Subscribe to our YouTube channel for the latest videos, updates, and tips.


Comparing Fractions



In comparing fractions, we may use the following steps:

STEP I 

Find the LCM of the denominators of the given fractions. 


STEP II 

Convert all fractions to its equivalent fraction with denominator equal to the LCM obtained in step I. 


STEP III

Arrange all the fractions in ascending or descending order by arranging numerators in ascending or descending order. 



To compare two or more fractions, we convert them to like fractions and compare their numerators.



Examples on comparing fractions;

1. Which is bigger ³/₄ or ⁵/₁₂?

Solution:


First find the Least Common Multiple (L.C.M) of 4 and 12.

We have,



Therefore, LCM Least Common Multiple (L.C.M) of 4 and 12 is 2 × 2 × 3 = 12.

Now we need to convert the given fractions (3/4 and 5/12) to equivalent fractions with denominator 12.

We have,

3/4 = (3 × 3)/(4 × 3) = 9/12

We know that 9 > 5

Therefore, 9/12 > 5/123/4 > 5/12



2. Arrange the fractions 7/8, 2/3, 5/6 in ascending order.

Solution:




L.C.M. of 8, 3 and 6 = 2 × 3 × 4= 24.

7/8 = (7 × 3)/(8 × 3) = 21/24;

2/3 = (2 × 2 × 4)/(3 × 2 × 4) = 16/24;

5/6 = (5 × 4)/(6 × 4) = 20/24.

As 16 < 20 <21,

16/24 < 20/24 < 21/242/3 < 5/6 < 7/8.

Hence, the given fractions in ascending order are 2/3, 5/6, 7/8.



3. Arrange the following fractions in ascending order;

⁵/₈, ⁵/₆, ⁷/₄, ³/₅

Solution:


Let us first find the LCM of the denominators:

We have,



Therefore, LCM = 2 × 2 × 5 × 2 × 3 = 120

Now, we convert each fraction to its equivalent fraction with
denominator 120.

We have,

3/5 = (3 × 24)/(5 × 24) = 72/120      [Since, 120 ÷ 5 = 24]

5/8 = (5 × 15)/(8 × 15) = 75/120       [Since, 120 ÷ 8 = 15]

5/6 = (5 × 20)/(6 × 20) = 100/120      [Since, 120 ÷ 6 = 20]

7/4 = (7 × 30)/(4 × 30) = 210/120      [Since, 120 ÷ 4 = 30]

We know that 72 < 75 < 100 < 210.

72/120 < 75/120 < 100/120 < 210/120

3/5 < 5/8 < 5/6 < 7/4

Note:

If two fractions have the same numerator but different denominators, the fraction with greater denominator is smaller.

For example; 9/14 < 9/10

Also, 7/25 < 7/18 < 7/11 < 7/10 < 7/8



4. State which of the two fractions 7/12 and 5/21 has higher value.

Solution:


L.C.M. of 12 and 21 is 84.

7/12 = (7 × 7)/(12 × 7) = 49/84

5/21 = (5 × 4)/(21 × 4) = 20/84

Now, 49>20

Therefore, 7/12 > 5/21



5. Arrange the following fractions in descending order:

(i) 2/9, 2/3, 8/21

(ii) 1/5, 3/7, 7/10, 13/28


(i) 2/9, 2/3, 8/21

Solution:


First we convert the given fractions into like fractions i.e., fractions having common denominator. For this, we first find the LCM of the denominator of the given fractions.

Denominators are 9, 3 and 21



LCM of 9, 3, 21 = 3 × 3 × 7 = 63

Now, we convert each fraction into equivalent fractions with 63 as its denominator.

2/9 = (2 × 7)/(9 × 7) = 14/63         [Since, 63 ÷ 9 = 7]

2/3 = (2 × 21)/(3 × 21) = 42/63      [Since, 63 ÷ 3 = 21]

8/21 = (8 × 3)/(21 × 3) = 24/63      [Since, 63 ÷ 21 = 3]

We know that 42 > 24 > 14

Therefore, 42/63 > 24/63 > 14/632/3 > 8/21 > 2/9



(ii) 1/5, 3/7, 7/10, 13/28

Solution:


Denominators of the given fractions are: 5, 7, 10 and 28



LCM of denominators = 5 × 7 × 2 × 2 = 140

We now convert each fraction into an equivalent fraction with 140 as its denominator.

Therefore, 1/5 = (1 × 28)/(5 × 28) = 28/140    [Since, 140 ÷ 5 = 28]

3/7 = (3 × 20)/(7 × 20) = 60/140                   [Since, 140 ÷ 7 = 20]

7/10 = (7 × 14)/(10 × 14) = 98/140                [Since, 140 ÷ 10 = 14]

13/28 = (13 × 5)/(28 × 5) = 65/140                [Since, 140 ÷ 28 = 5]

Therefore,

98/140 > 65/140 > 60/140 > 28/1407/10 > 13/28 > 3/7 > 1/5

Note:

We can also arrange the given fractions in descending order by making their numerators the same and using the result that the fraction having greater denominator is smaller, provided that they have the same numerator.









7th Grade Math Problems

From Comparing Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 10, 25 11:41 AM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More