Definition of "quotient" --> the number resulting from the divison of one number by another
To divide these fractions we will use a method I learned in 6th grade. It is called the reciprocal method and makes dividing fractions much easier. If you can multiply fractions well, this method is for you. I personally always use this method, for it's the only one I know and I find it the easiest.
Let's begin! I'll solve these divison problems in the order you listed them:
1.) 7 2/3 ÷ 5 3/8 = ?
(Here we can see that these are mixed fractions. To use the reciprocal method, it'll be much easier to simply these into improper fractions. I'll provide an image of how to do that.)
23/2 ÷ 43/8 = ?
(Once we've converted the mixed fractions into improper fractions, now we can start using the reciprocal method. I've proved another photo of how to apply said method.)
Using this reciprocal method changes the operation from division to multiplication, which is much easier :). You only invert ONE fraction and that's the one that's ALWAYS on the RIGHT, the one that you are dividing by.
Let's invert! :
23/2 ÷ 43/8
23/2 × 8/43
(Now multiply the numerator and denominators)
184/86
(We now have our answer, but to figure out the right bin to put this quotient in, it'll help to convert this improper fraction back to a mixed fraction. We do so by using ling divison. I've provided another image to show how that is done)
Now 184/86 is equal/simplified to 2 12/86
So this quotient, 2 12/86, belongs in the "Quotient Greater Than 1" column/bin
Now you can apply this same process to the rest of the problems. I will provide the answer for all, but it'll be straight forward since I've already explained how to solve these problems :)
2.) 6 2/3 ÷ 6 8/12
(simplify)
20/3 ÷ 80/12
(invert)
20/3 × 12/80
(multiply)
240/240 = 1
(Note: whenever the numerator and denominator in fraction are the same, it always equals/simplifies to 1)
This quotient belongs in the "Quotient Equal to 1" column/bin
3.) 3 2/5 ÷ 6 3/4
17/5 ÷ 27/4
17/5 × 4/27
68/135
(Note: This is clearly not an improper fraction because the numerator is less than the denominator. So we can clearly see that this quotient is less than 1)
This quotient belongs in the "Quotient Less than 1" bin.
4.) 5 1/6 ÷ 4 2/5
31/6 ÷ 22/5
31/6 × 5/22
155/132
1 23/132
This quotient belongs in the "Quotient Greater than 1" bin.
5.) 2 1/4 ÷ 2 1/2
9/4 ÷ 5/2
9/4 × 2/5
18/20
This quotient belongs in the "Quotient Less than 1" bin.
6.) 12 4/5 ÷ 8 1/4
64/5 ÷ 33/4
64/5 × 4/33
256/165
1 91/165
This quotient belongs in the "Quotient Greater than 1" bin.
7.) 8 3/8 ÷ 8 2/9
67/8 ÷ 74/9
67/8 × 9/74
603/592
1 11/592
This quotient belongs in the "Quotient Greater Than 1" bin.
(Hope this was helpful :) )
