CBSE Class 7 Mathematics Rational Numbers Assignment Set 02

Question. p: Every fraction is a rational number.
q: Every rational number is a fraction.
Which of the following is correct?
(A) p is true and q is false.
(B) p is false and q is true.
(C) Both p and q are true.
(D) Both p and q are false.
Answer : A

Question. Which of the following is not a rational number(s)?
(A) -2/9
(B) 4/- 7
(C) -3/17
(D) √2/3
Answer : D

Question. p: All integers are rational numbers.
q : Every rational number is an integer.
Which of the following statements is correct?
(A) p is false and q is true.
(B) p is true and q is false.
(C) Both p and q are true.
(D) Both p and q are false.
Answer : B

Question. What type of a number is -3/0 ?
(A) A positive rational number.
(B) A negative rational number.
(C) Either a positive or a negative rational number.
(D) Neither a positive nor a negative rational number.
Answer : D

Question. Which among the following is a rational number equivalent to 5/3?
(A) -20/15
(B) 25/-15
(C) 25/15
(D) 15/25
Answer : C

Question. What type of a numerator does 7 have?
(A) Positive
(B) Negative
(C) Either positive or negative
(D) Neither positive nor negative
Answer : D

Question. Which of the following statements is true?
A) 3/-8 > -12/32
(B) 3/-8 = -12/32
(C) 3/-8 < -12/32
(D) 3/5 > 4/3
Answer : B

Question. If -4/7 = -32/x, what is the value of x?
(A) -56
(B) 56
(C) 46
(D) -46
Answer : A

Question. Which is the greatest?
(A) -5/11
(B) 5/-12
(C) -5/17
(D) -5/13
Answer : C

Question. Which is the correct descending order of

Answer : B

Question. What is the average of the two middle rational numbers if 4/7. 1/3. 2/5 and 5/9 are arranged in ascending order?
(A) 86/90
(B) 86/45
(C) 43/45
(D) 43/90
Answer : D

Question. What is the percentage of the least number in the greatest number of 3/5, 9/5, 1/5 and 7/5 ?
(A) 11(1/9)%
(B) 10%
(C) 20%
(D) 25%
Answer : A

Question. What is the difference between the greatest and least numbers of 5/9. 1/9 and 11/9?
(A) 2/9
(B) 4/9
(C) 10/9
(D) 2/3
Answer : C

Question. Which of the fo ll owing pairs represent the same rational number ?
(A) -7/21 and 1/3
(C) -5/-9 and 5/-9
(B) 1/3 and -1/9
(D) 8/-5 and - 24/15
Answer : D

Question. P :The quotient of two integers is always a rational number.
Q : 1/0 is not rational. Which of the following statements is true?
(A) P is true and Q is the cor rect explanation of P.
(B) P is fa lse and Q is the co rrect explanation of P.
(C) P is true and Q is false.
(D) Both P and Q are false .
Answer : A

Question. What is the result of 2 - 11/39 + 5/26 ?
(A) 149
(B) 149
(C) 149
(D) 149
Answer : B

Question. Which is the equiva lent of - 143/21 ?
(A) -6 + 17/21
(B) 6 + (17/21)
(C) (-6) + ( -17/21)
(D) - 6
Answer : C

Question. Of which property is - 7/5 + (2/-11 + -13/25) = (-7/5 + 2/-11) + -13/25 an exa mp le?
(A) Closu re property
(B) Commutative property
(C) Associative property
(D) Identity property
Answer : C

Question. Which of the following statements is correct?
(A) 0 is called the additive identity for rational numbers.
(B) 1 is called the multiplicative identity for rationa l numbers.
(C) The add itive i nverse of 0 i s zero itself.
(D) All the above.
Answer : D

Question. The sum of two rational numbers is -3. If one of the numbers is -7/5 find the other number.
(A) - 8/5
(B) 8/5
(C) -6/5
(D) 6/5
Answer : A

Question. What number should be added to -5/6 to get 3/2?
(A) -7/3
(B) 2(1/3)
(C) 8/3
(D) -8/3
Answer : B

Question. Which of the following statements is true?
(A) The reciproca ls of 1 and -1 are themselves.
(B) Zero has no reciprocal.
(C) The product of two rational numbers is a rational number.
(D) All the above.
Answer : D

