Multiplying fractions mentally Mostly we multiply fractions in

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. . .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Is it enoug h?

E E H T D N

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