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### Course: 4th grade>Unit 6

Lesson 3: Math patterns

# Factors and multiples: days of the week

Sal uses factors and multiples to figure out days of the week. Created by Sal Khan.

## Want to join the conversation?

• I did it in a simpler way: so I knew that they wee 7 days in a week and needed to figure out the 300th day. I just divided 300 by 7 and got a decimal number. It as around 42 so I multiply 7 by 42 and got 294 and I just needed 6 more to have 300. and so I was left with 6 and well there were 7 days and the 6th day was sat and that was my answer. (this method works every time hope this helps with u guys!
• It's not simpler. You did it in two steps (divided, than multiplied), but Sal did it in one - just divided, which gave him a remainder that shows what day it is.

Also, using Sal's method, you don't need to know anything about decimals.
• If there is like a number 140 and there is no remainder so can we find that
• Forget 140 for a moment. Let's take 14 alright.

7 divides evenly into 14, leaving 0 as remainder.

If we refer Sal's table in the video, we see that 14 is Sunday.

And Sunday is 1 day before the day we started on which was Monday.

So what did that tell us?

It tells us that if the remainder is 0, then the answer (in our case = Sunday) is going to be the previous day from the day we started on (in our case = Monday)

Try figuring out what 140's gonna be now. ;)
All the best, hope that helped!
• If every month has a different amount of days (e.g. October has 31 days, November has 30), does this formula still work?
• The days in the month do not affect the final calculation of what day of the week it is.
• Day 1 is Monday. how about day 490? Find out the day of day 490.

So it goes like this:
490 divide 7, if there is no remainder, it is Monday, ​if there are 1 remaining number, it is Tuesday, ​if there are 2 remaining numbers, it is Wednesday.......
​If there are 6 remaining numbers, it is Sunday.
Remember, there are no seven remaining numbers! (6 is the maximum)
Hot questions:

1. If there is 17 remainder, what day is it?

2. a) How many remainders are there if there are 900 days?
b) What is that day at day 900?

If you think this is helpful to you, pls vote for my questions, help me to get to more than 50 votes. I believe that if everybody can vote for my questions, it will be just an easy one to achieve!
• Correct me if I am wrong, but I think if there is no remainder it is sunday not monday, because we are dividing with 7 and 7 is sunday so if the remainder is 0 there is nothing to add in the days.
If it is remainder 1 it is monday.
If it is remainder 2 it is tuesday.
If it is remainder 3 it is wednesday.
If it is remainder 4 it is thursday.
If it is remainder 5 it is friday.
If it is remainder 6 it is saturday.
If it is remainder 7 it is sunday.
• This thing is hard to understand if you know what I mean.
• i dont know why he divided 16 by 7
• If you'd follow along maybe you would understand I suggest slowing down the video
• This one threw me a bit, because I was dividing 300 by 7 on a calculator, which gives the answer 42.85.
So I multiplied 0.85 by 7 (days), and rounded up to 6.
Is this a correct approach? I'm not keen on the fact that I have to round up each value.
• Yes, that works (kind of). You or your calculator rounded to the 42.85 initially. If you did it, don't. Keep all the digits of the repeating decimal. If you subtract 42, this leaves only the decimal digits. Then multiply by 7 you get back the remainder as a whole number.
• how can we calculate day with the help of year month and day