Question. Name the property of multiplication illustrated by -4/3 x (-6/5 + 8/7) = (-4/3 X -6/5 ) + (-4/3 X 8/7)
(A) Associative property
(B) Commutative property
(C) Distributive property
(D) Closure property
Answer : C

Question. What is the product of a rational number and its reciprocal?
(A) 0
(B) 1
(C) - 1
(D) 2
Answer : B

Question. The product of two rational numbers is - 9/16 If one of the numbers is -4/3 what is the other number?
(A) 36/48
(B) 25/64
(C) 27/49
(D) 27/64
Answer : D

Question. By what rational number should -8/39 be multiplied to obtain 26 ?
(A) 507/4
(B) - 507/4
(C) 407/4
(D) - 407/4
Answer : B

Question. How many pieces of equal size can be cut from a rope of 30 metres long, each measuring 3(3/4) metres?
(A) 8
(B) 10
(C) 6
(D) 12
Answer : A

Question. Evaluate p + q given p = ( -2 1/5) and q = (-1 1/3).
(A) 1(8/15)
(C) ( -2 8/15)
(B) ( - 3 8/15)
(D) 3(8/15)
Answer : B

Question. Compute 1(1/4) + (-8/3) - (-5/9)
(A) - 31/36
(B) 13/36
(C) 15/36
(D) -29/36
Answer : A

Question. Find the value of - 6 2/3 x 2/5
(A) 2(2/3)
(B) 2(1/5)
(C) -2(2/3)
(D) -2(1/3)
Answer : C

Question. For what value of 'x' is
7/8 - (- 11/4) + X = 3(7/24) ?
(A) 3
(B) 3
(C) 3
(D) - 3
Answer : A

Question. Determine 'y' so that Y- 2(1/3) = ( - 3 7/12)
(A) - 14
(B) 1'4
(C) - 112
(D) 112
Answer : A

Question. Find the simplest form of ( - 1/2 + 1/3 + 1/6) (-2/5)
(A) 5
(B) 0
(C) 1
(D) 5
Answer : B

Question. Rohit, Peter and Santosh walk around a circularpark.Theytake (1/3)h, (2/5)h and (5/12)h to complete one round. What is the total time taken by them to complete a round in minutes?
(A) 79 minutes
(C) 60 minutes
(B) 50 minutes
(D) 69 minutes
Answer : D

Question. Find a rational number between 3/4 and 9/11
(A) 1/2
(B) 13/11
(C) 69/88
(D) 1/4
Answer : C

RATIONAL NUMBER (Lowest form)

Question. Determine whether the following rational numbers are in the lowest form or not:
(i) (65/84) (ii) (-15/32)
Solution: (i) Given (65/84) Here we can observe that 65 and 84 have no common factor their HCF is 1.
Thus, (65/84) is in its lowest form.

(ii) Given (-15/32) Here we can observe that -15 and 32 have no common factor i.e., their HCF is 1.
Thus, (-15/32) is in its lowest form.

Question. Express each of the following rational numbers to the lowest form:
(i) (4/22) (ii) (-36/180)
Solution: (i) Given (4/22) We know that HCF of 4 and 22 is 2
By dividing the given number by its HCF we get
(4 ÷ 2/22 ÷ 2) = (2/11)
Therefore (2/11) is the simplest form of the given number

(ii) Given (-36/180)
We know that HCF of 36 and 180 is 36
By dividing the given number by its HCF we get
(-36 ÷ 36/180 ÷ 36) = (-1/5)
Therefore (-1/5) is the simplest form of the given number

Question. Fill in the blanks:
(i) (-5/7) = (…/35) = (…/49)
(ii) (-4/-9) = (…/18) = (12/…)
Solution: (i) (-5/7) = (-25/35) = (-35/49)

Explanation:
Given (-5/7) = (…/35) = (…/49)
Here (-5/7) × (5/5) = (-25/35)
And also (-5/7) × (7/7) = (-35/49)

(ii) (-4/-9) = (8/18) = (12/27)
Explanation: Given (-4/-9) = (…/18) = (12/…)
On multiplying by -2 we get
(-4/-9) × (-2/-2) = (8/18)
Also on multiplying by -3
(-4/-9) × (-3/-3) = (12/27)

