GSEB Class 6 Maths Solutions Chapter 7 અપૂર્ણાંક સંખ્યાઓ Exercise 7.1

Question 1. Write the fraction for the shaded part.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
Answer:
(i) In the given figure, there are 4 equal parts, and 2 parts are shaded. So, the fraction is \( \frac{2}{4} \).
(ii) In the given figure, there are 9 equal parts, and 8 parts are shaded. So, the fraction is \( \frac{8}{9} \).
(iii) In the given figure, there are 8 total shapes, and 4 shapes are shaded. So, the fraction is \( \frac{4}{8} \).
(iv) In the given figure, there are 4 equal parts, and 1 part is shaded. So, the fraction is \( \frac{1}{4} \).
(v) In the given figure, there are 7 equal parts, and 3 parts are shaded. So, the fraction is \( \frac{3}{7} \).
(vi) In the given figure, there are 10 total flowers, and 3 flowers are shaded. So, the fraction is \( \frac{3}{10} \).
(vii) In the given figure, there are 10 total pencils, and 10 pencils are shaded. So, the fraction is \( \frac{10}{10} \).
(viii) In the given figure, there are 9 total flowers, and 4 flowers are shaded. So, the fraction is \( \frac{4}{9} \).
(ix) In the given figure, there are 8 total flowers, and 4 flowers are shaded. So, the fraction is \( \frac{4}{8} \).
(x) In the given figure, there are 2 equal parts, and 1 part is shaded. So, the fraction is \( \frac{1}{2} \).
In simple words: To find the fraction, simply count how many parts are colored in and then count the total number of equally-sized parts in the whole picture. Put the shaded count over the total count.

Exam Tip: For fraction questions with diagrams, always count the total parts and the shaded parts carefully to ensure accuracy in your answer.

Question 2. Shade the given figures according to the fraction:
(i) \( \frac{1}{6} \)
(ii) \( \frac{1}{4} \)
(iii) \( \frac{1}{3} \)
(iv) \( \frac{3}{4} \)
(v) \( \frac{4}{9} \)
Answer:
(i) Here, the given figure has 6 equal parts. To represent the fraction \( \frac{1}{6} \), we will shade 1 part.
(ii) Here, the given figure has 4 equal parts. To represent the fraction \( \frac{1}{4} \), we will shade 1 part.
(iii) Here, the given figure has 3 equal parts. To represent the fraction \( \frac{1}{3} \), we will shade 1 part.
(iv) Here, the given figure has 4 equal parts. To represent the fraction \( \frac{3}{4} \), we will shade 3 parts.
(v) Here, the given figure has 9 equal parts. To represent the fraction \( \frac{4}{9} \), we will shade 4 parts.
In simple words: Look at the bottom number of the fraction to see how many total pieces there are. Then, look at the top number to see how many of those pieces you need to color in.

Exam Tip: When shading figures, always make sure the parts you shade are equal in size if they represent a fraction. This ensures the fraction is accurately depicted.

Question 3. Identify if there is any mistake:
(i) \( \frac{1}{2} \)
(ii) \( \frac{1}{4} \)
(iii) \( \frac{1}{4} \)
Answer:
(i) The parts made in the given figure are not equal. Therefore, the shaded part is not \( \frac{1}{2} \) of the whole figure.
(ii) The parts made in the given figure are not equal. Therefore, the shaded part is not \( \frac{1}{4} \) of the whole figure.
(iii) The parts made in the given figure are not equal. Therefore, the shaded part is not \( \frac{1}{4} \) of the whole figure.
In simple words: A fraction only correctly shows a part of a whole when all the pieces are exactly the same size. If the parts are different sizes, then the fraction written for the shaded area is wrong.

Exam Tip: Always remember that for a fraction to be valid, the whole must be divided into equal parts. If the parts are unequal, a simple fraction cannot accurately represent the portion.

Question 4. What fraction of a day is eight hours?
Answer: We know that 1 day has 24 hours. Therefore, the required fraction is \( \frac{\text{8 hours}}{\text{24 hours}} = \frac{8}{24} \). After simplifying this, eight hours represent \( \frac{1}{3} \) part of a day.
In simple words: A day has 24 hours. We want to know what part 8 hours is. So, we put 8 over 24 and make the fraction simpler, which gives us one-third.

Exam Tip: When converting between units for fractions, always ensure the units are consistent (e.g., hours in a day) before forming the fraction.

Question 5. What fraction of an hour is 40 minutes?
Answer: We understand that 1 hour equals 60 minutes. Therefore, the fraction required is \( \frac{\text{40 minutes}}{\text{60 minutes}} = \frac{40}{60} \). As a result, 40 minutes make up \( \frac{2}{3} \) part of an hour after simplification.
In simple words: There are 60 minutes in an hour. We are looking for the fraction that 40 minutes makes up. So we write 40 over 60, and when we simplify it, we get two-thirds.

