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ML Aggarwal Class 7 Solutions Chapter 3 Rational Numbers Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 3 Rational Numbers Check Your Progress

Question 1.
Write five rational numbers equivalent to \(\frac { 5 }{ -11 }\)
Solution:

Question 2.
Express \(\frac { 9 }{ -15 }\) as a rational number with:
(i) denominator 5
(ii) numerator -12
(iii) denominator 30
Solution:

Question 3.
Write each of the following numbers in standard form:

Solution:

Question 4.
Which of the following are pairs of equivalent rational numbers?

Solution:

Question 5.
Arrange the following rational numbers in ascending order:

Solution:

Question 6.

Solution:

Question 7.
Insert five rational numbers between \(\frac { -3 }{ 5 }\) and \(\frac { -1 }{ 2 }\).
Solution:

Question 8.
Find the sum:

Solution:

Question 9.
Subtract:

Solution:

ML Aggarwal Class 7 Solutions Chapter 3 Rational Numbers Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 3 Rational Numbers Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) Two rational numbers are called equivalent if they have …… value.
(ii) The number \(\frac { -4 }{ 7 }\) lies to the …….. of zero on the number line.
(iii) The rational number \(\frac { -5 }{ -11 }\) lies to the ……. of zero on the number line.
(iv) The rational number \(\frac { -84 }{ 156 }\) reduced to simplest form is ………
(v) The standard form of the rational number \(\frac { 14 }{ -12 }\) is ………
(vi) There are ….. rational numbers between two different rational numbers.
(vii) Two rational numbers \(\frac { p }{ q }\)and \(\frac { r }{ s }\) are equal if an only if q × r = ……..
(viii)The multiplicative inverse of -3\(\frac { 1 }{ 5 }\) is ……..
(ix) \(\frac { -3 }{ 7 }\) ÷ \(\frac { -7 }{ 3 }\) = ………
(x) If p and q are positive integers, then \(\frac { p }{ q }\) is a …… rational number and \(\frac { p }{ -q }\) is a ……
Solution:

Question 2.
State whether the following statements are true (T) or false (F).
(i) Zero is the smallest rational number.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction.
(vi) The reciprocal of -1 is -1.
(vii) The quotient of two integers is always a rational number.
(viii) The value of a rational number remains the same if both its numerator and denominator are multiplied (or divided) by the same (nonzero) integer.
(ix) Between two distinct integers, we can always insert an integer.
(x) Between two distinct rational numbers, we can al ways insert a rational number.
(xi) There exists atleast one integer between two different rational numbers.
(xii) The reciprocal of 2\(\frac { 6 }{ 7 }\) is \(\frac { -7}{ 20 }\).
(xiii) All terminating decimal numbers are rational numbers.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 14):
Question 3.
The rational number \(\frac { 110 }{ -132 }\) when reduced to standard form is
(a) \(\frac { 10 }{ -12 }\)
(b) \(\frac { 5 }{ -6 }\)
(c) \(\frac { -5 }{ 6 }\)
(d) \(\frac { 110 }{ -132 }\)
Solution:

Question 4.
The Additive inverse of \(\frac { -7 }{ 12 }\) is
(a) \(\frac { 12 }{ -7 }\)
(b) \(\frac { -7 }{ 12 }\)
(c) \(\frac { -5 }{ 12 }\)
(d) \(\frac { 7 }{ 12 }\)
Solution:

Question 5.
The Multiplicative inverse of \(\frac { -4 }{ 9 }\) is
(a) \(\frac { 4 }{ 9 }\)
(b) \(\frac { -9 }{ 4 }\)
(c) \(\frac { 9 }{ 4 }\)
(d) none of these
Solution:

Question 6.
The reciprocal of the rational number -2\(\frac { 3 }{ 7 }\) is
(a) \(\frac { -17 }{ 7 }\)
(b) \(\frac { 7 }{ 17 }\)
(c) \(\frac { -7 }{ 17 }\)
(d) none of these
Solution:

Question 7.
The product of rational number \(\frac { -2 }{ 5 }\) and its multiplicative inverse is
(a) 1
(b) 0
(c) \(\frac { 4 }{ 25 }\)
(d) \(\frac { 2 }{ 5 }\)
Solution:

Question 8.
The product of rational number \(\frac { -2 }{ 3 }\) and its additive inverse is
(a) 1
(b) \(\frac { 2 }{ 3 }\)
(c) \(\frac { 4 }{ 9 }\)
(d) \(\frac { -4 }{ 9 }\)
Solution:

Question 9.
The sum of rational number \(\frac { -1 }{ 3 }\) and its reciprocal is
(a) 0
(b) 1
(c) \(\frac { -10 }{ 3 }\)
(d) \(\frac { -3 }{ 10 }\)
Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.
In the standard form of a rational number, the denominator is always
(a) 0
(b) a negative integer
(c) 1
(d) a positive integer
Solution:

Question 14.
The sum of two rational numbers is -1. If one of them is \(\frac { -5 }{ 7 }\), then the other is
(a) \(\frac { 5 }{ 7 }\)
(b) \(\frac { -2 }{ 7 }\)
(c) \(\frac { 12 }{ 7 }\)
(d) \(\frac { -12 }{ 7 }\)
Solution:

