Multiplying fractions mentally

Mostly, we multiply fractions in writing. However, in some cases we can multiply them mentally. It can be useful to know how to think in such cases. Let’s investigate it...

1st Calculate: a) 3 × = 1 2 __ 1 2 __ 3 times half of something = 1 2 __ + = 3 2 __ = 1 2 __ =

1st Calculate: a) 3 × = 1 2 __ 1 2 __ 3 times half of something = b) × 3 = 1 2 __ We are interested not only about result, but also how to imagine what happens in this example!

1st Calculate: a) 3 × = 1 2 __ 1 2 __ 3 times half of something = b) × 3 = 1 2 __ 1 2 __ half three = Let’s remember: 3 × 3 = triple three = 9 2 × 3 = ? double three = 6 1 × 3 = ? single three = 3 × 3 = 1 2 __ 1 2 __ half three = Continue the sequence!

1st Calculate: a) 3 × = 1 2 __ 1 2 __ 3 times half of something = b) × 3 = 1 2 __ 1 2 __ half three =

1st Calculate: a) 3 × = 1 2 __ 1 2 __ 3 times half of something = b) × 3 = 1 2 __ 1 2 __ half three =

3 times half of something = 1st Calculate: a) 3 × = 1 2 __ 1 2 __ 3 times half of something = b) × 3 = 1 2 __ 1 2 __ half three = = of 3 = 1 2 __ 1 2 __ First number tells us how many times to take second number. REMEMBER IT! If the first number is fraction, then imagine "of" instead of "times"!

1st Calculate: c) × 6 = 1 2 __ half of 6 = 3

1st Calculate: c) × 6 = 1 2 __ half of 6 = 3 d) 6 × = 1 2 __ 6 times half of something = 3 1 2 __ + = 6 2 __ = = 3

1st Calculate: e) × 6 = 1 3 __ of 6 = 1 3 __ 2

1st Calculate: e) × 6 = 1 3 __ of 6 = 1 3 __ 2 f) 6 × = 1 3 __ 6 times of something 1 3 __ = 2

1st Calculate: g) × 6 = 2 3 __ of 6 = 2 3 __ × 4 ÷ Calculation: 6 ÷ 3 × 2 = 4

1st Calculate: g) × 6 = 2 3 __ of 6 = 2 3 __ 4 h) 6 × = 2 3 __ 6 times of something 2 3 __ = 4

1st Calculate: i) × 21 = 2 7 __ of 21 = 2 7 __ × 6 ÷ Calculation : 21 ÷ 7 × 2 = 6

1st Calculate: j) × 36 = 5 9 __ of 36 = 5 9 __ × 20 ÷ Calculation : 36 ÷ 9 × 5 = 20

1st Calculate: k) × 24 = 2 3 __ of 24 = 2 3 __ × 16 ÷ Calculation : 24 ÷ 3 × 2 = 16

1st Calculate: l) 4 × = 1 2 __ 4 times half of something = 2 m) × 4 = 1 2 __ of 4 1 2 __ = 2

2nd Calculate: a) 2 × 3 = 1 2 __ 2 times 3 and a half of something = 7

2nd Calculate: a) 2 × 3 = 1 2 __ 2 times 3 and a half of something = 7

2nd Calculate: a) 2 × 3 = 1 2 __ 2 times 3 and a half of something = 7 b) 3 × 2 = 1 2 __ 3 and a half times 2 breads = 7 6 + 1 = 7

2nd Calculate: a) 2 × 3 = 1 2 __ 2 times 3 and a half of something = 7 b) 3 × 2 = 1 2 __ 3 and a half times 2 breads = 7 6 + 1 = 7

2nd Calculate: a) 2 × 3 = 1 2 __ 2 times 3 and a half of something = 7 6 + 1 = 7 b) 3 × 2 = 1 2 __ 3 and a half times 2 breads = 7 6 + 1 = 7

2nd Calculate: c) 4 × 6 = 1 2 __ 4 times 6 and a half of something = 26 24 + 2 = 26

2nd Calculate: c) 4 × 6 = 1 2 __ 4 times 6 and a half of something = 26 d) 6 × 4 = 1 2 __ 6 and a half times 4 strawberries = 26 24 + 2 = 26

2nd Calculate: e) 8 × 6 = 1 2 __ 52 48 + 4 = 52 Calculate mentaly…

2nd Calculate: e) 8 × 6 = 1 2 __ 52 f) 4 × 10 = 1 2 __ 45 40 + 5 = 45

2nd Calculate: e) 8 × 6 = 1 2 __ 52 f) 4 × 10 = 1 2 __ 45 g) 5 × 4 = 1 2 __ 22 1 2 __ 2 1 __ 22 1 2 __ 20 + =

2nd Calculate: e) 8 × 6 = 1 2 __ 52 f) 4 × 10 = 1 2 __ 45 g) 5 × 4 = 1 2 __ 22 1 2 __ h) 3 × 9 = 1 2 __ 31 1 2 __ Say just the solution...

2nd Calculate: e) 8 × 6 = 1 2 __ 52 f) 4 × 10 = 1 2 __ 45 g) 5 × 4 = 1 2 __ 22 1 2 __ h) 3 × 9 = 1 2 __ 31 1 2 __ i) × 15 = 1 2 __ 7 1 2 __

2nd Calculate: j) × 10 = 1 2 __ o) 1 × 7 = 1 2 __ 10 1 2 __ 5 k) × 19 = 1 2 __ 9 1 2 __ p) × 56 = 2 7 __ 16 l) × 100 = 1 2 __ 50 m) × 101 = 1 2 __ 50 1 2 __ n) × 102 = 1 2 __ 51

Is it enough?

T H E E N D

for support and help with the translation into fluent U.S. idiom With thanks to: Rex Boggs for support and help with the translation into fluent U.S. idiom (a.k.a. ‘American’).

Author of presentation: Antonija Horvatek Croatia , 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 Horvatek http://www.antonija-horvatek.from.hr/ ahorvatek@yahoo.com