Rational Numbers

Question 1. Using appropriate properties find:

(i) -2/5 x 3/5 + 5/2 - 3/5 x 1/6
(ii) 2/5 x (-3/7) - 1/6 x 3/2 + 1/14 x 2/5

Solution.

Question 2. Write the additive inverse of each of the following:

Solution.

Question 3. Verify that - (-x) = x for :

(i) x=11/15 (ii)x=-13/17

Solution

Question 4. Find the multiplicative inverse of the following:

1. (i)-13
2. (ii) -13/19
3. (iii) 1/5
4. (iv) -5/8 x -3/7
5. (v) -1 x -2/5
6. (vi) -1

Solution.

Question 5. Name the property under multiplication used in each of the following:

1. (i)-4/5 x (1)=1 x -4/5= - 4/5
2. (ii) - 13/17 x -2/7 = -2/7 x -13/17
3. (iii) -19/29 x 29/-19 = 1

Solution.

1. (i) 1 is the multiplicative identity
2. (ii) Commutativity of multiplication
3. (iii) Multiplicative inverse.

Question 6. Multiply 6/13 by the reciprocal of -7/16

Solution.

Reciprocal of -7/16 is -1/67 Now, 6/13×-16/7=6×(-16)/13×7=-96/91

Question 7. Tell what property allows you to compute : 1/3×(6×4/3) as (1/3×6)×4/3

Solution. Associativity.

Question 8. Is the 89 multiplicative inverse of -1 1/8 ? Why or why not?

Solution.

-1 1/8=-9/8
Now, 8/9×-9/8=-1=1
So, No ; 8/9 is not the multiplicative inverse of -1 1/8(=-9/8) because the product of 8/9 and -13(-) and -1 1/8(=-9/8) is not 1.

Question 9. Is 0.3 the multiplicative inverse of 313 ? Why or why not?

Solution.

Yes ; 0.3 is the multiplicative inverse of 10/3 because
3/10×10/3=3×10/10×3=30/30=1

Question 10. Write :

1. (i) The rational number that does not have a reciprocal.
2. (ii) The rational numbers that are equal to their reciprocals.
3. (iii) The rational number that is equal to its negative.

Solution.

1. (i) The rational number "0" does not have a reciprocal.
2. (ii) The rational numbers 1 and (-1) are equal to their own reciprocals.
3. (iii) The rational number 0 is equal to its negative.

Question 11. Fill in the blanks :

1. (i) Zero has....reciprocal.
2. (ii) The numbers....and...are their own reciprocals.
3. (iii) The reciprocal of - 5 is......
4. (iv) Reciprocal of 1x, where x?0
5. (v) The product of two rational numbers is always a....
6. (vi) The reciprocal of a positive rational number is....

Solution.

1. (i) Zero has no reciprocal.
2. (ii) The numbers 1 and -1 are their own reciprocals.
3. (iii) The reciprocal of - 5 is ?15
4. (iv) Reciprocal of 1x, where x?0 is x.
5. (v) The product of two rational numbers is always a rational number.
6. (vi) The reciprocal of a positive rational number is positive.