## Maths Flipped Learning – Division and interpreting remainders

**In Year 6 we are required to know not just how to divide, but how to deal with and understand the remainders we can end up with. The following two videos explain how you might convert these remainders into fractions or decimal depending on the context of the question.**

Have a look at how you might create a decimal remainder using division:

Did anyone notice anything about the remainder 0.125 in the previous video? This could be represented as the fraction 125/1000. Yet looking at this fraction it could also be simplifed to 1/8. So the answer could also be correctly shown as either **812.125** or** 812 1/8**

This second video explains how you can use the short division method (bus stop) to interpret remainders as fractions.

Once you have watched a few examples, use your homework book to pause and have a go at trying to answer some of the next questions in the fraction video and then watch and listen to the explaination to see if you were right. A key thing to remember with fraction remainders is of course to make sure you always SIMPLIFY YOUR FRACTIONS if you can.

*(This is also covered in the video but a reminder rap video can be found here if you need a few more reminders: https://www.youtube.com/watc**h?v=fp0wJ9d3pKE)*

EXT:

Hopefully this has been some helpful revision in how to interpret division remainders as either fractions or decimals. There are two important things to remember:

1: It is important to understand the * context of the question *to decide whether the remainder needs to be looked at as a decimal or a fraction. There are a few questions for you to have a go at below to help you think about this.

*a) The buses have broken down and a school has ended up taking 458 children on a school trip to the seaside in cars! Each car can take 5 children. How many cars would be needed for the journey? (Is it possible to take part of a car?)*

*b) 2536 people applied to preview T.V. shows for a new channel. 9 people were invited to preview each show. How many shows did they preview with full audiences and how many people were not invited? (Would this be best recorded as a fraction? why / why not?)*

*c) Sunita divides 8541 by 8. She says “I know there will be a remainder before I start.” Is she correct? Explain how you know. (How could you prove this using written workings? Can you find a fraction / decimal answer?)*

(Answers are at the bottom of this page but have a go before you peep)

2: Short division (the bus stop method) works for single digit divisiors. However if you were faced with a question that was asking you 6497 divided by 16 then this would NOT be the most efficient method although you would still need to deal with the remainder as either a fraction or a decimal in the same way. How would you find the answer to such a question? We would recommend a fact box. *Think of the question as: How many lots of 16 could you find in 6497?*

16 x 1 = 16

16 x 2 = 32

16 x 4 = 64

**16 x 6 = 96**

16 x 10 = 160

16 x 50 = 800

16 x 100 = 1600

16 x 200 =3200

**16 x 400 = 6400**

Therefore adding together the two facts that will get me closest to my answer:

16 x 6 = 96

16 x 400 = 6400

16 x **406** = 6496 This is as close to my answer as I can get but I am still 1 away from my original answer therefore I have a *remainder of 1* – This can also be interpreted as either a fraction using the method shown in the above video e.g. 406 1/16

* Answers*:

a) *92 Cars* – As 458 divided by 5 = 91.6 or 91 3/5 and all the children need to go so you need to round up to 92 cars in this context as you cannot take a part of a car or leave any children behind.

b) *281 shows would be previewed and 7 people would not be invited*. As 2536 divided by 9 = 281 r 7 or 281 7/9 . This means that there were 7 people who were NOT invited to a show. If you looked at this division problem with a decimal remainder it would have given you a answer that was tricky to interpret – 281.7777777 recurring. What does this mean in terms of people?

c)There will be a remainder because multiples of 8 are always even numbers and 8541 ends in the unit 1. I can further prove this by calculating 8541 divided by 8 = 1067.625 or 1067 r 5 or 1067 5/8