GSEB Class 6 Maths Solutions Chapter 7 Fractions Exercise 7.1

Question 1. Write the fraction representing the shaded portion.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
Answer:
(i) Total equal parts = 4
Shaded parts = 2
Fraction = \( \frac{2}{4} \)
(ii) Total equal parts = 9
Shaded parts = 8
Fraction = \( \frac{8}{9} \)
(iii) Number of total objects = 8
Number of shaded objects = 4
Fraction = \( \frac{4}{8} \)
(iv) Total equal parts = 4
Shaded parts = 1
Fraction = \( \frac{1}{4} \)
(v) Total equal parts = 8
Shaded parts = 4
Fraction = \( \frac{4}{8} \)
(vi) Number of total objects = 16
Number of shaded objects = 8
Fraction = \( \frac{8}{16} \)
(vii) Total number of objects = 10
Number of shaded objects = 10
Fraction = \( \frac{10}{10} \)
(viii) Total equal parts = 9
Shaded parts = 4
Fraction = \( \frac{4}{8} \)
(ix) Total equal parts = 2
Shaded parts = 4
Fraction = \( \frac{1}{2} \)
(x) Total equal parts = 2
Shaded part = 1
Fraction = \( \frac{1}{2} \)
In simple words: To find the fraction, count all the equal parts in the figure, that's your denominator. Then, count only the parts that are colored in, that's your numerator.

Exam Tip: Always make sure all parts are of equal size before counting them to form a fraction. If parts are unequal, you need to adjust or state that a simple fraction cannot be formed directly.

Question 2. Colour the part according to the given fraction.
(i) \( \frac{1}{6} \)
(ii) \( \frac{1}{4} \)
(iii) \( \frac{1}{3} \)
(iv) \( \frac{3}{4} \)
(v) \( \frac{4}{9} \)
Answer:
(i) The circle is divided into 6 equal parts, and 1 part is colored according to \( \frac{1}{6} \).
(ii) The triangle is divided into 4 equal parts, and 1 part is colored according to \( \frac{1}{4} \).
(iii) The rectangle is divided into 3 equal parts, and 1 part is colored according to \( \frac{1}{3} \).
(iv) The circle is divided into 4 equal parts, and 3 parts are colored according to \( \frac{3}{4} \).
(v) The square is divided into 9 equal parts, and 4 parts are colored according to \( \frac{4}{9} \).
In simple words: Look at the fraction's top number (numerator) to know how many parts to color. The bottom number (denominator) tells you the total equal parts.

Exam Tip: Pay close attention to the number of total parts and the numerator to accurately shade the correct portion of each figure.

Question 3. Identify the error if any
(i)
(ii)
(iii)
Answer:
(i) The error is that the parts are not equal. Therefore, the shaded part does not represent \( \frac{1}{2} \).
(ii) The error is that the parts are not equal. Therefore, the shaded part does not represent a fraction \( \left(\frac{1}{4}\right) \).
(iii) The error is that the parts are not equal. Therefore, the shaded part does not represent \( \frac{3}{4} \).
In simple words: For a fraction to be correct, all the smaller parts of a shape must be exactly the same size. If they are not equal, the fraction shown is wrong.

Exam Tip: Remember that fractions represent parts of a whole where all parts are *equal*. If the divisions are not equal, the figure does not correctly show the stated fraction.

Question 4. What fraction of a day is 8 hours?
Answer: Total number of hours in a day = 24
8 hours as a fraction = \( \frac{8}{24} \)
In simple words: Since there are 24 hours in a full day, 8 hours is \( \frac{8}{24} \) of that day.

Exam Tip: Always make sure your units are consistent (e.g., hours and hours) when forming a fraction. Simplify the fraction if possible for full marks.

Question 5. What fraction of an hour is 40 minutes?
Answer: 1 hour = 60 minutes
40 minutes as a fraction = \( \frac{40}{60} \)
In simple words: An hour has 60 minutes. So, 40 minutes is 40 out of 60 minutes, which is \( \frac{40}{60} \).

Exam Tip: When converting between units for fractions, first establish the total number of the smaller units in the larger unit (e.g., minutes in an hour).

Question 6. Arva, Abhimanvu and Vivek shared lunch. Aya has brought two sandwiches, one made of vegetables and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
(a) How can Arva divide his sandwiches so that – each person has an equal share?
(b) What part of a sandwich will each boy receive?
Answer:
(a) Arva will divide each sandwich into three equal parts. One part will be received by each of them.
(b) Each boy will get \( \frac{1}{3} \) parts or a fraction \( \frac{1}{3} \).
In simple words: Since there are three boys, Arva needs to cut each sandwich into three pieces. Each boy will then get one piece from each sandwich.

Exam Tip: For sharing questions, identify the total number of people sharing and divide the items equally among them to determine each person's share as a fraction.

Question 7. Kanchan dyes dresses. She has to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?
Answer: Number of dresses to be dyed = 30
Number of dresses finished = 20
Fraction of finished dresses = \( \frac{20}{30} = \frac{2}{3} \)
In simple words: Kanchan has finished 20 dresses out of 30 total, so the fraction is 20 over 30, which simplifies to 2 over 3.

Exam Tip: When calculating fractions of a whole, the 'part' goes in the numerator and the 'total' goes in the denominator. Always simplify your fraction to its lowest terms.

Question 8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Answer: Numbers from 2 to 12 are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Prime numbers are: 2, 3, 5, 7 and 11
Total given numbers = 11
Total number of prime numbers = 5
Required fraction = \( \frac{5}{11} \)
In simple words: First, list all the numbers between 2 and 12. Then, pick out only the prime numbers from that list. The fraction is the count of prime numbers divided by the total count of numbers.

Exam Tip: Clearly list all numbers in the specified range and then identify the prime numbers. Be careful not to include 1 as a prime number or composite numbers in your prime count.

Question 9. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Answer: Numbers from 102 to 113 are: 102, 103, 104, 105, 106, 107, 108. 109, 110, 111, 112, 113
Total number of given numbers = 12
Prime numbers are: 103, 107, 109, 113
Number of prime numbers = 4
Thus, the required fraction = \( \frac{4}{12} \)
In simple words: List all natural numbers from 102 to 113. Find which of these numbers are prime (only divisible by 1 and themselves). The fraction is the number of primes over the total numbers.

Exam Tip: To identify prime numbers efficiently, remember rules of divisibility (e.g., even numbers aren't prime, numbers ending in 5 aren't prime unless they are 5). Test small prime factors like 2, 3, 5, 7, 11. For 109, check divisibility by primes up to \( \sqrt{109} \approx 10.4 \), i.e., 2, 3, 5, 7.

Question 10. What fraction of these circles have x's in them?
Answer: Total number of given circles = 8
Number of circles with X's in them = 4
The required fraction = \( \frac{4}{8} \)
In simple words: Count all the circles shown. Then, count only the circles that have an 'X' inside them. The fraction is the number of 'X' circles divided by the total circles.

Exam Tip: Clearly differentiate between the total items and the specific items that meet the condition to form your fraction accurately.

Question 11. Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?
Answer: Number of CDs bought from market = 3
Number of CDs received as gifts = 5
Total number of CDs = \( 3 + 5 = 8 \)
Fraction of CDs (purchased) = \( \frac{3}{8} \)
Fraction of CDs (received as gifts) = \( \frac{5}{8} \)
In simple words: First, add up all the CDs Kristin has to find the total. Then, make a fraction for the CDs she bought by putting that number over the total. Do the same for the CDs she got as gifts.

Exam Tip: For problems with multiple questions, ensure you answer each part clearly and separately. Show all steps, including how you found the total number of items.