Dividing fractions mentally

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

In this presentation we’ll practice: 1st division when the numerator is divisible by numerator and the denominator by denominator 2nd dividing a natural number by a natural number, e.g. 4 ÷ 7, 3rd dividing a natural number by 2, e.g. 9 ÷ 2, 4th dividing a natural number by a proper fraction with the numerator equal to 1, e.g. 4 ÷ , __ 1 2 5th division when the result is natural number, e.g. 5 ÷ 2 . __ 1 2 Let’s gooooo…

Division when the numerator is divisible by numerator and the denominator by denominator

1. Calculate: a) 8 7 __ 24 35 ÷ = __ 3 5 b) 8 9 __ 72 63 ÷ = __ 9 __ 2 = 1 7 7 Can we calculate so in this case: 4 21 __ 32 3 ÷ ? No, because 3 is not divisible by 21 ! (21 is divisible by 3) It’s not allowed to divide from right to left, but only from the left to right! In this case we should calculate in writing (not now)…

1. Calculate: a) 8 7 __ 24 35 ÷ = __ 3 5 b) 8 9 __ 72 63 ÷ = __ 9 __ 2 = 1 7 7 c) 2 9 __ 8 ÷ = __ 4 = 4 1 We can imagine it… Let’s think: How many times does go into ? __ 2 9 8 __ 2 9 __ 2 9 __ 2 9 __ 2 9 __ 8 9 + + + = 4 times

1. Calculate: a) 8 7 __ 24 35 ÷ = __ 3 5 b) 8 9 __ 72 63 ÷ = __ 9 __ 2 = 1 7 7 c) 2 9 __ 8 ÷ = __ 4 = 4 1 Let’s think: How many times does go into ? __ 2 9 8

1. Calculate: a) 8 7 __ 24 35 ÷ = __ 3 5 b) 8 9 __ 72 63 ÷ = __ 9 __ 2 = 1 7 7 c) 2 9 __ 8 ÷ = __ 4 = 4 1 d) 2 3 __ ÷ = __ 1 __ 3 1 Let’s think: What part of the pizza will each girl get? Imagine…

1. Calculate: a) 8 7 __ 24 35 ÷ = __ 3 5 b) 8 9 __ 72 63 ÷ = __ 9 __ 2 = 1 7 7 c) 2 9 __ 8 ÷ = __ 4 = 4 1 d) 2 3 __ ÷ = __ 1 3 e) 4 8 9 __ ÷ = 2 9 __ How much of the cake will each kid get? Can you say the result? Imagine…

Dividing a natural number by a natural number

2. Calculate: __ 2 a) 2 ÷ 3 = 3 Imagine… How much of the pizza will each boy get?

2. Calculate: How much of pizza will each girl get? __ 3 __ 1 b) 3 ÷ 2 = = 1 2 2 Imagine…

2. Calculate: Let’s consider last two examples: __ 2 a) 2 ÷ 3 = 3 __ 3 __ 1 b) 3 ÷ 2 = = 1 2 2 In division, if numbers swap places, then we get the reciprocal! Compare the given numbers in these examples! They swapped places! Compare the results! The result is the reciprocal!

2. Calculate: How many candies will each child get? c) 15 ÷ 5 = 3 Imagine…

2. Calculate: How much of pizza will each child get? c) 15 ÷ 5 = 3 __ 5 __ 1 d) 5 ÷ 15 = = 15 3 Imagine…

2. Calculate: c) 15 ÷ 5 = 3 __ 5 __ 1 d) 5 ÷ 15 = = 15 3 Compare the given numbers and the results again… Given numbers swapped places, and the result is the reciprocal!

2. Calculate: c) 15 ÷ 5 = 3 __ 5 __ 1 d) 5 ÷ 15 = = 15 3 e) 24 ÷ 4 = 6 __ 4 __ 1 d) 4 ÷ 24 = = 24 6 Compare again…

2. Calculate: c) 15 ÷ 5 = 3 __ 5 __ 1 d) 5 ÷ 15 = = 15 3 e) 24 ÷ 4 = 6 __ 4 __ 1 d) 4 ÷ 24 = = 24 6 __ 1 e) 8 ÷ 40 = 5 Just give the final answer…

2. Calculate: c) 15 ÷ 5 = 3 __ 5 __ 1 d) 5 ÷ 15 = = 15 3 e) 24 ÷ 4 = 6 __ 4 __ 1 d) 4 ÷ 24 = = 24 6 __ 1 e) 8 ÷ 40 = 5 __ 1 f) 9 ÷ 72 = 8 __ 3 g) 3 ÷ 11 = 11

Dividing a natural number by 2

3. Give the final answer: How much strawberries will each boy get? __ 1 a) 7 ÷ 2 = 3 2 Imagine…

3. Give the final answer: __ 1 a) 7 ÷ 2 = 3 2 __ 1 b) 11 ÷ 2 = 5 2 __ 1 c) 27 ÷ 2 = 13 2 d) 40 ÷ 2 = 20 __ 1 e) 41 ÷ 2 = 20 2 __ 1 f) 203 ÷ 2 = 101 2

Dividing a natural number with the numerator equal to 1 by a proper fraction with the numerator equal to 1

4. Calculate: a) 1 ÷ = __ 1 2 2 Let’s think: How many times does go into 2 ? __ 1 2 1st time 2nd time __ 1 2 __ 1 2 + = 1 2 times

4. Calculate: b) 2 ÷ = __ 1 2 4 Let’s think: How many times does go into 1 ? __ 1 2 1st 2nd 3rd 4th __ 1 2 __ 1 2 __ 1 2 __ 1 2 + + + = 2 4 times

4. Calculate: c) 8 ÷ = __ 1 2 16 Just say the solution… What is the question here?

4. Calculate: d) 1 ÷ = __ 1 3 3 Let’s think: How many times does go into 1 ? __ 1 3 __ 1 3 __ 1 3 __ 1 3 + + = 1 3 times

4. Calculate: e) 2 ÷ = __ 1 3 6 What’s the question here? Just say the solution… Or…

4. Calculate: f) 1 ÷ = __ 1 4 4 What’s the question here? Just say the solution… Or…

4. Calculate: g) 3 ÷ = __ 1 5 15 What’s the question here? Just say the solution…

Dividing fractions and mixed numbers when the result is a natural number

5. Calculate: a) 3 ÷ 1 __ 1 2 = 2 Let’s think: How many times does 1 go into 3 ? __ 1 2 1st time 2nd time __ 1 2 __ 1 2 + = 3 2 times

5. Calculate: b) 4 ÷ 1 __ 1 2 = 3 Let’s think: How many times does 1 go into 4 ? __ 1 2 1st 2nd 3rd __ 1 2 __ 1 2 __ 1 2 __ 1 2 4 + + = 3 times

5. Calculate: c) 10 ÷ 2 __ 1 2 = 4 Let’s think: How many times does 2 go into 10 ? __ 1 2 1st 2nd 3rd 4th __ 1 2 __ 1 2 __ 1 2 __ 1 2 + + + = 10 4 times

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