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Practice each question, then open the answer or worked solution.
Write the additive inverse of each of the following:
(i) 2/8
The Additive inverse of 2/8 is – 2/8
(ii) -5/9
The additive inverse of -5/9 is 5/9
(iii) -6/-5 = 6/5
The additive inverse of 6/5 is -6/5
(iv) 2/-9 = -2/9
The additive inverse of -2/9 is 2/9
(v) 19/-16 = -19/16
The additive inverse of -19/16 is 19/16
Verify that: -(-x) = x for:
(i) x = 11/15
(ii) x = -13/17
(i) x = 11/15
We have, x = 11/15
The additive inverse of x is – x (as x + (-x) = 0).
Then, the additive inverse of 11/15 is – 11/15 (as 11/15 + (-11/15) = 0).
The same equality, 11/15 + (-11/15) = 0, shows that the additive inverse of -11/15 is 11/15.
Or, – (-11/15) = 11/15
i.e., -(-x) = x
(ii) -13/17
We have, x = -13/17
The additive inverse of x is – x (as x + (-x) = 0).
Then, the additive inverse of -13/17 is 13/17 (as 13/17 + (-13/17) = 0).
The same equality (-13/17 + 13/17) = 0, shows that the additive inverse of 13/17 is -13/17.
Or, – (13/17) = -13/17,
i.e., -(-x) = x
Find the multiplicative inverse of the following:
(i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × (-3/7) (v) -1 × (-2/5) (vi) -1
(i) -13
Multiplicative inverse of -13 is -1/13.
(ii) -13/19
Multiplicative inverse of -13/19 is -19/13.
(iii) 1/5
Multiplicative inverse of 1/5 is 5.
(iv) -5/8 × (-3/7) = 15/56
Multiplicative inverse of 15/56 is 56/15.
(v) -1 × (-2/5) = 2/5
Multiplicative inverse of 2/5 is 5/2.
(vi) -1
Multiplicative inverse of -1 is -1.
Name the property under multiplication used in each of the following:
(i) -4/5 × 1 = 1 × (-4/5) = -4/5
(ii) -13/17 × (-2/7) = -2/7 × (-13/17)
(iii) -19/29 × 29/-19 = 1
(i) -4/5 × 1 = 1 × (-4/5) = -4/5
Here 1 is the multiplicative identity.
(ii) -13/17 × (-2/7) = -2/7 × (-13/17)
The property of commutativity is used in the equation.
(iii) -19/29 × 29/-19 = 1
The multiplicative inverse is the property used in this equation.
Multiply 6/13 by the reciprocal of -7/16.
Reciprocal of -7/16 = 16/-7 = -16/7
According to the question,
6/13 × (Reciprocal of -7/16)
6/13 × (-16/7) = -96/91
Tell what property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3.
1/3 × (6 × 4/3) = (1/3 × 6) × 4/3
Here, the way in which factors are grouped in a multiplication problem supposedly does not change the product. Hence, the Associativity Property is used here.
Is 8/9 the multiplication inverse of –
? Why or why not?
–
= -9/8
According to the question,
8/9 × (-9/8) = -1 ≠ 1
Therefore, 8/9 is not the multiplicative inverse of –
.
If 0.3 is the multiplicative inverse of
? Why or why not?
= 10/3
0.3 = 3/10
According to the question,
3/10 × 10/3 = 1
Therefore, 0.3 is the multiplicative inverse of
.
Write:
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
(I) The rational number that does not have a reciprocal is 0.
Reason:
0 = 0/1
Reciprocal of 0 = 1/0, which is not defined.
(ii) The rational numbers that are equal to their reciprocals are 1 and -1.
Reason:
1 = 1/1
Reciprocal of 1 = 1/1 = 1, similarly, reciprocal of -1 = – 1
(iii) The rational number that is equal to its negative is 0.
Reason:
Negative of 0=-0=0
Fill in the blanks.
(i) Zero has _______reciprocal.
(ii) The numbers ______and _______are their own reciprocals
(iii) The reciprocal of – 5 is ________.
(iv) Reciprocal of 1/x, where x ≠ 0 is _________.
(v) The product of two rational numbers is always a ________.
(vi) The reciprocal of a positive rational number is _________.
(i) Zero has no reciprocal.
(ii) The numbers -1 and 1 are their own reciprocals
(iii) The reciprocal of – 5 is -1/5.
(iv) Reciprocal of 1/x, where x ≠ 0 is x.
(v) The product of two rational numbers is always a rational number.
(vi) The reciprocal of a positive rational number is positive.