5 is 12.5% of 40.
Step-by-step explanation:
So I think your question here is about long division? You're asking about how to divide 5 by 40? Well... you could techincally leave it as a fraction and multiply by 100. I don't know what your teacher is looking for.
Another way to do it, which is easier, in my opinion, is to simplify the fraction first.
Check if 40 is divisible by 5. (It's 5*8.)
So you have 5/(5*8). Dividing a number by itself is always 1, so your simplified fraction is 1/8. You multiply that by 100 to get 100/8. You divide both the numerator and the denominator by 4 to get 25/2. (You might have to change it to a decimal.)
You could also multiply 5 by 100 first and then divide it by 40. It won't change the outcome.
5/40 * 100 = (5*100)/40
Whether you set it up like that or not, you can cancel out factors that 40 and 100 have in common.
What I mean by that is... numbers are made up of their factors, right?
100 = 10 * 10
40 = 10 * 4
So (5*10*10)/(10*4)=(5*100)/40
Again, multiplying something by a number and dividing by the same number right after doesn't change the value. The processes cancel each other out. So, you can just go ahead and cancel out those 10's:
(5*10*10)/(10*4)=(5*10*1)/(1*4)
The underlined parts are to show which numbers cancel each other out. Because anything times 1 is just itself, you can remove the ones to get:
(5*10)/4
You can still simplify more.
10 = 2*5
4 = 2*2
And, using the same method we used earlier, we can simplify.
 (5*2*5)/(2*2)
=(5*1*5)/(1*2)
=(5*5)/2
5 and 2 are both prime numbers, so they don't share any factors. We can't simplify any further. So you multiply 5*5 and you have 25/2. Now you can't avoid the division. (Only if your answer has to be a decimal, though! Make sure to check with your teacher.)
So... the division part.
2⟌25
So you start by checking how many times the divisor (the number on the outside, the denominator, so 2) goes into the largest place value of the dividend (the number on the inside, the numerator). What I mean by that is, 25 is a two-digit number, right? You check the place on the very left.
25
So you need to know how many times 2 goes into 2. 2/2 is 1, so you write that 1 on the top.
  1
2⟌25
 -2
  ___
  0
So after you divide the tens place by 2, you subtract to find the remainder. In this case, there was none, but say you were dividing 35 by 2 instead, there would be a remainder of 1. That's why you can't miss that step. Then, you bring the digit from the units place down.
  1
2⟌25
 -2
  ___
  05
Now you need to divide 5 by 2. 2*2=4, that's too low. But 2*3=6, so that definitely doesn't work. You need to use 2 because you can have a remainder, but your answer can't be higher than the real thing. You write the 2 at the top next to the 1, and subtract 2*2 from 5 to get the remainder.
  12
2⟌25
 -2
  ___
  05
  - 4
  ___
   1
Now's where it gets kind of complicated. Because 2 doesn't go into 1 even once, you can't go any further without adding a decimal point at the top. When you do this, you can change the 1 at the bottom to a 10. (It won't actually be a 10-- it's 1.0, which is the same as 1. But because you've already added the decimal point on the top, you can continue your work as if it's a 10.) This is because 1.0=1.00=1.000, and so on, so there's an endless number of 0's you can bring down and continue your work with.
  12.
2⟌25
 -2
  ___
  05
  - 4
  ___
   10
Now you can divide 10 by 2 and put the result next to the decimal point on the top, and you're done! 10/2=5
  12.5
2⟌25
 -2
  ___
  05
  - 4
  ___
   10
   -10
   ___
    0
And that's it, you're done! 5 is 12.5% of 40. I'll show the same method of long division for 5/40. In this case, you can't get 40 into 5 even once without adding the decimal point on top.
   0. Â
40⟌50
And then you continue normally.
   0.1 Â
40⟌5.00000000...
   -40
   ___
   10
At first, it might seem like you don't have any more digits to bring down, but you've already put down that decimal point. Again, 5.0=5.00=5.000=5.0000 and on and on and on. You have an endless amount of 0's you can bring down each time.
40 goes into 100 twice.
   0.12 Â
40⟌5.00000000...
   -40
   ___
   100
   -80
   ___
    20
Again, bring down another 0. 40 goes into 200 5 times.
   0.125 Â
40⟌5.00000000...
   -40
   ___
   100
   -80
   ___
    200
    -200
  Â
       0
So 5/40 is 0.125.
I really hope I could help you! I'm so sorry if I overexplained things, I wasn't sure which part you were confused on...
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