Advertisements
Advertisements
Question
Which of the following expressions shows that rational numbers are associative under multiplication?
Options
`2/3 xx ((-6)/7 xx 3/5) = (2/3 xx (-6)/7) xx 3/5`
`2/3 xx ((-6)/7 xx 3/5) = 2/3 xx (3/5 xx (-6)/7)`
`2/3 xx ((-6)/7 xx 3/5) = (3/5 xx 2/3) xx (-6)/7`
`(2/3 xx (-6)/7) xx 3/5 = ((-6)/7 xx 2/3) xx 3/5`
Solution
`bb(2/3 xx ((-6)/7 xx 3/5) = (2/3 xx (-6)/7) xx 3/5)`
Explanation:
For assocatve multiplication property - a × (b × c) = (a × b) × c
Let a = `2/3`, b = `(-6)/7`, c = `3/5`
`2/3 xx (-18)/35 = (-12)/21 xx 3/5`
`(-12)/35 = (-12)/35` Proved.
APPEARS IN
RELATED QUESTIONS
Tell what property allows you to compute `1/3 xx(6xx4/3)` as `(1/3 xx 6) xx 4/3`
Verify associativity of addition of rational numbers i.e., (x + y) + z = x + (y + z), when:
Verify associativity of addition of rational numbers i.e., (x + y) + z = x + (y + z), when:
Verify associativity of addition of rational numbers i.e., (x + y) + z = x + (y + z), when:
Give an example and verify the following statement.
Division is not associative for rational numbers
Verify the property x × (y × z) = (x × y) × z of rational numbers by using
`x = 1, y = (-1)/2` and `z = 1/4`
and What is the name of this property?
Verify the property x × (y × z) = (x × y) × z of rational numbers by using
`x = 2/3, y = (-3)/7` and `z = 1/2`
and What is the name of this property?
Tell which property allows you to compare
`2/3 xx [3/4 xx 5/7]` and `[2/3 xx 5/7] xx 3/4`
Name the property used in the following.
`1/3 + [4/9 + ((-4)/3)] = [1/3 + 4/9] + [(-4)/3]`
Verify the property x × (y × z) = (x × y) × z of rational numbers by using
`x = 0, y = 1/2` and `z = 1/4`
and What is the name of this property?
