Rational Numbers
Exercise 9.1
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
Ans: The five rational numbers between -1 and 0 are -0.1, -0.2, -0.3, -0.4 and -0.5
(ii) –2 and –1
Ans: The five rational numbers between -2 and -1 are -1.1, -1.2, 1.3, -1.4 and -1.5
(iii) – 4/5 and -2/3
(iv) -1/2 and 2/3
2). Write four more rational numbers in each of the following patterns:
(i) -3/5, -6/10, -9/15, -12/20, . . . .
(ii) -1/4, -2/8, -3/12, -4/16, . . . . .
(iii) -1/6, 2/-12, 3/-18, -4/24, . . . . .
(iv) -2/3, 2/-3, 4/-6, 6/-9, . . . . . .
Answer:
(i) -3/5, -6/10, -9/15, -12/20, . . . .
Ans: The four more rational numbers in the pattern are -15/25, -18/30, -21/35, -24/40.
(ii) -1/4, -2/8, -3/12, -4/16, . . . . .
Ans: The four more rational numbers in the pattern are -5/20, -6/24, -7/28, -8/32.
(iii) -1/6, 2/-12, 3/-18, -4/24, . . . . .
Ans: The four more rational numbers in the pattern are -5/30, 7/-36,
-8/42, 9/-48.
(iv) -2/3, 2/-3, 4/-6, 6/-9, . . . . . .
Ans: The four more rational numbers in the pattern are -8/12, -18/30, -21/35, -24/40.
3). Give four rational numbers equivalent to:
(i) -2/7 (ii) 5/−3
(iii) 4/9
Answer:
(i) -2/7 (ii) 5/−3
iii) 4/9
4). Draw the number line and represent the following rational numbers on it:
(i) ¾ (ii) −5/8
(iii) −7/4 iv) 7/8
Answer:
(i) ¾
(ii) −5/8
(iii) −7/4
iv) 7/8
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.
Given:TR = RS = SU
It means that each unit is divided into three equal parts.
P ↔ 7/3
Q ↔ 8/3
R ↔ -4/3
S ↔ -5/3
6). Which of the following pairs represent the same rational number?
(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
7). Rewrite the following rational numbers in the simplest form:
(i) −8/6 (ii) 25/45
(iii) – 44/72 (iv) −8/10
Answer:
(i) −8/6 (ii) 25/45
(iii) – 44/72 (iv) −8/10
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) 5/11 □ 5/-11
(vii) 0 □ 7/6
Answer:
(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) 5/11 □ 5/-11
(vii) 0 □ 7/6
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 , ¼
(v) -3 2/7 , -3 4/5
Answer:
(i) 2/3 , 5/2 (ii) –5/6, -4/3
(iii) –3/4 , 2/-3 (iv) -1/4 , ¼
(v) -3 2/7 , -3 4/5
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:
(i) -3/5 , -2/5 , -1/5
(ii) -1/3 , -2/9, -4/3
(iii) -3/7 , -3/2, -3/4
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