Well-designed AP Board Solutions Class 6 Maths Chapter 7 Fractions Exercise 7.3 offers step-by-step explanations to help students understand problem-solving strategies.
Fractions Class 6 Exercise 7.3 Solutions – 6th Class Maths 7.3 Exercise Solutions
Question 1.
Write the fractions. Are all these fractions equivalent?
Solution:
\(\frac { 1 }{ 2 }\), \(\frac { 2 }{ 4 }\), \(\frac { 3 }{ 6 }\), \(\frac { 4 }{ 8 }\)
\(\frac { 4 }{ 12 }\), \(\frac { 3 }{ 9 }\), \(\frac { 2 }{ 6 }\), \(\frac { 1 }{ 3 }\), \(\frac { 6 }{ 15 }\)
Question 2.
Write the fractions and pair up the equivalent fractions from each row.
Solution:
a) \(\frac { 1 }{ 2 }\)
b) \(\frac { 4 }{ 6 }\)
c) \(\frac { 3 }{ 9 }\)
d) \(\frac { 2 }{ 8 }\)
e) \(\frac { 3 }{ 4 }\)
i) \(\frac { 6 }{ 18 }\)
ii) \(\frac { 4 }{ 8 }\)
iii) \(\frac { 12 }{ 16 }\)
iv) \(\frac { 8 }{ 12 }\)
v) \(\frac { 4 }{ 16 }\)
Question 3.
Replace in each of the following by the correct number:
Question 4.
Find the equivalent fraction of \(\frac { 3 }{ 5 }\) having
a) denominator 20
b) numerator 9
c) denominator 30
d) numerator 27.
Solution:
a) Given fraction = \(\frac { 3 }{ 5 }\)
Here, we required denominator = 20
(5 × 4 = 20), ∴ \(\frac { 3 }{ 5 }\) = \(\frac{3 \times 4}{5 \times 4}\) = \(\frac { 12 }{ 20 }\)
∴ Required fraction = \(\frac { 12 }{ 20 }\)
b) Here, we required numerator = 9
(3 × 3 = 9), ∴ \(\frac { 3 }{ 5 }\) = \(\frac{3 \times 3}{5 \times 3}\) = \(\frac { 9 }{ 15 }\)
∴ Required fraction \(\frac { 9 }{ 15 }\)
c) Here, we required denominator $=30$
(5 × 6 = 30), ∴ \(\frac { 3 }{ 5 }\) = \(\frac{3 \times 6}{5 \times 6}\) = \(\frac { 18 }{ 30 }\)
∴ Required fraction = \(\frac { 18 }{ 30 }\)
d) Here, we required numerator = 27
(3 × 9 = 27), ∴ \(\frac { 3 }{ 5 }\) = \(\frac{3 \times 9}{5 \times 9}\) = \(\frac { 27 }{ 45 }\)
∴ Required fraction = \(\frac { 27 }{ 45 }\)
Question 5.
Find the equivalent fraction of \(\frac { 36 }{ 48 }\) with
a) numerator 9
b) denominator 4.
Solution:
a) Given fraction = \(\frac { 36 }{ 48 }\)
Here, we required numerator = 9
(36 ÷ 4 = 9), ∴ \(\frac { 36 }{ 48 }\) = \(\frac{36 \div 4}{48 \div 4}\) = \(\frac { 9 }{ 12 }\)
∴ The required fraction = \(\frac { 9 }{ 12 }\)
b) Here, we required denominator = 4
(48 ÷ 12 = 4), ∴ \(\frac { 36 }{ 48 }\) = \(\frac{36 \div 12}{48 \div 12}\) = \(\frac { 3 }{ 4 }\)
∴ Required fraction = \(\frac { 3 }{ 4 }\)
Question 6.
Check whether the given fractions are equivalent :
a) \(\frac { 5 }{ 9 }\), \(\frac { 30 }{ 54 }\)
b) \(\frac { 3 }{ 10 }\), \(\frac { 12 }{ 50 }\)
c) \(\frac { 7 }{ 3 }\), \(\frac { 5 }{ 11 }\)
Solution:
a) \(\frac { 5 }{ 9 }\), \(\frac { 30 }{ 54 }\) (HCF of 30,54 is 6 )
Simplest form of \(\frac { 30 }{ 54 }\) = \(\frac{30 \div 6}{54 \div 66}\) = \(\frac { 5 }{ 9 }\)
∴ \(\frac { 5 }{ 9 }\) and \(\frac { 30 }{ 54 }\) are equivalent fractions.
b) \(\frac { 3 }{ 10 }\), \(\frac { 12 }{ 50 }\)( HCF of 12,50 = 2)
Simplest form of \(\frac { 12 }{ 50 }\) = \(\frac{12 \div 2}{50 \div 2}\) = \(\frac { 6 }{ 25 }\)
∴ \(\frac { 3 }{ 10 }\) and \(\frac { 12 }{ 50 }\) are not equivalent fractions.
c) \(\frac { 7 }{ 13 }\), \(\frac { 5 }{ 11 }\) are not equivalent fractions. (Both \(\frac { 7 }{ 13 }\), \(\frac { 5 }{ 11 }\) are not in simplest form)
Question 7.
