NCERT Solutions for Class 6 Maths Chapter 7 - Fractions Exercise 7.6

Exercise 7.6

Answer the following questions after looking at the fraction wall:

1. Are the lengths $\dfrac{1}{2}$​ and $\dfrac{3}{6}$​ equal?

The lengths $\dfrac{1}{2}$​ and $\dfrac{3}{6}$ are equal because $\dfrac{3}{6}$​ simplifies to $\dfrac{1}{2}$​.

2. Are $\dfrac{2}{3}$​ and $\dfrac{4}{6}$​ equivalent fractions? Why?

Yes, $\dfrac{2}{3}$​ and $\dfrac{4}{6}$​ are equivalent fractions because when you multiply both the numerator and denominator of $\dfrac{2}{3}$ by 2, you get $\dfrac{4}{6}$​.

3. How many pieces of length $\dfrac{1}{6}$​ will make a length of $\dfrac{1}{2}$​?

Three pieces of length $\dfrac{1}{6}$​ will make a length of $\dfrac{1}{2}$​, because $\dfrac{3}{6} = \dfrac{1}{2}$.

4. How many pieces of length $\dfrac{1}{6}$​ will make a length of $\dfrac{1}{3}$​?

Two pieces of length $\dfrac{1}{6}$​ will make a length of $\dfrac{1}{3}$​, because $\dfrac{2}{6} = \dfrac{1}{3}$.

1) Figure it Out:

1. Are $\dfrac{3}{6}$, $\dfrac{4}{8}$, and $\frac{5}{10}$​ equivalent fractions? Why?

Answer: Yes, $\dfrac{3}{6}$​, $\dfrac{4}{8}$​, and $\dfrac{5}{10}$​ are equivalent fractions because they all simplify to $\dfrac{1}{2}$.

2. Write two equivalent fractions for $\frac{2}{6}$.

Answer: Two equivalent fractions for $\dfrac{2}{6}$​ are:

• $\dfrac{1}{3}$ (simplified by dividing the numerator and denominator by 2)

• $\dfrac{4}{12}$​ (multiplied both the numerator and denominator by 2)

3. Write as many equivalent fractions as you can for $\frac{4}{6}$

Answer:​ Some equivalent fractions for $\dfrac{4}{6}$​ are:

• $\dfrac{2}{3}$ (simplified by dividing by 2)

• $\dfrac{8}{12}$​ (multiplied both the numerator and denominator by 2)

• $\dfrac{12}{18}$​ (multiplied both the numerator and denominator by 3)

• $\dfrac{16}{24}$​ (multiplied both the numerator and denominator by 4)

2) Figure it Out:

1. Three rotis are shared equally by four children.
Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and multiplication facts.

• Fraction of roti each child gets is: ______.

• Division fact: ______.

• Addition fact: ______.

• Multiplication fact: ______.

Answer: The fraction of roti each child gets is: $\dfrac{3}{4}$​.

Division fact: $3 \div 4 = \frac{3}{4}$​.

Addition fact:$\dfrac{3}{4} + \dfrac{3}{4} + \dfrac{3}{4} + \dfrac{3}{4} = 3$

Multiplication fact: $4 \times \dfrac{3}{4} = 3$

2. Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.

Answer:

• Each child gets $\dfrac{2}{4} = \dfrac{1}{2}$

• Division fact: $2 \div 4 = \frac{1}{2}$

• Addition fact:$\dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} = 2.$

• Multiplication fact: $4 \times \dfrac{1}{2} = 2$.

3. Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?

Answer: Anil would get $\dfrac{2}{5}$​ of a cake.

a. 5 glasses of juice shared equally among 4 friends is the same as ____ glasses of juice shared equally among 8 friends.
So,$\frac{5}{4} = \frac{\_}{8}$​.

Answer: 5 glasses of juice shared equally among 4 friends is the same as 10 glasses of juice shared equally among 8 friends.

So, $\dfrac{5}{4} = \dfrac{10}{8}$​.

b. 4 kg of potatoes divided equally in 3 bags is the same as 12 kg of potatoes divided equally in ____ bags.
So, $\dfrac{4}{3} = \dfrac{12}{\_}$​.

