Which of the numbers 3 / 5 and 3 / 6 is greater?

Expert Answers
pohnpei397 eNotes educator| Certified Educator

Clearly, 3/5 is greater than 3/6.  You may figure this out mathematically or you may figure it out simply by logic.

By logic, look at what a these fractions mean.  In three fifths, you are taking three and dividing it five times.  In 3/6, you are taking the same three and dividing it six times.  If you cut a pie in five pieces, the slices will be bigger than if you cut it in six pieces.  Therefore 3/5 is greater.

You can figure this mathematically as well.  The least common multiple of 6 and 5 is 30 so we will make both into fractions with 30 on the bottom.

We multiply the first fraction by 6 and get 18/30 and we multiply the second by 5 and get 15/30.  18 is more than 15, so the first number is greater.

sheryll-pickett eNotes educator| Certified Educator

3/6 can be reduced to 1/2 which is 0.5

3/5 can be changed to 6/10 which is 0.6

 

3/5 is greater than 3/6 because 0.6 is greater than 0.5

amitparmar | Student

we solve it mathematically;

we have

3/5=.6

and

also we have

3/6=.5

since .6>.5

so,3/5>3/6.

krishna-agrawala | Student

When the numerator of two fractions are same, then the fraction with smaller denominator is greater.

I this question the two fractions are, 3/5 and 3/6.  They have a common numerator, that is 3. Therefore we can directly conclude that  fraction with smaller denominator is greater of the two.

Thus 3/5 is greater than 3/6.

giorgiana1976 | Student

One way  to compare the two fractions would be to both have the same denominator, so that numerators will be easily compared.

The common denominator of 5 and 6 is 5*6=30.

In order to obtain the common denominator, the first ratio will be amplified with 6 and the second ratio will be multiplied with 5.

3 / 5 and 3 / 6

3*6/5*6 and 3*5/6*5

18/30 and 15/30

0.6 and 0.5

0.6 > 0.5

So 0.6=3/5 is bigger.

Another way to compare would be to consider the rule that if the same number is divided by more consecutive numbers, differen as size, the smaller result would be found from dividing the number to the the biggest of these numbers and the smallest result, from dividing to the smallest of these numbers.

In our case,  the biggest is 3 / 5, because 3 is divided by the lowest.

 

malkaam | Student

Which of the numbers 3 / 5 and 3 / 6 is greater?

In order to see which numbers are greater we simplify each term in decimal form so that it could be easier to see that which number is greater than the other.
 
Taking the first number, 3/5:
3/5= 0.6
 
Taking the second number, 3/6:
3/6= 0.5
 
hence, we have the decimal values of each number, and therefore we find out that 3/5 is greater than 3/6 since we know that 0.6 is a bigger number than 0.5. 
ik9744 | Student

There is multiple ways to solve this, but I will show you two.

Which of the numbers 3 / 5 and 3 / 6 is greater?

  1. First way to solve this is change the denominator into common denominator
  2. By looking at it. Since they both have the same numerator, but one of the denominator is smaller.

I will be solving the first way. To find a common denominator you could just simply multiply the 5 by the 6. Making the denominator 30.

5•6=30

/30  /30

Now we would need to find the numerator Multiply the 3 by 6 making it 18 and the 3 by 5 making it 15.

3•5 and 3•6

18/30 15/30

Now you can see that the one on the left is bigger. I could also change it to a decimal because it gives you a better visual of which one is bigger.

3/5 = 18/30 = 0.6 As you can see it is bigger by .5

3/6 = 15/30 = 0.5 It is smaller by .5

Now I'll show yo another way to do this, is by looking at this. Since it's numerator is both 3, and the denominator is only one away. The one with the smaller denominator of course have to be the greater one.

3/5 is greater

I hoped I answered your question and I hope you  learned something from this.

crystaltu001 | Student

One way to see which of the fractions are bigger is by looking at the numerators. In this case, they are the same number, 3. Next, you could look at the denominators. They are different: 5 & 6. To put it simply, a pizza was cut into 5 slices and another was sliced into 6 pieces. They were the same size. Three slices of the 5 slices pizza would obviously be bigger.

udonbutterfly | Student

 3 / 5 __ 3 / 6

There are two ways you can do this convert both numbers into decimals which will get you

3 / 5 = 0.60

3 / 6 = 0.50

This 3 / 5 being the greatest

Or you can give each fraction common denominators which is one by

3 / 5 X 6 / 6 = 18/30

3 / 6 X 5 / 5 = 15/30

Again the first one is the greatest.

nisarg | Student

I had trouble with fractions too but I understood it better when I had examples.

For 3/5 and 3/6

so imagine that you have 2 pizzas of the same size

you cut one pizza into 5 equal pieces and the other into 6 equal pieces

if you take three slices from the first pizza then it would be more pizza than three slices from the second pizza. 

also in any case where the top numbers of fractions are the same then the one with the lower denominator is larger.

jess1999 | Student

In order to find whether 3/6 or 3/5 is bigger you can change these fractions into decimals. For example ,

3/6 = .5 ; 3/5 = .6

Since .6 ( 3 / 5 ) is greater than .5 ( 3 / 6 )

the answer is 3/5 is greater than 3/6

Wiggin42 | Student

We need to compare these to fractions: (3)/(5) and (3)/(6). 

There are several ways. In one way, you must realize that (3)/(6) is (1)/(2) and that (3)/(5) is greater than (1/2). 

Another way is to convert these fractions to decimals since they are easy: 

(3)/(5) becomes 0.6 
(3)/(6) becomes 0.5

Lastly, the best way is to realize that when fractions have the same numerator but different denominators, the one with the smaller denominator is the larger fraction. 

zumba96 | Student

3 / 5 and 3 / 6 

Well first you can find out the decimal value for both of these

3/5 =.6 while 3/6 =.5

There 3/5 is bigger since it is more than a half

atyourservice | Student

3 / 5 and 3 / 6

the both have a common multiple of 30 try to get the denomanaters the same

`3 / 5 xx 6 = 18/30 `

`3/6 xx 5= 15/30  `

3/5 is greater than 3/6

drewblay | Student

Try this site for learing comparing numbers games freely: comparing numbers interactive activities

rnk | Student

since the L.C.M of 5 and 6 is 30

we will make both the denominators 30

3 /5 = 3*6/5*6 = 18/30

3/6 = 3*5/6*5 = 15/30

On comparing the numerators we find,

18>15

so, 18/30 > 15/30

therefore 3/5 > 3/6

 

princessenotes | Student

3/5 is greater than 3/6.

Just imagine the slices of a pizza. It should help you more on fractions.

If you need anymore help, please contact my teacher at helpmathtutor@gmail.com