RBSE Solutions Class 6 Maths Chapter 5 Fractions Exercise 5.1

Question 1. Write the fractions to represent shaded parts of the following.
(i)
(ii)
(iii)
Answer:
(i) \( \frac {2}{4} = \frac {1}{2} \)
(ii) \( \frac {4}{6} = \frac {2}{3} \)
(iii) \( \frac {6}{10} = \frac {3}{5} \) This shows that 6 out of 10 parts are shaded.
In simple words: We count the total number of equal parts in each shape and then count how many of those parts are colored. The fraction is the number of colored parts over the total parts, then simplified.

🎯 Exam Tip: Always simplify the fraction to its lowest terms. Make sure your fraction clearly shows the relationship between the shaded and total parts.

Question 2. Show the following fractions by diagram.
(i) \( \frac {3}{5} \)
(iii) \( \frac {3}{6} \)
(iv) \( 2 \frac {2}{5} \)
Answer:
(i) \( \frac {3}{5} \)
(iii) \( \frac {3}{6} \)
(iv) \( 2 \frac{2}{5} \)
In simple words: To show fractions using diagrams, we divide a shape into the total number of parts (the denominator) and then color the number of parts needed (the numerator). For mixed fractions, we draw full shapes for the whole number and then a partial shape for the fraction.

🎯 Exam Tip: Always divide the shapes into equal parts. This is very important for correctly showing fractions.

Question 4. Write the fraction for even numbers 1 to 15.
Answer: The even numbers between 1 and 15 are 2, 4, 6, 8, 10, 12, and 14. There are 7 even numbers in total. The total numbers from 1 to 15 are 15.
Hence, the fraction representing even numbers from 1 to 15 is \( \frac {7}{15} \). This represents 7 even numbers out of 15 total numbers.
In simple words: First, list all the even numbers between 1 and 15. Then count how many there are. Put that count over the total number of items from 1 to 15 to get your fraction.

🎯 Exam Tip: When finding a fraction for a subset of numbers, always clearly list both the subset and the total set to avoid errors in counting.

Question 5. Look at the following figures and write the fraction for its uncolored parts.
(i)
(ii)
(iii)
Answer: The fractions for the uncolored parts are:
(i) Out of 4 parts, 1 is colored, so 3 are uncolored. Fraction: \( \frac {3}{4} \)
(ii) Out of 10 parts, 4 are colored, so 6 are uncolored. Fraction: \( \frac {6}{10} = \frac {3}{5} \)
(iii) Out of 3 parts, 1 is colored, so 2 are uncolored. Fraction: \( \frac {2}{3} \) The uncolored portions are visually distinct from the single shaded part.
In simple words: First, count the total parts. Then, count the parts that are NOT colored. Write this as a fraction, with uncolored parts on top and total parts at the bottom. Remember to simplify if you can.

🎯 Exam Tip: Pay close attention to whether the question asks for "colored" or "uncolored" parts, as it changes the numerator of your fraction.

Question 6. Show the following fractions on number line.
(i) \( \frac {3}{5} \)
(ii) \( \frac {3}{7} \)
(iii) \( \frac {8}{3} = 2 \frac{2}{3} \)
Answer:
(i) \( \frac {3}{5} \) (ii) \( \frac {3}{7} \) (iii) \( \frac {8}{3} = 2 \frac{2}{3} \)
In simple words: To show fractions on a number line, you first divide the space between whole numbers into equal parts, based on the bottom number (denominator) of the fraction. Then, you count those parts from zero to find where the top number (numerator) of the fraction falls, and mark it.

🎯 Exam Tip: For improper fractions, convert them to mixed numbers first. Then, locate the whole number and place the remaining fraction between that whole number and the next one on the number line.

Question 7. Express the following in mixed fractions.
(i) \( \frac {20}{3} \)
(ii) \( \frac {11}{5} \)
(iii) \( \frac {19}{6} \)
Answer: To convert an improper fraction to a mixed fraction, we divide the numerator by the denominator. The quotient is the whole number part, the remainder is the new numerator, and the denominator stays the same.
(i) \( \frac{20}{3} \)
When 20 is divided by 3, the quotient is 6 and the remainder is 2.
\( \implies \frac{20}{3} = 6 \frac{2}{3} \)
(ii) \( \frac{11}{5} \)
When 11 is divided by 5, the quotient is 2 and the remainder is 1.
\( \implies \frac{11}{5} = 2 \frac{1}{5} \)
(iii) \( \frac{19}{6} \)
When 19 is divided by 6, the quotient is 3 and the remainder is 1.
\( \implies \frac{19}{6} = 3 \frac{1}{6} \)
In simple words: To change a fraction like 20/3 into a mixed number, you divide 20 by 3. The main answer (6) is the whole number. The leftover (2) is the new top number, and the bottom number (3) stays the same. So 20/3 becomes 6 and 2/3.

🎯 Exam Tip: Remember the format: Quotient (whole number), Remainder (new numerator), Divisor (same denominator). This is crucial for accurate conversion.

Question 8. Express the following in improper fractions.
(i) \( 7 \frac {2}{3} \)
(ii) \( 5 \frac {3}{4} \)
(iii) \( 4 \frac {1}{2} \)
Answer: To convert a mixed fraction into an improper fraction, multiply the whole number by the denominator and then add the numerator. The result becomes the new numerator, and the denominator remains unchanged.
(i) \( 7 \frac {2}{3} \)
Multiply the whole number (7) by the denominator (3), then add the numerator (2):
\( 3 \times 7 + 2 = 21 + 2 = 23 \)
Thus, the improper fraction is \( \frac {23}{3} \).
(ii) \( 5 \frac {3}{4} \)
Multiply the whole number (5) by the denominator (4), then add the numerator (3):
\( 4 \times 5 + 3 = 20 + 3 = 23 \)
Thus, the improper fraction is \( \frac {23}{4} \).
(iii) \( 4 \frac {1}{2} \)
Multiply the whole number (4) by the denominator (2), then add the numerator (1):
\( 2 \times 4 + 1 = 8 + 1 = 9 \)
Thus, the improper fraction is \( \frac {9}{2} \).
In simple words: To change a mixed number like 7 and 2/3 into a simple fraction, you multiply the big number (7) by the bottom number (3), then add the top number (2). This new number (23) goes on top, and the bottom number (3) stays the same.

🎯 Exam Tip: Always remember the steps: multiply whole number by denominator, add numerator, and keep the original denominator. This ensures you convert correctly every time.