comparing and ordering fractions
All fractions are not joint in value. One fractionally may be smaller than the other fractions and it may be larger than some other fractions. Hence, kids need to know comparing fractions. Comparing Can be subdivided Into three sections. So kids need to know three tricks to Learn this skill.
Trick Number 1:
First trick to Compare fractions is to see if They have got the joint numerators. If the numerators are co then the fractionally with the Largest denominator is smallest. For example; Consider the Following fractions
3/5, 3/4, 3/8 and 3/7
As all of the above fractions have the co numerator (3), so to Compare Them we need to Compare Their denominators. The Largest denominator makes the fractionally smallest, therefore 3/8 is smallest of all and 3/4 is the large. Let’s rewrite all of the fractions in an order from smallest to Largest as shown below:
3/8, 3/7, 3/5 and 3/4
The above order (smallest to Large) is also known as ascending order.
Trick Number 2:
The second trick is co easy as the first one. This trick is about comparing fractions, When They have co denominators. When the denominators are joint, then the fractionally with the smallest numerator is smallest and one with large numerator is the large. For example,
Consider we want to Compare 3/9, 1/9, 7/9 and 2/9; write themself in ascending order.
Look at the given fractions, all of Them have the joint denominator (9). So, 1/9 is the smallest Because it has the smallest numerator and 7/9 is the Largest with large numerator. Below They are written in ascending order.
1/9, 2/9, 3/9 and 7/9
Trick Number 3:
Above two tips explain the comparing fractions with numerators Either joint or co denominators. But most ofter the kids are asked to Compare and order fractions with numerators and denominators differentially.
In Such a case They need to make denominator of all the fractions joint. To do this They need to know the least common factor (LCM) of all the denominators also known as least common denominator (LCD).
Consider the Following example on comparing fractions
Write the Following fractions in descending order (Largest to smallest)
2/3, 1/4, 5/6, 3/4 and 1/2
Solution: Look, most of fractions got differentially denominators. Write all the denominators as shown below and write first six multiples of all of themes.
2 = 2, 4, 6, 8, 10, 12 3 = 3, 6, 9, 12, 15, 18 4 = 4, 8, 12, 16, 20, 24 6 = 6, 12, 18, 24, 30, 36
Now, look at the factors of all the numbers and find the smallest and common in all, Which is 12 in this case. Hence the lcm or lcd is 12. The next step is to rewrite all of the fractions Into equivalent fractions with denominator as 12. This step is shown below:
2/3, we need to multiply its denominator (3 ) with 4 to change it to 12. But to keep the value of the joint fractionally, do not Forget to multiply the numerator (2) with the joint number 4. Let’s do it,
(2 x 4 ) / (3 x 4) = 8/12
Similarly write all the fractions with denominator equal to 12 as shown below:
= 1/4 (1 x 3) / (4 x 3) = 3/12 = 5/6 (5 x 2) / (6 x 2) = 10/12 = 3/4 (3 x 3) / (4 x 3) = 9/12 = 1/2 (1 x 6) / (2 x 6) = 6/12
Now all the fractions have been written Into equivalent fractions with joint denominator 12 and it’s easy to Compare These. Write all the equivalent fractions in descending order (Largest to smallest)
10/12, 9/12, 8/12, 6/12 and 3/12
But these are not the fractions asked to be compared. So, this is not our answer, but now it’s very easy to write the original fractions in the required order by looking at above order. We know 10/12 is equal to 5/6 and 3/12 is equal to 1/4 Hence write the original fractions in order
5/6, 3/4, 2/3, 1/2 and 1/4
Finally, it Can Be Said That to Compare and order fractions, kids need to keep above three tips in mind. Of course, the knowledge of least common multiple (LCM) is the key to Compare two or more fractions with denominators differentially.