Value Based Questions

Question 1.
Rohit donated \(\frac { 1 }{ 5 }\) of his monthly income to an NGO working for the education of old women, \(\frac { 1 }{ 4 }\) of his salary spent on food, \(\frac { 1 }{ 3 }\) on rent and \(\frac { 1 }{ 15 }\) on other expenses. If he is left with ₹ 9000, find his monthly income. What values are being promoted?
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
From a rope 15 m long, 4\(\frac { 1 }{ 3 }\) m is cut off and \(\frac { 3 }{ 5 }\) of the remaining is cut off again. Find the length of the remaining part of the rope.
Solution:

Question 2.
Perimeter of a rectangle is 2 m less than \(\frac { 2 }{ 5 }\) of the perimeter of a square, if the perimeter of the square is 40 m, find the length and breadth of the rectangle given that the breadth is \(\frac { 1 }{ 3 }\) of the length.
Solution:

ML Aggarwal Class 7 Solutions Chapter 3 Rational Numbers Ex 3.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 3 Rational Numbers Ex 3.3

Question 1.
Add the following pairs of rational numbers:

Solution:

Question 2.
Find the sum:

Solution:

Question 3.
Subtract:

Solution:

Question 4.
Find:

Solution:

Question 5.
The sum of two rational numbers is \(\frac { 2 }{ 5 }\) if one of them is \(\frac { -4 }{ 7 }\), find the other.
Solution:

Question 6.
What rational number should be added to \(\frac { -5 }{ 12 }\) to get \(\frac { -7 }{ 8 }\)?
Solution:

Question 7.
What rational number should be subtracted from \(\frac { -2 }{ 3 }\) to get \(\frac { -5 }{ 6 }\)?
Solution:

Question 8.
Find the product:

Solution:

Question 9.
Find the value of:

Solution:

Question 10.
The product of two rational numbers is \(\frac { 18 }{ 35 }\) If one of them is \(\frac { -2 }{ 5 }\), find the other.
Solution:

Question 11.
Find the value of:

Solution:

Question 12.
Find the reciprocal of the following:

Solution:

ML Aggarwal Class 7 Solutions Chapter 3 Rational Numbers Ex 3.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 3 Rational Numbers Ex 3.2

Question 1.
Draw a number line and represent the following rational numbers on it:
(i) \(\frac { 3 }{ 8 }\)
(ii) \(\frac { -3 }{ 4 }\)
(iii) \(\frac { -7 }{ 8 }\)
(iv) \(\frac { -17 }{ 8 }\)
Solution:

Question 2.
The points P, Q, R, S, T, U, A and B on the number line are such that TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S respectively.

Solution:

Question 3.
State whether the following statements are true or false:
(i) The rational number \(\frac { -13 }{ -5 }\) lies to the right of zeroxin the number line.
(ii) The rational numbers \(\frac { -5 }{ -7 }\) and \(\frac { 7 }{ -9 }\) lie on opposite sides of zero on the number line.
(iii) The rational numbers \(\frac { -17 }{ 6 }\) and \(\frac { 8 }{ -15 }\) lie on opposite sides of zero on the number line.
Solution:

Question 4.
Which of the two rational numbers is greater in each of tl following pairs?

Solution:

Question 5.
Fill in the boxes with the correct symbol out of >, < and =:

Solution:

Question 6.
Arrange the following rational numbers in ascending order:

Solution:

Question 7.
Arrange the following rational numbers in descending order:

Solution:

Question 8.
Insert five rational numbers between:
(i) -3 and -2
(ii) \(\frac { -2 }{ 3 }\) and \(\frac { -1 }{ 3 }\)
Solution:

Question 9.
Insert five rational numbers between:
(i) \(\frac { -4 }{ 5 }\) and [lat3.1
ex]\frac { -2 }{ 3 }[/latex]
(ii) \(\frac { -1 }{ 2 }\) and \(\frac { 2 }{ 3 }\)
Solution:

ML Aggarwal Class 7 Solutions Chapter 3 Rational Numbers Ex 3.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 3 Rational Numbers Ex 3.1

Question 1.
Which of the following are positive rational numbers?

Solution:

Question 2.
Which of the following are negative rational numbers?

Solution:

Question 3.
Find four rational numbers equivalent to each of the following rational numbers:
(i) \(\frac { 3 }{ -7 }\)
(ii) \(\frac { -5 }{ -9 }\)
Solution:

Question 4.
Write each of the following ratinoal numbers with positive denominators:
(i) \(\frac { 4 }{ -9 }\)
(ii) \(\frac { 17 }{ -33 }\)
(iii) \(\frac { -15 }{ -38 }\)
Solution:

Question 5.
Write next four rational numbers in each of the following patterns:

Solution:
Next four rational numbers in the same patterns.

Question 6.
Which of the following pairs of rational numbers are equal?

Solution:

Question 7.
Which of the following pairs represent the same rational number?

Solution:

Question 8.
Fill in the blanks:

Solution:

Question 9.
Reduce each of the following rational numbers in standard form:

Solution: