EXERCISE 7.7
1). Represent the following on the number line.
i) 2/6, ii) 4/6, iii) 7/6 , iv) 10/6
Ans.
2). Write the fraction representing the shaded portion
Ans . a) 4/8 b) 2/4 c) no region d) 3/6 e) 2/8
3). Identify proper and improper fraction
6/9 , 7/12 , 4/8 , 10/5 , 25/4 , 2/9 , 18/12 , 15/5 , 3/2 , 3/7
Ans.
Proper fraction = 6/9 , 7/12 , 4/8 , 2/9 , 3/7
Improper fraction = 10/5 , 25/4 , 18/12 , 15/5 , 3/2
4). Identify the unlike fraction from the following
7/11 , 1/2 , 4/11 , 5/7 , 9/12, 15/11, 2/11
Ans. Unlike fractions = 1/2 , 5/7 , 9/12.
5). Identify like fraction from the following
13/5 , 9/12 , 1/2 , 3/9 , 7/5 , 10/5 , 3/4 , 18/5 , 7/10
Ans. Like fractions = 13/5 , 7/5 , 10/5 , 18/5
6). Convert the following improper fraction into like fraction.
a) 13/2 b) 28/5 c) 45/6 d) 38/(9 )
Ans.
a)
∴ 13/2 = 6 ½
b)
∴ 28/5 = 5 ³⁄ 5
c)
∴ 45/6 = 7½
d)
∴ 38/9 = 4²⁄ 9
7). Write the following fraction into ascending and descending orders using {< , >}
5/12 , 8/12 , 1/12 , 4/12 , 11/12 , 0/12 , 7/12
Ans. Ascending order = 0/12 < 1/12 < 4/12 < 5/12 < 7/12 < 8/12 < 11/12
Descending order = 11/12 > 8/12 > 7/12 > 5/12 > 4/12 > 1/12 > 0/12
8). Color the parts according to the fraction given.
a) 3/8 b) 3/4 c) 6/8 d) 5/8
9). Write.
a) Any 2 proper fraction and 2 improper fractions with denominator 5
b) Any 3 proper fraction and 3 improper fractions with denominator 11
Ans.
a) Proper fractions :- 2/5 and 3/5
Improper fractions :- 7/5 and 9/5
b) Proper fractions :- 7/11 and 9/11
Improper fractions :- 15/11 and 19/11
10). Compare the following fractions
1) 3/4 And 2/5 2) 4/5 And 5/6 3) 32/4 And 21/4 4) 7/11 And 2/11 5) 31/3 And 32/6
Ans.
1) 3/4 and 2/5. Here LCM = 20
= (3×5)/(4×5) = 15/20 , (2×4)/(5×4) = 8/20
= 15/20 > 8/20
= 3/4 > 2/5
2) 4/5 and 5/6. Here LCM = 30
= (4×6)/(5×6) = 24/30 , (5×5)/(6×5) = 25/30
= 24/30 < 25/30
= 4/5 < 5/6
3) 32/4 and 21/4
= (3×4+2)/4 = 14/4 , (2×4+1)/4 = 9/4
= 14/4 > 9/4
= 32/4 > 21/4
4) 7/11 and 2/11
= 7/11 > 2/11
5) 31/3 and 32/6. Here LCM =6
= (3×3+1)/3 = 10/3 , (3×6+2)/6 = 20/6
= (10 ×2)/(3×2) = 20/6 , (20×1)/(6×1) = 20/6
= 20/6 = 20/6
= 31/3 = 32/6
11) Reduce the following fractions to their simplest form
a) 16/72 b) 80/24 c) 15/75 d) 42/28
Ans:
a) 16/72 HCF of 16 and 72 is 8
= (16÷8) / (72÷8) = 2/9
b) 80/24 HCF of 80 and 24 is 8
= (80÷8)/(24÷8) = 10/3
c) 15/75 HCF of 15 and 75 is 15
= (15÷15)/(75÷15) = 1/5
d) 42/28 HCF of 42 and 28 is 14
= (42÷14)/(28÷14) = 3/2½
12). Meenakshi ate 2½ Chapattis for breakfast and 1 Chapatti for lunch. How many chapatti did she eat?
Ans. Fraction of chapattis eaten for breakfast = 2½
Fraction of chapatti eaten for lunch = 1½
Total chapattis eaten by Meenakshi
= 2½ + 1½
= 5/2 + 3/2
= 8/2 = 4
Therefore Meenakshi ate a total of 4 chapattis.
13). Joseph cleaned 2/3 of his room. His sister Tina helped him clean more 1/5 of his room. How much did they clean together? What part of the whole space is left to be cleaned?
Ans. Fraction of place cleaned by Joseph = 2/3
Total space cleaned by both = 2/3 + 1/3
= (2×5)/(3×5) + (1×3)/(5×3)
= (10+3)/15 = 13/15
Space left to be cleaned is 1−13/15
= (1×15)/(1×15) – (13×1)/(15×1)
= 15/15 − 13/15
= (15−13)/15 = 2/15
Hence both of them cleaned 13/15 of Joseph’s room and 2/15 is remaining to be cleaned