Exam Tip: To find a fraction of a larger unit, express both quantities in the same smaller unit, then simplify the resulting fraction.

Question 6. Arya, Abhimanyu, and Vivek share lunch. Arya brings two sandwiches, one made of vegetables and the other of jam. The other two boys forgot their lunch. Arya is ready to share her sandwiches so that each boy gets an equal share.
(a) How will Arya distribute her sandwiches so that everyone gets an equal share?
(b) What fraction of a sandwich will each boy receive?
Answer:
Total number of sandwiches = 2.
Total number of boys = 3.
(a) Arya will divide each of the two sandwiches into three equal parts. Then, she will give one part from each sandwich to each boy. This way, every person gets an equal amount.
(b) Since there are 2 sandwiches and 3 boys, each boy will get \( \frac{2}{3} \) of a sandwich.
In simple words: Arya has two sandwiches for three people. She cuts each sandwich into three equal pieces. Then, she gives two pieces (one from each sandwich) to each person. So, each person gets two-thirds of a sandwich.

Exam Tip: In sharing problems, ensure all items are divided equally among all participants to determine the correct fraction for each person's share.

Question 7. Kanchan dyes clothes. She has to dye 30 clothes. She had already dyed 20 clothes. What fraction of the clothes has she dyed?
Answer:
Total number of clothes to dye = 30.
Number of clothes she has already dyed = 20.
Therefore, the fraction of clothes she has dyed is \( \frac{\text{Number of dyed clothes}}{\text{Total number of clothes}} = \frac{20}{30} = \frac{2}{3} \).
In simple words: Kanchan finished 20 clothes out of 30. The fraction of clothes she dyed is 20 over 30, which simplifies to two-thirds.

Exam Tip: To find the fraction of a completed task, always divide the completed amount by the total required amount and simplify if possible.

Question 8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Answer:
Natural numbers from 2 to 12 are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
Here, the total count of natural numbers from 2 to 12 is 11.
Prime numbers found between 2 and 12 are: 2, 3, 5, 7, 11.
The total count of these prime numbers is 5.
Therefore, the desired fraction is \( \frac{\text{Total prime numbers}}{\text{Total natural numbers}} = \frac{5}{11} \).
In simple words: First, list all numbers from 2 to 12. Then, find the prime numbers in that list. The fraction will be how many prime numbers there are out of the total numbers in your list.

Exam Tip: When identifying prime numbers, remember they are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. Also, 1 is not a prime number.

Question 9. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Answer:
Natural numbers from 102 to 113 are: 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, and 113.
The total number of these natural numbers is 12.
Prime numbers occurring between 102 and 113 are: 103, 107, 109, 113.
The total number of these prime numbers is 4.
Therefore, the required fraction is \( \frac{\text{Total prime numbers}}{\text{Total natural numbers}} = \frac{4}{12} \).
In simple words: First, write out all the numbers from 102 to 113. Next, pick out only the prime numbers from that list. Finally, make a fraction: the count of prime numbers over the total count of numbers you started with.

Exam Tip: Be careful to list all natural numbers in the given range accurately and then correctly identify all prime numbers within that list to avoid errors.

Question 10. In the given circles, 4 (crosses) are marked. What is the fraction representing them?

Answer:
Total number of circles = 8.
Number of circles marked with a cross = 4.
Therefore, the required fraction is \( \frac{\text{Number of circles with crosses}}{\text{Total number of circles}} = \frac{4}{8} \).
In simple words: Count all the circles, then count how many of them have crosses. The fraction is the number with crosses over the total number of circles.

Exam Tip: Clearly identify the total number of items and the number of items meeting the specific criteria to form the correct fraction. Count carefully to avoid errors.

Question 11. Kristine received a CD player for her birthday. She bought 3 CDs, and received 5 more as gifts. What fraction of the total CDs does the number of purchased CDs and the number of gifted CDs represent?
Answer:
Number of CDs Kristine bought = 3.
Number of CDs Kristine received as gifts = 5.
Therefore, Kristine has a total of CDs \( = 3+5 = 8 \).
The fraction of CDs Kristine bought is \( \frac{\text{Purchased CDs}}{\text{Total CDs}} = \frac{3}{8} \).
And the fraction of CDs Kristine received as gifts is \( \frac{\text{Gifted CDs}}{\text{Total CDs}} = \frac{5}{8} \).
In simple words: Kristine has 3 CDs she bought and 5 CDs as gifts, making 8 CDs in total. The part she bought is 3 out of 8, and the part she got as gifts is 5 out of 8.

Exam Tip: To find fractions for different categories within a total, always calculate the overall total first. Then, divide each category's count by this total to get its respective fraction.