Advertisements
Advertisements
प्रश्न
Verify the distributive property a × (b + c) = (a × b) + (a + c) for the rational numbers a = `(-1)/2`, b = `2/3` and c = `(-5)/6`
उत्तर
Given the rational number a = `(-1)/2`, b = `2/3` and c = `(-5)/6`
a × (b + c) = `(-1)/2 xx (2/3 + ((-5)/6))`
= `(-1)/2 xx (((2 xx 2) + (-5 xx 1))/6)`
= `(-1)/2 xx ((4 + (-5))/6)`
= `(-1)/2 xx ((-1)/6)`
a × (b + c) = `1/12` ...(1)
(a × b) + (a × c) = `((-1)/2 xx 2/3) + ((-1)/2 xx ((-5)/6))`
= `(-2)/6 + 5/12`
= `((-2 xx 2) + 5 xx 1)/12`
= `(-4 + 5)/12`
(a × b) + (a × c) = `1/12` ...(2)
From (1) and (2) we have a × (b + c) = (a × b) + (a × c) is true
Hence multiplication is distributive over addition for rational numbers Q.
APPEARS IN
संबंधित प्रश्न
Verify the property: x × y = y × x by taking:
Use the distributivity of multiplication of rational numbers over their addition to simplify:
Use the distributivity of multiplication of rational numbers over their addition to simplify:
Name the property of multiplication of rational numbers illustrated by the following statements:
By what number should we multiply \[\frac{- 1}{6}\] so that the product may be \[\frac{- 23}{9}?\]
By what number should we multiply \[\frac{- 15}{28}\] so that the product may be\[\frac{- 5}{7}?\]
By what number should \[\frac{- 3}{4}\] be multiplied in order to produce \[\frac{2}{3}?\]
Give an example and verify the following statement.
Distributive property of multiplication over subtraction is true for rational numbers. That is, a(b – c) = ab – ac
Simplify the following by using suitable property. Also name the property.
`[1/5 xx 2/15] - [1/5 xx 2/5]`
Name the property used in the following.
`-2/3 xx [3/4 + (-1)/2] = [(-2)/3 xx 3/4] + [(-2)/3 xx (-1)/2]`