Question 1. Represent the following on number line. \(\frac{-7}{4}, \frac{-3}{4}, \frac{1}{4}\) and \(\frac{5}{4}\)
Answer: To represent the given rational numbers on a number line, draw a straight line with arrows on both sides. Mark a point as \(0\). Since the denominators are all \(4\), divide each unit length into \(4\) equal parts (sub-divisions).
Mark points to the left of \(0\) for negative fractions at intervals of \(\frac{1}{4}\): \(\frac{-1}{4}, \frac{-2}{4}, \frac{-3}{4}, \frac{-4}{4}, \frac{-5}{4}, \frac{-6}{4}, \frac{-7}{4}\).
Mark points to the right of \(0\) for positive fractions at intervals of \(\frac{1}{4}\): \(\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \frac{5}{4}\).
The required numbers \(\frac{-7}{4}, \frac{-3}{4}, \frac{1}{4},\) and \(\frac{5}{4}\) are located at their respective positions on the number line.
In simple words: Divide the space between integers on a number line into four equal parts and locate the given fractions based on their numerator and sign.

Exam Tip: Always make sure the denominator is the same before dividing the scale into equal parts on the number line.

Question 2. Find the sum: (a) \(\left(-2 \frac{3}{10}\right) + \left(-3 \frac{1}{10}\right)\) (b) \(\left(-2 \frac{3}{25}\right) + \left(1 \frac{4}{25}\right)\)
Answer: (a) Convert mixed fractions to improper fractions:
\(-2 \frac{3}{10} = \frac{-23}{10}\)
\(-3 \frac{1}{10} = \frac{-31}{10}\)
Now add them:
\(\frac{-23}{10} + \left(\frac{-31}{10}\right) = \frac{-23 - 31}{10} = \frac{-54}{10} = \frac{-27}{5} = -5 \frac{2}{5}\)

(b) Convert mixed fractions to improper fractions:
\(-2 \frac{3}{25} = \frac{-53}{25}\)
\(1 \frac{4}{25} = \frac{29}{25}\)
Now add them:
\(\frac{-53}{25} + \frac{29}{25} = \frac{-53 + 29}{25} = \frac{-24}{25}\)
In simple words: First change mixed numbers into improper fractions, make sure denominators are same, and then add their numerators.

Exam Tip: Be very careful with negative signs when adding numerators together.

Question 3. Simplify: (a) \(\left(\frac{-11}{9} \times \frac{12}{11}\right) + \left(\frac{-8}{9} \times \frac{-5}{16}\right)\) (b) \(\left(\frac{-3}{5} \times \frac{6}{-7}\right) - \left(\frac{5}{-7} \times \frac{-8}{6}\right)\)
Answer: (a) Simplify each term by cross-multiplication / cancellation:
First term: \(\left(\frac{-11}{9} \times \frac{12}{11}\right) = \frac{-12}{9} = \frac{-4}{3}\)
Second term: \(\left(\frac{-8}{9} \times \frac{-5}{16}\right) = \frac{40}{144} = \frac{5}{18}\)
Now add both terms by taking the LCM of \(3\) and \(18\), which is \(18\):
\(\frac{-4}{3} + \frac{5}{18} = \frac{-24 + 5}{18} = \frac{-19}{18}\)

(b) Simplify each term:
First term: \(\left(\frac{-3}{5} \times \frac{6}{-7}\right) = \frac{-18}{-35} = \frac{18}{35}\)
Second term: \(\left(\frac{-5}{7} \times \frac{-8}{6}\right) = \frac{40}{42} = \frac{20}{21}\)
Now subtract:
\(\frac{18}{35} - \frac{20}{21}\)
LCM of \(35\) and \(21\) is \(105\):
\(\frac{18 \times 3}{105} - \frac{20 \times 5}{105} = \frac{54 - 100}{105} = \frac{-46}{105}\)
In simple words: Perform multiplication inside brackets first by canceling common factors, then add or subtract the resulting fractions using a common denominator.

Exam Tip: Cancel out common factors in numerators and denominators before multiplying to make calculations simpler.

