CHAPTER 1: RATIONAL NUMBERS
Rational number: A number ‘r’ is called a rational number, if it can be written in the form ofwhere p and q are integers and q≠0.
EXERCISE 1.1
1. Using appropriate properties find.
(i)
Solution:
[Using commutative property]
[Using distributive property]
(ii)
Solution:
[Using commutative property]
[Using distributive property]
2. Write the additive inverse of each of the following.
(i) (ii) (iii)
(iv) (v)
Answer:
(i) Additive inverse of is
(ii) Additive inverse of is
(iii) Additive inverse of is
(iv) Additive inverse of is
(v) Additive inverse of is
3. Verify that – (– x) = x for.
(i) x =
Solution:
We have, x =⇒ – x =
⸪= 0 and
= 0
⸫The additive inverse of is
⇒=
⇒ – (– x) = x.
(ii) x =
Solution:
We have, x =⇒ – x =
⸪= 0 and
= 0
⸫The additive inverse of is
⇒
⇒ – (– x) = x.
4. Find the multiplicative inverse of the following.
(i) – 13 (ii) (iii) (iv) (v) (vi) – 1
Answer:
(i) Multiplicative inverse of –13 is
(ii) Multiplicative inverse of is
(iii) Multiplicative inverse of is 5
(iv) Multiplicative inverse ofis
(v) Multiplicative inverse ofis
(vi) Multiplicative inverse of –1 is –1
5. Name the property under multiplication used in each of the following.
(i)
Answer: 1 is the multiplicative identity.
(ii)
Answer: Commutative property.
(iii)
Answer: Multiplicative Inverse property.
6. Multiply by the reciprocal of .
Solution:
The reciprocal ofis.
Now,
7. Tell what property allows you to compute as
Solution:
By using associative property of multiplication, a× (b×c) = (a×b) ×c
8. Is the multiplicative inverse of ? Why or why not?
Solution:
⸫is not the multiplicative inverse of .
9. Is 0.3 the multiplicative inverse of? Why or why not?
Solution:
⸫0.3 is the multiplicative inverse of .
10. Write.
(i) The rational number that does not have a reciprocal.
Answer: 0
(ii) The rational numbers those are equal to their reciprocals.
Answer: 1 and –1
(iii) The rational number that is equal to its negative.
Answer: 0
11. 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, where x ≠ 0 is ________.
(v) The product of two rational numbers is always a _______.
(vi) The reciprocal of a positive rational number is ________.
Answer:
(i) No (ii) 1, –1
(iii) (iv) x
(v) Rational Number (vi) Positive
EXERCISE 1.2
1. Represent these numbers on the number line.
(i)
Solution:
Here, P is
(ii)
Solution:
Here, M is
2. Represent , , on the number line.
Solution:
Here, B = , C = and D =
3. Write five rational numbers which are smaller than 2.
Answer: 1,, 0.
4. Find ten rational numbers betweenand.
Solution:
Now,
–8< –7<–6<–5<–4< –3<–2<–1<0<1<2<10
The required numbers are
5. Find five rational numbers between.
(i) and
Solution:
Now,
60<61<62<63<64<65<72
The required numbers are
(ii) and
Solution:
Now,
–9<–8<–7<–6<–5<–4<10
The required numbers are
and
(iii) and
6. Write five rational numbers greater than –2.
Answer:
Five rational numbers greater than –2 = –1, 0,, 1,
7. Find ten rational numbers between and .
Solution:
Now,
48<49<50<51<52<53<54<55<56<57<58<60
The required numbers are
No comments:
Post a Comment