3

1st Calculate:

e) × 6 =13__ of 6 =1

3__ 2

1st Calculate:

e) × 6 =13__ of 6 =1

3__ 2

f) 6 × =13__ 6 times of something

13__

= 2

1st Calculate:

g) × 6 =23__ of 6 =2

3__ 4

Calculation: 6 ÷ 3 × 2

÷

×

= 4

1st Calculate:

g) × 6 =23__

h) 6 × =23__ 6 times of something

23__

= 4

of 6 =23__ 4

1st Calculate:

i) × 21 =27__ of 21 =2

7__ 6

Calculation :

÷

×

21 ÷ 7 × 2 = 6

1st Calculate:

j) × 36 =59__ of 36 =5

9__ 20

Calculation :

÷

×

36 ÷ 9 × 5 = 20

1st Calculate:

k) × 24 =23__ of 24 =2

3__ 16

Calculation :

÷

×

24 ÷ 3 × 2 = 16

1st Calculate:

l) 4 × =12__ 4 times half of something = 2

m) × 4 =12__ of 4 1

2__ = 2

2nd Calculate:

a) 2 × 3 =12__ 2 times 3 and a half of something = 7

2nd Calculate:

a) 2 × 3 =12__ 2 times 3 and a half of something = 7

2nd Calculate:

a) 2 × 3 =12__

b) 3 × 2 =12__ 3 and a half times 2 breads = 7

6 1+ = 7

2 times 3 and a half of something = 7

2nd Calculate:

a) 2 × 3 =12__

b) 3 × 2 =12__

6 1+ = 7

3 and a half times 2 breads = 7

2 times 3 and a half of something = 7

2nd Calculate:

a) 2 × 3 =12__

b) 3 × 2 =12__

6 1+ = 7

6 1+ = 7

3 and a half times 2 breads = 7

2 times 3 and a half of something = 7

2nd Calculate:

c) 4 × 6 =12__ 4 times 6 and a half of something = 26

24 2+ = 26

2nd Calculate:

c) 4 × 6 =12__

d) 6 × 4 =12__ 6 and a half times 4 strawberries = 26

24 2+ = 26

4 times 6 and a half of something = 26

2nd Calculate:

e) 8 × 6 =12__

48 4+ = 52

Calculate mentaly…

52

2nd Calculate:

e) 8 × 6 =12__

52

f) 4 × 10 =12__

40 5+ = 45

45

2nd Calculate:

e) 8 × 6 =12__

52

f) 4 × 10 =12__ 45

g) 5 × 4 =12__

20 + 212__

= 2212__

2212__

2nd Calculate:

e) 8 × 6 =12__

52

f) 4 × 10 =12__ 45

g) 5 × 4 =12__ 22

12__

h) 3 × 9 =12__

Say just the solution...

3112__

2nd Calculate:

e) 8 × 6 =12__

52

f) 4 × 10 =12__ 45

g) 5 × 4 =12__ 22

12__

h) 3 × 9 =12__ 31

12__

i) × 15 =12__ 7

12__

2nd Calculate:

j) × 10 =12__ 5

k) × 19 =12__ 9

12__

l) × 100 =12__ 50

m) × 101 =12__ 50

12__

n) × 102 =12__ 51

o) 1 × 7 =12__ 10

12__

p) × 56 =27__ 16

Is it enough?

T H E E N D

With thanks to:

Rex BoggsRex Boggsfor support and help with the translation into fluent U.S. idiom (a.k.a. ‘American’).

Author of presentation:

Antonija HorvatekAntonija HorvatekCroatia , January 2014

You are welcome to use this presentation in your teaching.Additionally, you can change some parts of it if used solely for teaching.

However, if you want to use it in public lectures, workshops,websites, in writing books, articles, on CDs or any public forum or for any commercial purpose, please ask for specific permission from the author.

Antonija Horvatekhttp://www.antonija-horvatek.from.hr/ ahorvatek@yahoo.com