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Verify the property x × y = y × x by taking:
Verify the property: x × (y × z) = (x × y) × z
We have to verify that, x × (y × z) = (x × y) × z
Verify the property: x × (y × z) = x × y + x × z:
We have to verify that, x × (y × z) = x × y + x × z
Use the distributivity of multiplication of rational numbers over their addition to simplify:
Find the multiplicative inverse (reciprocal) of each of the following rational numbers:
Name the property of multiplication of rational numbers illustrated by the following statements:
(i) Commutative property
(ii) Commutative Property
(iii) Distributivity of multiplication over addition
(iv) Associativity of multiplication.
(v) The existence of identity for multiplication.
(vi) Existence of multiplicative inverse
(vii) Multiplication by 0
(viii) Distributive property
Fill in the blanks:
(i) The product of two positive rational numbers is always ……………….
(ii) The product of a positive rational number and a negative rational number is always ……………
(iii) The product of two negative rational numbers is always …………………
(iv) The reciprocal of a positive rational number is ……………….
(v) The reciprocal of a negative rational number is ……………….
(vi) Zero has ………… reciprocal.
(vii) The product of a rational number and its reciprocal is ……………….
(viii) The numbers ………. and ……….. are their own reciprocals.
(ix) If a is reciprocal of b, then the reciprocal of b is …………………
(x) The number 0 is …………. The reciprocal of any number.
(xi) Reciprocal of 1a, a ≠ 0 is …………………
(xii) (17 × 12)-1 = (17)-1 ×………
(i) Positive
(ii) Negative
(iii) Positive
(iv) Positive
(v) Negative
(vi) No
(vii) 1
(viii) -1 and 1
(ix) a
(x) not
(xi) a
(xii) 12−1
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