ARRANGE THE FRACTIONS IN ASCENDING AND DESCENDING ORDER

Example 1 :

Place these fractions in ascending order:

1/8, -2/3, 3/11, -1/6, -3/4

Solution :

LCM of (8, 3, 11, 6, 4)

LCM  =  264

1/8  =  (1/8) ⋅ (33/33)  ==>  33/264

-2/3  =  (-2/3) ⋅ (88/88)  ==>  -176/264

3/11  =  (3/11) ⋅ (24/24)  ==>  72/264

-1/6  =  (-1/6) ⋅ (44/44)  ==>  -44/264

-3/4  =  (-3/4) ⋅ (66/66)  ==>  -198/264

Arranging the equivalent fractions in ascending order.

-198/264, -176/264, -44/264, 33/264, 72/264

Arranging corresponding fractions of equivalent fractions in ascending order, we get

-3/4, -2/3, -1/6, 1/8, 3/11

Example 2 :

Place these fractions in ascending order:

-4/5, -1  1/3, 1/2, -1/10, 5/6

Solution :

LCM of (3, 2, 5, 6, 10)

LCM  =  30

-4/5  =  (-4/5) ⋅ (6/6)  ==>  -24/30

-4/3  =  (-4/3) ⋅ (10/10)  ==>  -40/30

1/2  =  (1/2) ⋅ (15/15)  ==>  2/30

-1/10  =  (-1/10) ⋅ (3/3)  ==>  -3/30

5/6  =  (5/6) ⋅ (5/5)  ==>  25/30

Arranging the equivalent fractions in ascending order.

-40/30, -24/30, -3/30, 2/30, 25/30

Arranging corresponding fractions of equivalent fractions in ascending order, we get

-4/3, -4/5, -1/10, 1/2, 5/6

Example 3 :

Place these fractions in ascending order:

-3/4, 1  1/4, 2/3, -1  1/2, 4/5

Solution :

LCM of (2, 3, 4, 5)

LCM  =  60

-3/4, 1  1/4, 2/3, -1  1/2, 4/5

-3/4  =  (-3/4) ⋅ (15/15)  ==>  -45/60

5/4  =  (5/4) ⋅ (15/15)  ==>  75/60

2/3  =  (2/3) ⋅ (20/20)  ==>  40/60

-3/2  =  (-3/2) ⋅ (30/30)  ==>  -90/60

4/5  =  (4/5) ⋅ (12/12)  ==>  48/60

Arranging the equivalent fractions in ascending order.

-90/60, -45/60, 40/60, 48/60, 75/60

Arranging corresponding fractions of equivalent fractions in ascending order, we get

-3/2, -3/4, 2/3, 4/5, 5/4

Example 4 :

Sonita plans to make a dessert using five ingredients: sugar, all-purpose flour, cocoa powder, mixed fruits, and vanilla essence. She will use these ingredients in 1/3, 5/8, 2/7, 3/5, and 4/9 respectively.

Arrange these substances in descending order according to the amount she uses and determine which ingredient she uses the most.

Solution :

• 1/3 = quantity of sugar
• 5/8 = quantity of all purpose flour
• 2/7 = quantity of cocoa powder
• 3/5 = quantity of mixed fruits
• 4/9 = quantity of vannila essence

To find which ingredient she use the most, we have to find the lcm of the denominators 3, 8, 7, 5 and 9.

LCM = 3 x 8 x 7 x 5 x 3

= 2520

Let us find the equivalent fractions for the fractions above with the denominator of 2520.

• 1/3 = (1/3) x (840/840) = 840/2520
• 5/8 = (5/8) x (315/315) = 1575/2520
• 2/7 = (2/7) x (360/360) = 720/2520
• 3/5 = (3/5) x (504/504) = 1512/2520
• 4/9 = (4/9) x (280/280) = 1120/2520

Now we have all fractions with the same denominator, now comparing the numerators, we know that 1575/2520 is greater. Then all purpose flour is the most used quantity.

Example 5 :

There are 482 students in the school and there are two Grade 4 classes:

Ms. Ashley’s and Mr. Ben’s classes. Ms. Ashley’s class has 15 boys and 6 girls.

Mr. Ben’s class has 14 girls and 10 boys.

• In Ms. Ashley’s class, 2/3 of students wear glasses.
• In Mr. Ben’s class, 1/4 of the kids have other siblings in the school.

a)  What fraction of the students in the school are in grade 4?

b)  What fraction of the grade 4 students are boys ?

c) What fraction of the grade 4 students are in Mr.Ashley's class ?

d)  What fraction of the students in Mr. Ben’s class that do not have siblings in the same school?

e)  In Ms. Ashley’s class, are there more students that wear glasses or do not wear glasses?

Solution :

a)  Total number of students = 482

Number of students in grade 4 = Number of students in Ashley's class + Number of students in Ben's class

= (15 + 6) + (14 + 10)

= 21 + 24

= 45

Fraction part of students who are in grade 4 = 45/482

b)  Number of boys in Ms. Ashley’s class = 15

Number of boys in Mr. Ben’s class = 10

Total number of boys = 15 + 10

= 25

Fraction of students who are boys = 25/45

c) Number of students in Mr.Ashley's class = (15 + 6)

= 21

Fraction of students who are in Mr.Ashley's class

= 21/45

d)  In Mr. Ben’s class, 1/4 of the kids have other siblings in the school.

Fraction of kids who do not have other siblings in the school = 3/4

= 3/4

e)  In Ms. Ashley’s class, 2/3 of students wear glasses.

1/3 of the students who do not wear glasses.

More number of students they wear glasses.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.