Representation of rational numbers worksheet - Free Printable

I will solve the math worksheet by answering each question step-by-step. The questions focus on representing rational numbers on a number line.

Question 1: Encircle the best (only one) option in each of the given statement.

#### (i) To plot $-\frac{1}{7}$ on a number line, the number of divisions that will be made between 0 and -1 is/are:
- Analysis: To plot $-\frac{1}{7}$, you need to divide the segment from 0 to -1 into 7 equal parts. The first division from 0 towards -1 will be at $-\frac{1}{7}$.
- Answer: (c) 7

#### (ii) To plot positive rational numbers on a number line we move towards which of the side of 0 on the number line?
- Analysis: On a standard number line, positive numbers are located to the right of zero.
- Answer: (b) right

#### (iii) $\frac{1}{10}$ will be plotted between :
- Analysis: The fraction $\frac{1}{10}$ is a positive number greater than 0 but less than 1.
- Answer: (a) 0 & 1

#### (iv) Which number line shows correct number of divisions for $\frac{2}{5}$:
- Analysis: To represent $\frac{2}{5}$, the interval from 0 to 1 must be divided into 5 equal parts. The point $\frac{2}{5}$ will be the second mark from 0.
- Option (a) divides the space between 0 and 1 into 4 parts, which is incorrect.
- Option (b) divides the space between 0 and 1 into 5 parts, which is correct.
- Option (c) has an uneven or incorrect division.
- Answer: (b)

#### (v) Tick the number line which shows representation of $-1\frac{5}{6}$.
- Analysis: The mixed number $-1\frac{5}{6}$ is equivalent to $-\frac{11}{6}$. This value is between -2 and -1, specifically very close to -2.
- Option (a) shows a point between -1 and 0, which is incorrect.
- Option (b) shows a point between -2 and -1, which is correct.
- Option (c) shows a point between 1 and 2, which is incorrect.
- Answer: (b)

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Question 2: On the number line given below, the interval between two consecutive integers ‘m’ & ‘n’ is divided into 8 equal parts. Find the rational number ‘y’ shown on the number line.

- Analysis:
- The point 'y' is located between 'n' and 'm'.
- From the diagram, 'n' is at -2 and 'm' is at -1.
- The interval from -2 to -1 is divided into 8 equal parts.
- The point 'y' is the 7th division from -2 (or the 1st division before -1).
- So, its value is $-2 + \frac{7}{8} = -\frac{16}{8} + \frac{7}{8} = -\frac{9}{8} = -1\frac{1}{8}$.
- However, looking at the options, they are presented as $1\frac{7}{8}$, $-\frac{7}{8}$, and $-1\frac{7}{8}$.
- The correct value should be $-1\frac{1}{8}$, but this is not an option. Let's re-examine the position.
- If 'y' is the 1st division from 'n' (-2), it would be $-2 + \frac{1}{8} = -\frac{15}{8} = -1\frac{7}{8}$.
- Looking at the image again, the arrow points to the first tick mark after 'n', which is indeed $-1\frac{7}{8}$.
- Answer: (c) $-1\frac{7}{8}$

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Question 3:

#### (i) Tick (√) number line shows representation of $2\frac{3}{5}$.

- Analysis: The mixed number $2\frac{3}{5}$ is between 2 and 3. The interval from 2 to 3 must be divided into 5 equal parts, and the point should be at the 3rd mark from 2.
- Option (a): The point is at the 3rd mark from 2, which is correct.
- Option (b): The point is at the 2nd mark from 2, which is incorrect.
- Option (c): The point is at the 4th mark from 2, which is incorrect.
- Option (d): The point is at the 3rd mark from 2, which is also correct.
- Wait, both (a) and (d) seem to show the point at the 3rd mark. Let me zoom in to check the details.
- Upon closer inspection, option (a) has the point correctly placed at the 3rd division, while option (d) has the point slightly off or the labeling might be different. But both appear similar. Let's assume the question expects only one correct answer. Typically, the most clearly marked one is chosen. Option (a) is unambiguously correct.
- Answer: (a)

#### (ii) Encircle the rational number which is represented on number line given below.

- Analysis: The point is located between 3 and 4. It appears to be at the 2nd division if the interval from 3 to 4 is divided into 5 parts.
- So, the value is $3 + \frac{2}{5} = 3\frac{2}{5}$.
- Looking at the options:
- (a) $4\frac{2}{5}$
- (b) $3\frac{2}{4}$ (which simplifies to $3\frac{1}{2}$)
- (c) $\frac{2}{5}$
- (d) $-\frac{17}{5}$ (which is $-3\frac{2}{5}$)
- None of the options exactly match $3\frac{2}{5}$. Option (b) is $3\frac{2}{4}$, which is not the same. Let's re-examine the number line.
- The point is at the 2nd tick mark after 3. If the interval from 3 to 4 is divided into 5 parts, then it is $3\frac{2}{5}$. But this is not listed.
- Perhaps the interval is divided into 4 parts? If so, the 2nd mark would be $3\frac{2}{4} = 3\frac{1}{2}$, which is option (b).
- Looking at the number line, there are 4 intervals between 3 and 4, meaning 5 tick marks including the endpoints. So, the divisions are quarters.
- Therefore, the point is at $3 + \frac{2}{4} = 3\frac{2}{4}$.
- Answer: (b) $3\frac{2}{4}$

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Final Answers:

Q1:
(i) (c) 7
(ii) (b) right
(iii) (a) 0 & 1
(iv) (b)
(v) (b)

Q2: (c) $-1\frac{7}{8}$

Q3:
(i) (a)
(ii) (b) $3\frac{2}{4}$