List five rational numbers between: (i) -1 and 0 (ii) -2 and -1 (iii) -⅘ and -⅔ (iv) -½ and ⅔

(i) -1 and 0

Let us multiply both numerator and denominator by 6

(-1 x 6)/(1 x 6) = -6/6

(0 x 6)/(1 x 6) = 0/6

Five rational numbers between -1 and 0 are

-6/6 < -5/6 < -4/6 < -3/6 < -2/6 < -1/6 < 0/6

-1 < -5/6 < -4/6 < -3/6 < -2/6 < -1/6 < 0

Therefore, the five rational numbers between -1 and 0 are -⅚, -⅔, -1/2;, -⅓, and -⅙.

(ii) -2 and -1

Let us multiply both numerator and denominator by 6

(-2 x 6)/(1 x 6) = (-12/6)

(-1 x 6)/(1 x 6) = -(6/6)

Five rational numbers between -2 and -1 are

-12/6 < -11/6 < -10/6 < -9/6 < -8/6 < -7/6 < -6/6

-2 < -11/6 < -10/6 < -9/6 < -8/6 < -7/6 < -1

Therefore, the five rational numbers between -2 and -1 are -11/6, -5/3, -3/2, -4/3, and -7/6.

(iii) -⅘ and -⅔

Let us convert -⅘ and -⅔ into like fractions

-4/5 = (-4 x 9)/(5 x 9) = -36/45

-2/3 = (-2 x 15)/(3 x 15) = -30/45

Five rational numbers between -⅘ and -⅔ are

-36/45 < -35/45 < -34/45 < -33/45 < -32/45 < -31/45 < -30/45

-4/5 < -35/45 < -34/45 < -33/45 < -32/45 < -31/45 < -2/3

Therefore, the five rational numbers between -⅘ and -⅔ are -7/9, -34/45, -11/15, -32/45, and -31/45.

(iv) -1/2 and ⅔

Let us convert -1/2 and ⅔ into like fractions

-1/2 = (-1 x 3)/(2 x 3) = -3/6

2/3 = (2 x 2)/(3 x 2) = 4/6

Five rational numbers between -1/2 and ⅔ are

-3/6 < -2/6 < -1/6 < 0 < 2/6 < 3/6 < 4/6

Therefore, the five rational numbers between -1/2 and ⅔ are -⅓, -⅙, 0, ⅓, and 1/2.

Summary:

List five rational numbers between: (i) -1 and 0, (ii) -2 and -1, (iii) -⅘ and -⅔, (iv) -1/2 and ⅔.

The five rational numbers between:

(i) -1 and 0 are -⅚, -⅔, -1/2, -⅓ and -⅙.

(ii) -2 and -1 are -11/6, -5/3, -3/2, -4/3 and -7/6.

(iii) -⅘ and -⅔ are -7/9, -34/45, -11/15, -32/45 and -31/45.

(iv) -1/2 and ⅔ are -⅓, -⅙, 0, ⅓, and 1/2.

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