Well-designed AP Board Solutions Class 6 Maths Chapter 7 Fractions Exercise 7.5 offers step-by-step explanations to help students understand problem-solving strategies.
Fractions Class 6 Exercise 7.5 Solutions – 6th Class Maths 7.5 Exercise Solutions
Question 1.
Write these fractions appropriately as additions or subtractions :
Question 2.
Solve :
a) \(\frac { 1 }{ 18 }\) + \(\frac { 1 }{ 18 }\)
Solution:
\(\frac { 1 }{ 18 }\) + \(\frac { 1 }{ 18 }\) = \(\frac { 1+1 }{ 18 }\) = \(\frac { 2 }{ 18 }\) = \(\frac{2 \div 2}{18 \div 2}\) = \(\frac { 1 }{ 9 }\)
b) \(\frac { 8 }{ 15 }\) + \(\frac { 3 }{ 15 }\)
Solution:
\(\frac { 8 }{ 15 }\) + \(\frac { 3 }{ 15 }\) = \(\frac { 8+3 }{ 15 }\) = \(\frac { 11 }{ 15 }\)
c) \(\frac { 7 }{ 7 }\) – \(\frac { 5 }{ 7 }\)
Solution:
\(\frac { 7 }{ 7 }\) – \(\frac { 5 }{ 7 }\) = \(\frac { 7-5 }{ 7 }\) = \(\frac { 2 }{ 7 }\)
d) \(\frac { 1 }{ 22 }\) + \(\frac { 21 }{ 22 }\)
Solution:
\(\frac { 1 }{ 22 }\) – \(\frac { 21 }{ 22 }\) = \(\frac { 1+21 }{ 22 }\) = \(\frac { 22 }{ 22 }\) = 1
e) \(\frac { 12 }{ 15 }\) – \(\frac { 7 }{ 15 }\)
Solution:
\(\frac { 12 }{ 15 }\) – \(\frac { 7 }{ 15 }\) = \(\frac { 12-7 }{ 15 }\) = \(\frac { 5 }{ 15 }\) = \(\frac{5 \div 5}{15 \div 5}\) = \(\frac{1}{3}\)
f) \(\frac { 5 }{ 8 }\) – \(\frac { 3 }{ 8 }\)
Solution:
\(\frac { 5 }{ 8 }\) – \(\frac { 3 }{ 8 }\) = \(\frac { 5-3 }{ 8 }\) = \(\frac { 8 }{ 8 }\) = 1
g) 1 – \(\frac { 2 }{ 3 }\)(1 = \(\frac { 3 }{ 3 }\))
Solution:
1 – \(\frac { 2 }{ 3 }\) = \(\frac { 3 }{ 3 }\) – \(\frac { 2 }{ 3 }\) = \(\frac { 3 – 2 }{ 3 }\) = \(\frac { 1 }{ 3 }\)
h) \(\frac { 1 }{ 4 }\) + \(\frac { 0 }{ 4 }\)
Solution:
\(\frac { 1 }{ 4 }\) + \(\frac { 0 }{ 4 }\) = \(\frac { 1 }{ 4 }\) + 0 = \(\frac { 1 }{ 4 }\) (∵ \(\frac { 0 }{ 4 }\) = 0)
i) 3 – \(\frac { 12 }{ 5 }\)
Solution:
3 – \(\frac { 12 }{ 5 }\) = \(\frac{3 \times 5}{5}\) – \(\frac { 12 }{ 5 }\) = \(\frac { 15 }{ 5 }\) – \(\frac { 12 }{ 5 }\) = \(\frac { 15 – 12 }{ 5 }\) = \(\frac { 3 }{ 5 }\)
Question 3.
Shubham painted \(\frac { 2 }{ 3 }\) of the wall space in his room. His sister Madhavi helped and painted \(\frac { 1 }{ 3 }\) of the wall space. How much did they paint together?
Solution:
Fraction of wall painted by Shubham = \(\frac { 2 }{ 3 }\) Fraction of wall painted by Madhavi = \(\frac { 1 }{ 3 }\) Fraction of wall painted by Shubham and Madhavi = \(\frac { 2 }{ 3 }\) + \(\frac { 1 }{ 3 }\) = \(\frac { 2+1 }{ 3 }\) =\(\frac { 3 }{ 3 }\) =1
Thus, the fraction of wall painted by both = 1
Question 4.
Fill in the missing fractions.
a) \(\frac { 7 }{ 10 }\) – ______ = \(\frac { 3 }{ 10 }\)
b) ______ – \(\frac { 3 }{ 21 }\) = \(\frac { 5 }{ 21 }\)
c) ______ – \(\frac { 3 }{ 6 }\) = \(\frac { 3 }{ 6 }\)
d) ______ + \(\frac { 5 }{ 27 }\) = \(\frac { 12 }{ 27 }\)
Solution:
a) \(\frac { 7 }{ 10 }\) – \(\frac { 4 }{ 10 }\) = \(\frac { 3 }{ 10 }\)
b) \(\frac { 8 }{ 21 }\) – \(\frac { 3 }{ 21 }\) = \(\frac { 5 }{ 21 }\)
c) \(\frac { 6 }{ 6 }\) – \(\frac { 3 }{ 6 }\) = \(\frac { 3 }{ 6 }\)
d) \(\frac { 7 }{ 27 }\) + \(\frac { 5 }{ 27 }\) = \(\frac { 12 }{ 27 }\)
Question 5.
Javed was given \(\frac { 5 }{ 7 }\) of a basket of oranges. What fraction of oranges was left in the basket ?
Solution:
Fraction of basket of oranges given to Javed = \(\frac { 5 }{ 7 }\)
Fraction of basket of oranges left = 1 – \(\frac { 5 }{ 7 }\) = \(\frac { 7 }{ 7 }\) – \(\frac { 5 }{ 7 }\) = \(\frac { 7 – 5 }{ 7 }\) = \(\frac { 2 }{ 7 }\)
Thus, the fraction of oranges was left in the basket = \(\frac { 2 }{ 7 }\)