CBSE Class 6 Mathematics Fractions Assignment Set 10

VI - Mathematics Assignment No - 01 - Fractions

Question 1. What part of the shaded portion is, in the following diagrams.
(i) Circle divided into 8 equal parts with 3 shaded parts.
(ii) Rectangle divided into 8 equal smaller rectangles with 2 shaded parts.
(iii) Triangle divided into 4 smaller triangles with 2 shaded parts.
Answer: (i) Total parts = 8, Shaded parts = 3
Fraction = \(\frac{3}{8}\)
(ii) Total parts = 8, Shaded parts = 2
Fraction = \(\frac{2}{8} = \frac{1}{4}\)
(iii) Total parts = 4, Shaded parts = 2
Fraction = \(\frac{2}{4} = \frac{1}{2}\)
In simple words: Count the number of shaded regions and divide by the total number of equal parts.

Exam Tip: Always reduce the fraction to its simplest form if possible.

Question 2. Colour the part of \(\frac{1}{4}\), \(\frac{2}{5}\), \(\frac{3}{7}\) by drawing a suitable diagram.
Answer: To represent \(\frac{1}{4}\), draw a figure divided into 4 equal parts and shade 1 part.
To represent \(\frac{2}{5}\), draw a figure divided into 5 equal parts and shade 2 parts.
To represent \(\frac{3}{7}\), draw a figure divided into 7 equal parts and shade 3 parts.
In simple words: The numerator tells you how many parts to colour out of the total parts given by the denominator.

Exam Tip: Ensure all parts in your diagram are equal in size before shading.

Question 3. What fraction of a day in a year?
Answer: Total days in a standard year = 365
Fraction = \(\frac{1}{365}\)
In simple words: 1 day out of 365 days makes the fraction \(\frac{1}{365}\).

Exam Tip: Assume a normal non-leap year (365 days) unless specified otherwise.

Question 4. What fraction of a month in a year?
Answer: Total months in a year = 12
Fraction = \(\frac{1}{12}\)
In simple words: 1 month out of 12 months is \(\frac{1}{12}\).

Exam Tip: Remember there are 12 months in a calendar year.

Question 5. What fraction of a day is 12 hours?
Answer: Total hours in a day = 24 hours
Given hours = 12 hours
Fraction = \(\frac{12}{24} = \frac{1}{2}\)
In simple words: 12 hours is half of a full day (24 hours).

Exam Tip: Convert both quantities to the same unit (hours) before writing the fraction.

Question 6. What fraction of an hour is 50 minutes?
Answer: Total minutes in an hour = 60 minutes
Given minutes = 50 minutes
Fraction = \(\frac{50}{60} = \frac{5}{6}\)
In simple words: Divide 50 by 60 and simplify by canceling the trailing zeros.

Question 7. Out of the whole numbers from 0 to 10, what fraction of them are
(i) odd number
(ii) Prime number
(iii) Even number
Answer: Whole numbers from 0 to 10 are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (Total numbers = 11)
(i) Odd numbers: 1, 3, 5, 7, 9 (Total = 5)
Fraction = \(\frac{5}{11}\)
(ii) Prime numbers: 2, 3, 5, 7 (Total = 4)
Fraction = \(\frac{4}{11}\)
(iii) Even numbers: 0, 2, 4, 6, 8, 10 (Total = 6)
Fraction = \(\frac{6}{11}\)
In simple words: First count total numbers from 0 to 10 inclusively, which is 11, then count the required specific numbers for each part.

Exam Tip: Remember that 0 is neither prime nor composite, but it is a whole number and an even number.

Question 8. Write the following in numerals
(i) Three-fourth
(ii) Two-seventh
(iii) One-third
(iv) Four-fifth
Answer: (i) Three-fourth = \(\frac{3}{4}\)
(ii) Two-seventh = \(\frac{2}{7}\)
(iii) One-third = \(\frac{1}{3}\)
(iv) Four-fifth = \(\frac{4}{5}\)
In simple words: The word before the hyphen is the numerator and the word after is the denominator.

Exam Tip: Denominators take ordinal word forms like fourth, seventh, third, fifth.

Question 9. Write the following in words
(i) \(\frac{2}{3}\)
(ii) \(\frac{4}{7}\)
(iii) \(\frac{2}{5}\)
Answer: (i) \(\frac{2}{3}\) = Two-third
(ii) \(\frac{4}{7}\) = Four-seventh
(iii) \(\frac{2}{5}\) = Two-fifth
In simple words: Write the top number normally and the bottom number as an ordinal number.

Exam Tip: Use hyphens when writing fractions in words.

Question 10. Find \(\frac{2}{3}\) of 27
Answer: \(\frac{2}{3} \times 27 = 2 \times \frac{27}{3}\)
\(= 2 \times 9 = 18\)
In simple words: Multiply 27 by 2 and then divide the result by 3.

Exam Tip: Divide the whole number by the denominator first to keep numbers small and calculation easy.

Question 11. An apple is divided into 6 equal parts and Arun eats 4 of these. What fraction of apple has he eaten?
Answer: Total equal parts of the apple = 6
Parts eaten by Arun = 4
Fraction eaten = \(\frac{4}{6} = \frac{2}{3}\)
In simple words: Parts eaten divided by total parts gives the eaten fraction, which simplifies to \(\frac{2}{3}\).

Exam Tip: Always reduce fractions to lowest terms.

Question 12. Arun has 25 chocolates. He had given 19 to his friends. What fraction of chocolates are with him?
Answer: Total chocolates = 25
Chocolates given to friends = 19
Chocolates remaining with Arun = 25 - 19 = 6
Fraction of chocolates with him = \(\frac{6}{25}\)
In simple words: Find how many chocolates are left by subtracting given ones from the total, then put it over the total number of chocolates.

Exam Tip: Read carefully whether the question asks for the fraction given away or the fraction remaining.