DAV Class 7 Maths Chapter 1 Worksheet 1
Rational Numbers Worksheet 1
1. Which of the following are rational numbers?
(i) \( -3 \)
Answer \( \displaystyle \frac{-3}{1} \)
Rational number
(ii) \( \displaystyle -\frac{2}{3} \)
Answer \( \text{Rational number} \)
(iii) \( \displaystyle \frac{4}{0} \)
Answer \( \text{Not a rational number } \)
(iv) \( \displaystyle \frac{0}{-5} \)
Answer \( \text{Rational number } \)
2. Write down the rational numbers in the form \( \displaystyle \frac{p}{q} \) whose numerators and denominators are given below:
(i) \( (-5) \times 4 \) and \( (-5) + 4 \)
Answer
\[ \begin{align*} \text{Numerator } &= (-5) \times 4 \\ &= -20 \\ \text{ Denominator } &= -5 + 4 \\ &= -1 \\ \\ \frac{p}{q} & = \frac{\text{Numerator}}{\text{Denominator}} \\ \\ \frac{p}{q} & = \color{red} \frac{-20}{-1} \end{align*} \]
(ii) \( 64 \div 4 \) and \( 32 - 18 \)
Answer
\[ \begin{align*} \text{Numerator } &= 64 \div 4 \\ &= 16\\ \text{Denominator } &= 32 - 18\\ &= 14 \\ \\ \frac{p}{q} & = \frac{\text{Numerator}}{\text{Denominator}} \\ \\ \frac{p}{q} & = \color{red} \frac{16}{14} \\ \end{align*} \]
3. Which of the following are positive rational numbers ?
(i) \( \displaystyle \frac{-2}{9} \)
Answer \( \text{Negative rational number } \)
(ii) \( \displaystyle \frac{3}{-5} \)
Answer \( \text{Negative rational number } \)
(iii) \( \displaystyle \frac{4}{9} \)
Answer \( \text{Positive rational number } \)
(iv) \( \displaystyle \frac{-3}{-19} \)
Answer \( \text{Positive rational number } \)
(v) \( \displaystyle \frac{0}{-3} \)
Answer \( \text{Negative rational number } \)
4. Answer the following
(i) Which integer is neither positive nor negative?
Answer 0
(ii) A rational number can always be written as \( \displaystyle \frac{p}{q} \). Is it necessary that any number written as \( \displaystyle \frac{q}{p} \) is a rational number?
Answer No
\[ \begin{align*} &\text{Example } \\ \frac{p}{q} & = -\frac{0}{5} \quad \color{green} \text{(Rational Number)}\\ \\ \frac{q}{p} & = -\frac{5}{0} \quad \color{green} \text{(Not Rational Number)}\\ \\ \end{align*} \]
5. State whether the following statements are true. If not, justify your answer with an example.
(i) Every whole number is a natural number.
Answer False
\[ \begin{align*} \text{Natural Number } &= 1,2,3,4... \\ \text{Whole Number } &= 0,1,2,3,4... \\ \end{align*} \] \( \text{ The statements is not true because 0 is not a natural number.} \)
(ii) Every natural number is an integer.
Answer True
\[ \begin{align*} \text{Natural numbers } &= 1, 2, 3, 4... \\ \text{Integers } &= ..., -2, -1, 0, 1, 2, ... \\ \end{align*} \] \( \text{ The statements is true because all natural numbers are included in the Integers.} \)
(iii) Every integer is a whole number.
Answer False
\[ \begin{align*} \text{Integers } &= ..., -2, -1, 0, 1, 2, ... \\ \text{Whole numbers } &= 0, 1, 2, 3, 4... \\ \end{align*} \] \( \text{ The statements is not true because Negative integers are not whole numbers.} \)
(iv) Every integer is a rational number.
Answer True
\[ \begin{align*} \text{Integers } &= ..., -2, -1, 0, 1, 2, ... \\ \\ \text{Rational number } &= ..., \frac{-2}{1}, \frac{-1}{1}, \frac{0}{1}, \frac{1}{1}, \frac{2}{1}, ... \\ \end{align*} \] \( \text{ The statements is true because any integer can be written as rational number.} \)
(v) Every rational number is a fraction.
Answer False
\[ \begin{align*} \text{Rational numbers } &= \frac{p}{q} \text{ where } p, q \text{ are integers and } q \neq 0 \\ \\ \text{Rational numbers } &= \frac{8}{-6}, \frac{0}{6},\frac{4}{8} \\ \\ \text{Fraction} & \text{ is the ratio of two natural numbers} \\ \\ \text{Fraction } &= \frac{8}{6}, \frac{3}{6},\frac{4}{8} \\ \end{align*} \] \( \text{ The statements is not true because Negative rational numbers are not fractions} \)
(vi) Every fraction is a rational number.
Answer True