Math sense

Question

a: How many 3/4s are in 1 ?

b: Use the answer to part a to find the number of 3/4s in 3 ?

 

Please explain this fraction problem in very detail. I am totally stuck here.

Answer 1

1 = 4/4 = 3/4 + 1/4

 

           1/4 is 1/3 of 3/4

 

So, the number of 3/4 in 1 is 1 1/3

 

Another way to do this is to divide 1 by 3/4:

 1÷3/4=1·4/3= 4/3 = 1 1/3

-------------------------------------------------------------------------------------

The number of 3/4 in 3 is three times the number of 3/4 in 1.

 

So, the number of 3/4 in 3 is 3(4/3) = 4

 

Note that 3 = 12/4 = 3/4 + 3/4 + 3/4 + 3/4 = 4(3/4)

Answer 2

a)

 

There is only one 3/4s in 1.  This is because 3/4 is less than 1.  If we had another 3/4s, then we would have had 6/4, which is an improper fraction that reduces to 3/2.  This improper fraction is greater than 1.  Also, an improper fraction can be converted to a mixed number.  Mixed numbers are greater than 1 on the positive side.  Therefore, it cannot fit in 1.

 

 

Here is a mathematical approach to this.

 

3/4 = 3/4

 

3/4 + 3/4 = 6/4 = 4/4 + 2/4 = 1 1/2

 

 

b)

 

If there is only one 3/4s in 1, then there is only three 3/4s in 3.  Here is why. 

 

3/4 + 3/4 + 3/4  = 9 / 4 = 4/4 + 4/4 + 1/4 = 1 + 1 + 1/4 = 2 1/4

 

 

Adding a fourth 3/4s will give one more whole, resulting in 3 wholes.  Plus the 1/4.  That 1/4 will make it go over 3.