Question

Subtract the first rational number from the second in each of the following:

(i) 3/8, 5/8

(ii) -7/9, 4/9

(iii) -2/11, -9/11

(iv) 11/13, -4/13

(v) ¼, -3/8

(vi) -2/3, 5/6

(vii) -6/7, -13/14

(viii) -8/33, -7/22​

Answer 1

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(i) let us subtract

5/8 – 3/8

Since the denominators are same we can subtract directly

(5-3)/8 = 2/8

Further we can divide by 2 we get,

2/8 = 1/4

(ii) let us subtract

4/9 – -7/9

Since the denominators are same we can subtract directly

(4+7)/9 = 11/9

(iii) let us subtract

-9/11 – -2/11

Since the denominators are same we can subtract directly

(-9+2)/11 = -7/11

(iv) let us subtract

-4/13 – 11/13

Since the denominators are same we can subtract directly

(-4-11)/13 = -15/13

(v) let us subtract

-3/8 – 1/4

By taking LCM for 8 and 4 which is 8

-3/8 – 1/4 = (-3×1)/(8×1) – (1×2)/(4×2) = -3/8 – 2/8

Since the denominators are same we can subtract directly

(-3-2)/8 = -5/8

(vi) let us subtract

5/6 – -2/3

By taking LCM for 6 and 3 which is 6

5/6 – -2/3 = (5×1)/(6×1) – (-2×2)/(3×2) = 5/6 – -4/6

Since the denominators are same we can subtract directly

(5+4)/6 = 9/6

Further we can divide by 3 we get,

9/6 = 3/2

(vii) let us subtract

-13/14 – -6/7

By taking LCM for 14 and 7 which is 14

-13/14 – -6/7 = (-13×1)/(14×1) – (-6×2)/(7×2) = -13/14 – -12/14

Since the denominators are same we can subtract directly

(-13+12)/14 = -1/14

(viii) let us subtract

-7/22 – -8/33

By taking LCM for 22 and 33 which is 66

-7/22 – -8/33 = (-7×3)/(22×3) – (-8×2)/(33×2) = -21/66 – -16/66

Since the denominators are same we can subtract directly

(-21+16)/66 = -5/66

Answer 2

4/13 – 11/13

Since the denominators are same we can subtract directly

(-4-11)/13 = -15/13