Reduce the following fractions to simplest form:
a) \(\frac { 48 }{ 60 }\)
b) \(\frac { 150 }{ 60 }\)
c) \(\frac { 84 }{ 98 }\)
d) \(\frac { 12 }{ 52 }\)
e) \(\frac { 7 }{ 28 }\)
Solution:
a) \(\frac { 48 }{ 60 }\) [HCF of 48 and 60 is 12]
\(\frac { 48 }{ 60 }\) = \(\frac{48 \div 12}{60 \div 12}\) = \(\frac { 4 }{ 5 }\)
∴ The simplest form of \(\frac { 48 }{ 60 }\) = \(\frac { 4 }{ 5 }\)
b) \(\frac { 150 }{ 60 }\) [HCF of 150 and 60 is 30]
\(\frac { 150 }{ 60 }\) = \(\frac{150 \div 30}{60 \div 30}\) = \(\frac { 5 }{ 2 }\)
∴ The simplest form of \(\frac { 150 }{ 60 }\) = \(\frac { 5 }{ 2 }\)
c) \(\frac { 84 }{ 98 }\) [HCF of 84 and 98 is 14]
\(\frac { 84 }{ 98 }\) = \(\frac{84 \div 14}{98 \div 14}\) = \(\frac { 6 }{ 7 }\)
∴ The simplest form of \(\frac { 84 }{ 98 }\) = \(\frac { 6 }{ 7 }\)
d) \(\frac { 12 }{ 52 }\) [HCF of 12 and 52 is 4]
\(\frac { 12 }{ 52 }\) = \(\frac{12 \div 4}{52 \div 4}\) = \(\frac { 3 }{ 13 }\)
∴ The simplest form of \(\frac { 12 }{ 52 }\) = \(\frac { 3 }{ 13 }\)
e) \(\frac { 7 }{ 28 }\) [HCF of 7 and 28 is 7]
\(\frac { 7 }{ 28 }\) = \(\frac{7 \div 7}{28 \div 7}\) = \(\frac { 1 }{ 4 }\)
∴ The simplest form of \(\frac { 7 }{ 28 }\) = \(\frac { 1 }{ 4 }\)
Question 8.
Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/ his pencils?
Solution:
Ramesh used up 10 pencils out of 20 pencils.
∴ Fraction = \(\frac { 10 }{ 20 }\) = \(\frac{10 \div 10}{20 \div 10}\) = \(\frac { 1 }{ 2 }\)
Sheelu used up 25 pencils out of 50 pencils.
∴ Fraction = \(\frac { 25 }{ 50 }\) = \(\frac{25 \div 25}{50 \div 25}\) = \(\frac { 1 }{ 2 }\)
Jamaal used up 40 pencils out of 80 pencils.
∴ Fraction = \(\frac { 40 }{ 80 }\) = \(\frac{40 \div 40}{80 \div 40}\) = \(\frac { 1 }{ 2 }\)
Yes, each has used up an equal fraction. i.e., \(\frac { 1 }{ 2 }\)
Question 9.
Match the equivalent fractions and write two more for each.
\(\frac { 250 }{ 400 }\) | \(\frac { 2 }{ 3 }\) |
\(\frac { 180 }{ 200 }\) | \(\frac { 2 }{ 5 }\) |
\(\frac { 660 }{ 990 }\) | \(\frac { 1 }{ 2 }\) |
\(\frac { 180 }{ 360 }\) | \(\frac { 5 }{ 8 }\) |
\(\frac { 220 }{ 550 }\) | \(\frac { 9 }{ 10 }\) |
Solution:
i) \(\frac { 250 }{ 400 }\) = \(\frac{250 \div 50}{400 \div 50}\) = \(\frac { 5 }{ 8 }\) – (d)
ii) \(\frac { 180 }{ 200 }\) = \(\frac{180 \div 20}{200 \div 20}\) = \(\frac { 9 }{ 10 }\) – (e)
iii) \(\frac { 660 }{ 990 }\) = \(\frac{660 \div 10}{990 \div 10}\) = \(\frac{66 \div 33}{99 \div 33}\) = \(\frac { 2 }{ 3 }\) – (c)
v) \(\frac { 220 }{ 550 }\) = \(\frac{220 \div 10}{550 \div 10}\) = \(\frac{22 \div 11}{55 \div 11}\) = \(\frac { 2 }{ 5 }\) – (b)
Two more equivalent fractions :
i) \(\frac { 250 }{ 400 }\) = \(\frac{250 \div 10}{400 \div 10}\) = \(\frac { 25 }{ 40 }\)
\(\frac { 250 }{ 400 }\) = \(\frac{250 \div 2}{400 \div 2}\) = \(\frac { 125 }{ 200 }\)
ii) \(\frac { 180 }{ 200 }\) = \(\frac{180 \div 10}{200 \div 10}\) = \(\frac { 18 }{ 20 }\)
\(\frac { 180 }{ 200 }\) = \(\frac{180 \div 5}{200 \div 5}\) = \(\frac { 36 }{ 40 }\)
iii) \(\frac { 660 }{ 990 }\) = \(\frac{660 \div 5}{990 \div 5}\) = \(\frac { 132 }{ 198 }\)
\(\frac { 990 }{ 200 }\) = \(\frac{660 \div 2}{990 \div 2}\) = \(\frac { 330 }{ 495 }\)
iv) \(\frac { 180 }{ 360 }\) = \(\frac{180 \div 60}{360 \div 60}\) = \(\frac { 3 }{ 6 }\)
\(\frac { 180 }{ 360 }\) = \(\frac{180 \div 30}{360 \div 30}\) = \(\frac { 6 }{ 12 }\)
v) \(\frac { 220 }{ 550 }\) = \(\frac{220 \div 5}{550 \div 5}\) = \(\frac { 44 }{ 110 }\)
\(\frac { 220 }{ 550 }\) = \(\frac{220 \div 10}{550 \div 10}\) = \(\frac { 22 }{ 55 }\)