To Solve Problems on Dividing Rational Numbers easily you need to be aware of the Properties of Division of Rational Numbers by which you can make your calculations simple. Practice using the Worksheet on Properties of Division of Rational Numbers and solve a variety of questions. The Questions covered here include different properties like Closure Property, Commutative Property, Associative Property, etc.
For more information regarding the Rational Numbers Properties, you can check out Rational Numbers Worksheets. Check out Solved Examples provided for a better understanding of the concept.
1. Verify whether the given statement is true or false
3/9 · 4/11 = 5/9 · 5/13
Solution:
(3/9)/(4/11) = 3/9*11/4
= 3*11/9*4
= 33/36
= 11/12
5/9 · 5/13 = (5/9)/(5/13)
= 5/9*13/5
= 5*13/9*5
= 65/45
= 13/9
Therefore, 3/9 · 4/11 is not equal to 5/9 · 5/13 and the statement is false.
2. Check whether the following statement is true or false -7 · 5/4 = 5/4 · (-7)
Solution:
-7 · 5/4 = -7/(5/4) = -7*4/5
= -28/5
5/4 · (-7) = (5/4)/(-7)
= (5/4)*(1/-7)
= 5*1/4*-7
= 5/-28
Therefore, -7 · 5/4 is not equal to 5/4 · (-7). Hence, the Statement is false. Commutative Property is not true for the division.
3. Check whether the following statement is true or false
{-8/5 · 2/3} · 4/5 = -8/5 · {2/3 · 4/5}
Solution:
{-8/5 · 2/3} · 4/5 = {(-8/5)/(2/3)}·4/5
= (-8/5*3/2)·4/5
= (-24/10)/(4/5)
= -24/10*5/4
= -120/40
= -3/1
-8/5 · {2/3 · 4/5} = -8/5·{(2/3)/(4/5)}
= -8/5·{(2/3)*(5/4)}
= -8/5·{10/12}
= -8/5/(10/12)
= -8/5*12/10
= -96/50
= -48/25
Therefore, {-8/5 · 2/3} · 4/5is not the same as -8/5 · {2/3 · 4/5}. Hence, the Statement is false.
Associative Property is not true for the division.
4. Simplify 2/5 · 1/4?
Solution:
= (2/5)/(1/4)
= 2/5*4/1
=2*4/5*1
= 8/5
Rational Numbers are closed under Division.
5. State whether the following statements are true or false.
1. Rational Numbers are always Closed Under Division.
2. Rational Numbers obeys the Commutative Property under Division.
3. Division of Rational Numbers obeys the Associative Property.
4. Can we divide 1 by 0
Solution:
1. True
2. False
3. False
4. No as it is undefined