Solved Questions of Ascending and Descending Order of Fractions
1. There are four different fractions: 3/4, 5/6, 1/3, and 2/5. Arrange these fractions in descending order.
a) 5/6 > 1/3 > 2/5 > 3/4
b) 5/6 > 3/4 > 1/3 > 2/5
c) 5/6 > 2/5 > 3/4 > 1/3
d) 5/6 > 3/4 > 2/5 > 1/3
Answer: d) 5/6 > 3/4 > 2/5 > 1/3
Explanation: We find a common denominator by using the LCM method.
The LCM of denominators 4, 6, 3, and 5 is 60.
We find equivalent fractions.
3/4 = (3/5) x (15/15) = 45/60
5/6 = (5/6) x (10/10) = 50/60
1/3 = (1/3) x (20/20) = 20/60
2/5 = (2/5) x (12/12) = 24/60
So, the largest fraction is 5/6. Next, we compare the remaining fractions to find the next largest one. We can see that 45/60 is larger than 24/60, so the order is:
Therefore, 5/6 > 3/4 > 2/5 > 1/3.
2. Arrange the following fractions in ascending order: 17/3, 17/11, 17/9, 17/15.
a) 17/15 < 17/11 < 17/9 < 17/3
b) 17/11 < 17/15 < 17/9 < 17/3
c) 17/15 < 17/9 < 17/11 < 17/3
d) 17/3 < 17/9 < 17/11 < 17/15
Answer: a) 17/15 < 17/11 < 17/9 < 17/3
Explanation: For fractions with the same numerators,
> A fraction with the smallest denominator is the greatest fraction.
> A fraction with the greatest denominator is the smallest fraction.
So, ascending order of the fraction is 17/15 < 17/11 < 17/9 < 17/3.
3. Arrange the following fraction in ascending order: 7/3, 5/3, 9/3, 11/3.
a)7/3 < 5/3 < 9/3 < 11/3
b) 7/3 > 5/3 > 9/3 > 11/3
c) 5/3 < 7/3 < 9/3 < 11/3
d) 11/3 > 9/3 > 7/3 > 5/3
Answer: c) 5/3 < 7/3 < 9/3 < 11/3
Explanation: For fractions with the same denominator,
> The fraction with the smallest numerator is the smallest fraction.
> The fraction with the greatest numerator is the greatest fraction.
So, ascending order of the fraction is 5/3 < 7/3 < 9/3 < 11/3.
4. Arrange the following fractions in descending order: 4/3, 5/6, 7/8, 6/5.
a) 4/3 > 6/5 > 7/8 > 5/6
b) 4/3 > 5/6 > 7/8 > 6/5
c) 4/3 < 6/5 < 7/8 < 5/6
d) 4/3 > 6/5 < 7/8 > 5/6
Answer: a) 4/3 > 6/5 > 7/8 > 5/6
Explanation: The correct option is 4/3 > 6/5 > 7/8 > 5/6
LCM (3, 5, 6 and 8) = 120
4/3 = (4 x 40)/(3x 40) = 160/120
5/6 = 5 x 20 / 6 x 20 = 100/120
7/8 = (7 x 15)/(8x 15) = 105/120
6/5 = (6 x 24)/(5 x 24) = 144/120
So, 4/3 > 6/5 > 7/8 > 5/6
5. 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.
a) Sugar
b) All-purpose flour
c) Cocoa powder
d) Vanilla essence
Answer: b) All-purpose flour
Explanation: To arrange these fractions in descending order, we find LCM.
The LCM of 1/3, 3/5, 2/7, 5/8, and 4/9 is 2520.
1/3 = 840/2520
5/8 = 1575/2520
2/7 = 720/2520
3/5 = 1512/2520
4/9 = 1120/2520
So, the largest fraction is 5/8. Next, we compare the remaining fractions to find the next largest one. We can see that 1575/2520 is larger than 1512/2520.
Similarly, the order is: 1575/2520 > 1512/2520 > 1120/2520 > 840/2520 > 720/2520
5/8 > 3/5 > 4/9 > 1/3 > 2/7
All-purpose flour > Mixed fruits > Sugar > Vanilla essence > Choco powder
The most used ingredient by Sonita is All-purpose flour.
Practice Questions of Ascending and Descending Order of Fraction
1. Arrange the fractions 5/16, 9/16, 8/16 and 7/16 in ascending order.
a) 5/16 < 7/16 < 8/16 < 9/16
b) 5/16 < 8/16 < 7/16 < 9/16
c) 5/16 < 7/16 < 9/16 < 8/16
d) 5/16 < 8/16 < 8/16 < 7/16
Answer: a) 5/16 < 7/16 < 8/16 < 9/16
2. Arrange the following fractions in ascending order to find which is the largest among all: 1/3, 1/6, 1/2, 1/4.
a) 1/3
b) 1/6
c) 1/2
d) 1/4
Answer: c) 1/2
3. Arrange the following fractions in descending order: 3/4, 1/2, 4/5, 3/8.
a) 4/5 > 1/2 > 3/4 > 3/8
b) 4/5 > 3/4 > 3/8 > 1/4
c) 4/5 > 3/4 > 1/2 > 3/8
d) 3/4 > 4/5 > 1/2 > 3/8
Answer: c) 4/5 > 3/4 > 1/2 > 3/8
4. Arrange the following fractions in descending order: 1/2, 2/3, 7/12, 5/6, 1/4.
a) 1/4 > 1/2 > 7/12 > 2/3 > 5/6
b) 1/4 > 1/2 > 7/12 > 5/6 > 2/3
c) 1/4 > 7/12 > 1/2 > 2/3 > 5/6
d) 5/6 > 2/3 > 7/12 > 1/2 > 1/4
Answer: d) 5/6 > 2/3 > 7/12 > 1/2 > 1/4
5. Arrange the following fractions in ascending order: 4/5, 6/7, 11/14, 3/20.
a) 6/7, 11/14, 4/5, 3/20
b) 3/20, 11/14, 4/5, 6/7
c) 6/7, 4/5, 3/20, 11/14
d) 6/7, 4/5, 11/14, 3/20
Answer: b) 3/20, 11/14, 4/5, 6/7
6. Arrange the following fractions in ascending order: 5/6, 1/2, 4/9, 6/7.
a) 6/7, 4/9, 1/2, 5/6
b) 6/7, 4/9, 5/6, 1/2
c) 4/9, 1/2, 5/6, 6/7
d) 5/6, 1/2, 4/9, 6/7
Answer: c) 4/9, 1/2, 5/6, 6/7
7. Arrange the following fractions 1/2, 3/4, 7/8, 5/12 in descending order.
a) 7/8 > 1/2 > 3/4 > 5/12
b) 7/8 > 3/4 > 1/2 > 5/12
c) 7/8 > 3/4 > 5/12 > 1/2
d) 7/8 > 1/2 > 5/12 > 3/4
Answer: b) 7/8 > 3/4 > 1/2 > 5/12
8. Out of the fractions 9/31, 3/17, 6/23, 4/11 and 7/25. Which is the largest fraction?
a) 9/31
b) 3/17
c) 4/11
d) 6/23
Answer: c) 4/11
9. Which of the following fractions is the smallest?
a) 12/119
b) 1/10
c) 4/39
d) 7/69
Answer: b) 1/10
10. If the fractions 3/5, 5/8, 16/25, 4/5, 9/16 are arranged in ascending order of their values, which one will be the second from left?
a) 3/5
b) 16/25
c) 9/16
d) 4/5
Answer: a) 3/5