Question 4. Find the area of a rectangle whose length and breadth are \(31 \frac{1}{4}\) m and \(16 \frac{4}{5}\) m respectively.
Answer: Length (\(l\)) = \(31 \frac{1}{4} \text{ m} = \frac{125}{4} \text{ m}\)
Breadth (\(b\)) = \(16 \frac{4}{5} \text{ m} = \frac{84}{5} \text{ m}\)
Area of rectangle = \(l \times b\)
\(\text{Area} = \frac{125}{4} \times \frac{84}{5}\)
Simplify by canceling terms: \(\frac{125}{5} = 25\) and \(\frac{84}{4} = 21\)
\(\text{Area} = 25 \times 21 = 525 \text{ m}^2\)
In simple words: Multiply the length and breadth after converting them into improper fractions.

Exam Tip: Don't forget to write the square unit (\(\text{m}^2\)) in the final answer for area.

Question 5. Evaluate: \(\left(\frac{14}{33} \div \frac{21}{22}\right) \div \frac{-4}{9}\)
Answer: First, solve the division inside the bracket:
\(\frac{14}{33} \div \frac{21}{22} = \frac{14}{33} \times \frac{22}{21}\)
Cancel common factors (\(14\) and \(21\) divided by \(7\); \(22\) and \(33\) divided by \(11\)):
\(= \frac{2}{3} \times \frac{2}{3} = \frac{4}{9}\)
Now, evaluate the remaining expression:
\(\frac{4}{9} \div \frac{-4}{9} = \frac{4}{9} \times \frac{9}{-4} = -1\)
In simple words: Change division into multiplication by taking the reciprocal of the divisor, solve step-by-step from left to right.

Exam Tip: Always evaluate expressions inside parentheses or brackets first following the BODMAS rule.

Question 6. Write the following rational numbers in standard form: (a) \(\frac{-135}{-240}\) (b) \(\frac{168}{-264}\)
Answer: (a) \(\frac{-135}{-240}\)
Both numerator and denominator are negative, so the fraction becomes positive:
\(= \frac{135}{240}\)
Find the HCF of \(135\) and \(240\), which is \(15\):
\(= \frac{135 \div 15}{240 \div 15} = \frac{9}{16}\)

(b) \(\frac{168}{-264}\)
Shift the negative sign to the numerator:
\(= \frac{-168}{264}\)
Find the HCF of \(168\) and \(264\), which is \(24\):
\(= \frac{-168 \div 24}{264 \div 24} = \frac{-7}{11}\)
In simple words: Reduce the fraction to its lowest terms by dividing the numerator and denominator by their HCF, and keep the denominator positive.

Question 7. Find the cost of \(4 \frac{2}{3}\) kg sugar at the rate of Rs \(36 \frac{3}{7}\) per kg.
Answer: Quantity of sugar = \(4 \frac{2}{3} \text{ kg} = \frac{14}{3} \text{ kg}\)
Rate of sugar per kg = Rs \(36 \frac{3}{7} = \text{Rs } \frac{255}{7}\)
Total cost = Quantity \(\times\) Rate
\(\text{Total Cost} = \frac{14}{3} \times \frac{255}{7}\)
Simplify by canceling terms: \(\frac{14}{7} = 2\) and \(\frac{255}{3} = 85\)
\(\text{Total Cost} = 2 \times 85 = \text{Rs } 170\)
In simple words: Multiply the total weight of sugar by the price per kg after converting them into improper fractions.
Exam Tip: Always include the currency unit (Rs) in your final cost calculation statement.

Question 8. By what number should \(-2 \frac{1}{7}\) be divided to obtain \(-2 \frac{1}{2}\).
Answer: Let the required number be \(x\).
According to the question:
\(-2 \frac{1}{7} \div x = -2 \frac{1}{2}\)
Convert mixed fractions into improper fractions:
\(\frac{-15}{7} \div x = \frac{-5}{2}\)
\(\frac{-15}{7} \times \frac{1}{x} = \frac{-5}{2}\)
\(\frac{1}{x} = \frac{-5}{2} \div \left(\frac{-15}{7}\right)\)
\(\frac{1}{x} = \frac{-5}{2} \times \left(\frac{7}{-15}\right)\)
\(\frac{1}{x} = \frac{-35}{-30} = \frac{35}{30} = \frac{7}{6}\)
Taking the reciprocal to find \(x\):
\(x = \frac{6}{7}\)
In simple words: Set up the division equation, convert mixed numbers to fractions, and solve for the unknown variable by isolating it.

Exam Tip: Double-check your equation setup; "A divided by B to obtain C" means \(A \div B = C\).