Answer: 4 kg of potatoes divided equally in 3 bags is the same as 12 kg of potatoes divided equally in 9 bags.

So,$\dfrac{4}{3} = \dfrac{12}{9}$​.

c. 7 rotis divided among 5 children is the same as ____ rotis divided among ____ children.

So,$\dfrac{7}{5} = \dfrac{\_}{\_}$. 

Answer: 7 rotis divided among 5 children is the same as 14 rotis divided among 10 children.

So,$\dfrac{7}{5} = \frac{14}{10}$.

4. Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.

a. $\dfrac{7}{2}$ $and $\dfrac{3}{5}$
b. $\dfrac{8}{3}$​ and $\dfrac{5}{6}$​
c. $\dfrac{3}{4}$ and $\dfrac{3}{5}$
d. $\dfrac{6}{7}$​ and $\dfrac{8}{5}$​
e. $\dfrac{9}{4}$​ and $\dfrac{5}{2}$
f. $\dfrac{1}{10}$​ and $\dfrac{2}{9}$​
g. $\dfrac{8}{3}$ and $\dfrac{11}{4}$
h. $\dfrac{13}{6}$ and $\dfrac{1}{9}$

Answer:

a. Equivalent fractions: $\dfrac{35}{10}$​ and $\dfrac{6}{10}$

b. Equivalent fractions: $\dfrac{16}{6}$​ and $\dfrac{5}{6}$

c. Equivalent fractions: $\dfrac{15}{20}$​ and $\dfrac{12}{20}$

d. Equivalent fractions: $\dfrac{30}{35}$​ and $\dfrac{56}{35}$​

e. Equivalent fractions: $\dfrac{18}{8}$​ and $\dfrac{20}{8}$

f. Equivalent fractions: $\dfrac{9}{90}$​ and $\dfrac{20}{90}$​

g. Equivalent fractions: $\dfrac{32}{12}$​ and $\dfrac{33}{12}$​

h. Equivalent fractions: $\dfrac{39}{18}$​ and $\dfrac{2}{18}$​

3) Figure it Out:

Express the following fractions in lowest terms:

a. $\dfrac{17}{51}$

Find the GCD: The GCD of 17 and 51 is 17 (since 51 = 3 × 17).

Simplify:$\dfrac{17 \div 17}{51 \div 17} = \dfrac{1}{3}$​

Lowest term: $\dfrac{1}{3}$

B. $\dfrac{64}{144}$

Find the GCD: The GCD of 64 and 144 is 16.

Simplify:$\dfrac{64 \div 16}{144 \div 16} = \dfrac{4}{9}$

Lowest term: $\dfrac{4}{9}$

C. $\dfrac{126}{147}$

Find the GCD: The GCD of 126 and 147 is 21.

Simplify:$\dfrac{126 \div 21}{147 \div 21} = \dfrac{6}{7}$​

Lowest term: $\dfrac{6}{7}$​

D. $\dfrac{527}{112}$

1. Find the GCD: The GCD of 527 and 112 is 1 (no common factors).

2. Simplify: Since the GCD is 1, it is already in the lowest terms.$\dfrac{527 \div 1}{112 \div 1} = \frac{527}{112}$

Lowest term:$\dfrac{527}{112}$

Benefits of NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.6 

• The solutions provide clear explanations that help students understand equivalent fractions easily.

• Each solution is presented step-by-step, making it simpler for students to follow the process.

• There are plenty of practice questions to help reinforce learning and build confidence.

• Understanding equivalent fractions is important for future maths topics, and these solutions lay a good foundation.

• The solutions are designed for self-study, so students can practice and learn at their own pace.

• Practising with these solutions prepares students to handle similar questions in exams.

Class 6 Maths Chapter 7: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 7 - Fractions

Conclusion

NCERT Solutions for Class 6 Maths Chapter 7 Exercise 7.6 provides essential support for understanding equivalent fractions. With clear explanations and step-by-step guidance, students can easily grasp how to identify and create equivalent fractions. The practice questions included help reinforce their learning and build confidence in their skills. By mastering this topic, students will be well-prepared for future math challenges and exams. Overall, these solutions are a valuable resource for enhancing understanding and improving performance in mathematics.

Chapter-Specific NCERT Solutions for Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Class 6  Maths 

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6-