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