Question

If x = `1/10` and y = `(-3)/8`, then evaluate x + y, x – y, x × y and x ÷ y.

Answer 1

Given, x = `1/10` and y = `(-3)/8`

Now, x + y = `1/10 + ((-3))/8 = 1/10 - 3/8`

= `(1 xx 4)/(10 xx 4) - (3 xx 5)/(8 xx 5)`  ......[∵ LCM of 10 and 8 = 40]

= `4/40 - 15/40`

= `(4 - 15)/40`

= `-11/40`

and x – y = `1/10 - (-3/8) = 1/10 + 3/8`

= `(1 xx 4)/(10 xx 4) + (3 xx 5)/(8 xx 5)`  ......[∵ LCM of 10 and 8 = 40]

= `4/40 + 15/40`

= `(4 + 15)/40`

= `19/40`

∴ Product of rational numbers = `"Product of numerators"/"Product of denominators"`

⇒ x × y = `1/10 xx ((-3))/8 = (1 xx (-3))/(10 xx 8) = (-3)/80`

and x ÷ y = `1/10 ÷ ((-3)/8)`

The reciprocal of `((-3)/8)` is `8/(-3)`

So, x ÷ y = `1/10 xx 8/(-3)`

= `(1 xx 8)/(10 xx - 3)`

= `(-8)/30`

= `(-8 ÷ 2)/(30 ÷ 2)`  ......[Dividing numerator and denominator by 2]

= `(-4)/15`