Class 6 - Mathematics
Chapter - Rational Numbers : Exercise 9.1
Top Block 1
Question: 1.List five rational numbers between:
(i) –1 and 0
(ii) –2 and –1
(iii) -4⁄5 and -2⁄3
(iv) -1⁄2 and 2⁄3
Answer :
(i) –1 and 0
Let us write –1 and 0 as rational numbers with denominator 6.
⇒ –1 = -6⁄6 and 0 = 0⁄6
∴ -6⁄6 < -5⁄6 < -4⁄6 < -3⁄6 < -2⁄6 < -1⁄6 < 0
⇒ –1 < -5⁄6 < -2⁄3 < -1⁄2 < -1⁄3 < -1⁄6 < 0
Therefore, five rational numbers between –1 and 0 would be
-5⁄6, -2⁄3, -1⁄2, -1⁄3, -1⁄6
(ii) –2 and –1
Let us write –2 and –1 as rational numbers with denominator 6.
⇒ –2 = -12⁄6 and –1 = -6⁄6
∴ -12⁄6 < -11⁄6 < -10⁄6 < -9⁄6 < -8⁄6 < -7⁄6 < -6⁄6
⇒ –2 < -11⁄6 < -5⁄3 < -3⁄2 < -4⁄3 < -7⁄6 < –1
Therefore, five rational numbers between –2 and –1 would be
-11⁄6, -5⁄3, -3⁄2, -4⁄3, -7⁄6
(iii) -4⁄5 and -2⁄3
Question: 2.Write four more rational numbers in each of the following patterns:
(i) -4⁄5, -6⁄10, -9⁄15, -12⁄20, ………
(ii) -1⁄4, -2⁄8, -3⁄12, ……….
(iii) -1⁄6, 2⁄-12, -3⁄-18, 4⁄-24, ………
(iv) -2⁄3, 2⁄-3, 4⁄-6, 6⁄-9, ……….
Answer :
Mddle block 1
Question: 3.Give four rational numbers equivalent to:
(i) -2⁄7
(ii) 5⁄-3
(iii) 4⁄9
Answer :
Question: 4.Draw the number line and represent the following rational numbers on it:
(i) 3⁄4
(ii) –5⁄8
(iii) –7⁄4
(iv) 7⁄8
Answer :
(i) 3⁄4
Question: 5.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.
Answer :
Each part which is between the two numbers is divided into 3 parts.
Therefore, A = 6⁄3, P = 7⁄3, Q = 8⁄3 and B = 9⁄3
Similarly T = -3⁄3, R = –4⁄8 , S = –5⁄3 and U = –6⁄3
Thus, the rational numbers represented P, Q, R and S are 7⁄3, 8⁄3, –4⁄3 and –5⁄3 respectively.
Question: 6.Which of the following pairs represent the same rational numbers:
(i) –7⁄21 and 3⁄9
(ii) –16⁄20 and 20⁄–25
(iii) –2⁄-3 and 2⁄3
(iv) –3⁄5 and –12⁄20
(v) 8⁄-5 and –24⁄15
(vi) 1⁄3 and –1⁄9
(vii) –5⁄-9 and 5⁄-9
Answer :
Question: 7.Rewrite the following rational numbers in the simplest form:
(i) –8⁄6
(ii) 25⁄45
(iii) –44⁄72
(iv) –8⁄10
Answer :
Question: 8.Fill in the boxes with the correct symbol out of < , > and =:
(i) –5⁄7 2⁄3
(ii) 4⁄5 –5⁄7
(iii) –7⁄8 14⁄-16
(iv) –8⁄5 –7⁄4
(v) 1⁄-3 –1⁄4
(vi) 5⁄-115–11 –5⁄11
(vii) 0⁄ –7⁄6
Answer :
Question: 9.Which is greater in each of the following:
(i) 2⁄3, 5⁄2
(ii) -5⁄6, -4⁄3
(iii) -3⁄4, 2⁄-3
(iv) -1⁄4, 1⁄4
(v) –3⁄27, –3⁄45
Answer :
Question: 10.Write the following rational numbers in ascending order:
(i) –3⁄5, –2⁄5, –1⁄5
(ii) 1⁄3, –2⁄9, –4⁄3
(iii) –3⁄7, –3⁄2, –3⁄4
Answer :
