RBSE Solutions Class 5 Maths Chapter 6 Understanding the Fractions Exercise 6.1

Question 1. See the following fractions and put the suitable sign in the box (<, >, =)-
(i) \( \frac { 1 }{ 4 } \) [] \( \frac { 3 }{ 4 } \)
(ii) \( \frac { 1 }{ 2 } \) [] \( \frac { 1 }{ 2 } \)
(iii) \( \frac { 1 }{ 3 } \) [] \( \frac { 1 }{ 2 } \)
(iv) \( \frac { 1 }{ 4 } \) [] \( \frac { 2 }{ 3 } \)
Answer:
(i) \( \frac { 1 }{ 4 } < \frac { 3 }{ 4 } \)
(ii) \( \frac { 1 }{ 2 } = \frac { 1 }{ 2 } \)
(iii) \( \frac { 1 }{ 3 } < \frac { 1 }{ 2 } \)
(iv) \( \frac { 1 }{ 4 } < \frac { 2 }{ 3 } \) To compare fractions easily, it's often helpful to find a common bottom number (denominator) for both fractions.
In simple words: When comparing fractions, if the bottom numbers are the same, just look at the top numbers. If the bottom numbers are different, make them the same first, then compare.

🎯 Exam Tip: When comparing fractions with different denominators, always find a common denominator first. This step makes the comparison accurate and easier to understand.

Question 2. Write the following fractions as mixed fraction.
(i) \( \frac { 7 }{ 5 } \)
(ii) \( \frac { 13 }{ 6 } \)
(iii) \( \frac { 3 }{ 2 } \)
(iv) \( \frac { 7 }{ 4 } \)
Answer:
(i) \( \frac { 7 }{ 5 } = 1\frac { 2 }{ 5 } \)
(ii) \( \frac { 13 }{ 6 } = 2\frac { 1 }{ 6 } \)
(iii) \( \frac { 3 }{ 2 } = 1\frac { 1 }{ 2 } \)
(iv) \( \frac { 7 }{ 4 } = 1\frac { 3 }{ 4 } \) A mixed fraction shows both a whole number and a part of a whole.
In simple words: If the top number of a fraction is bigger than the bottom number (called an improper fraction), you can turn it into a mixed fraction by dividing. The answer is a whole number, and any leftover becomes a new fraction.

🎯 Exam Tip: To convert an improper fraction to a mixed fraction, divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.

Question 3. Write following fractions in words-
(i) \( \frac { 3 }{ 4 } \)
(ii) \( 1\frac { 2 }{ 5 } \)
(iii) \( 2\frac { 3 }{ 5 } \)
Answer:
(i) \( \frac { 3 }{ 4 } \) = Three by four
(ii) \( 1\frac { 2 }{ 5 } \) = One and two by five
(iii) \( 2\frac { 3 }{ 5 } \) = Two and three by five Saying fractions aloud helps in understanding their value and what part of a whole they represent.
In simple words: When we read fractions, we say the top number first, then "by" and the bottom number. For mixed fractions, we say the whole number, then "and", then the fraction part.

🎯 Exam Tip: Practice saying different fractions out loud. Remember to use "by" for simple fractions (like half, third, quarter) and "and" when a fraction is combined with a whole number.

Question 4. Represent following fractions on a number line
(i) \( 4\frac { 1 }{ 2 } \)
(ii) \( 3\frac { 3 }{ 4 } \)
(iii) \( \frac { 2 }{ 3 } \)
Answer:
(i) \( 4\frac { 1 }{ 2 } \)
(ii) \( 3\frac { 3 }{ 4 } \)
(iii) \( \frac { 2 }{ 3 } \) A number line helps us visualize where fractions are located in relation to whole numbers. In simple words: To show a fraction on a number line, first find the whole number parts. Then, divide the space between the whole numbers into equal parts as shown by the bottom number of the fraction, and mark the correct part.

🎯 Exam Tip: When drawing fractions on a number line, always divide the space between whole numbers into equal segments based on the denominator to ensure accuracy.