**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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