Students preparing the Division of Rational Numbers can find the Worksheet on Division of Rational Numbers quite useful. Practice using the Dividing Rational Numbers Worksheet and test your preparation knowledge. We tried providing various examples on the Rational Numbers Division. Check out the step by step solution provided for solved examples and get a better idea of the concept.
For the sake of your comfort, we even provided the Word Problems on Division of Rational Numbers with Answers. Make use of them during your preparation and try to have an idea of different questions. To know more about the chapter have a look at the Rational Numbers Worksheets.
1. Divide the Rationals
(i) 3 by 1/2
(ii) 3 by -5/7
(iii) -2/4 by 9/-8
(iv) -5/8 by -11/14
Solution:
(i) 3 by 1/2
Take the reciprocal of the second rational number and multiply it with the first rational number
= 3/(1/2)
= 3*2/1
= 6/1
(ii) 3 by -5/7
Take the reciprocal of the second rational number and multiply it with the first rational number
= 3/(-5/7)
= 3*7/-5
= 21/-5
(iii) -2/4 by 9/-8
= -2/4/(9/-8)
Take the reciprocal of the second rational number and multiply it with the first rational number
= -2/4*(-8)/9
= 16/36
= 4/9
(iv) -5/8 by -11/14
= (-5/8)/(-11/14)
Take the reciprocal of the second rational number and multiply it with the first rational number
= -5/8*14/-11
= -70/-88
= 35/44
2. Divide 7/5 by 3?
Solution:
= (7/5)/3
Take the reciprocal of the second rational number and multiply it with the first rational number
= 7/5*1/3
= 7/15
3. Divide -3 by 4/3?
Solution:
= -3/(4/3)
Take the reciprocal of the second rational number and multiply it with the first rational number
= (-3)*3/4
= -9/4
4. A Diver needs to descent to a depth of 120 feet below sea level. He wants to do it in 10 equal descents. How far he should travel in each descent?
Solution:
In order to tell how far he should travel in each descent, we need to divide 120 by 10
Firstly take the reciprocal of the divisor 10
10 reciprocal – 1/10
Multiply 120 by 1/10
= 120*1/10
= 12
Thus, he should travel 12 feet in each descent.
5. Mason made 3/4 of a pound of trail mix and if he puts 1/8 of a pound into each bag, how many bags can the mason fill?
Solution:
To find the number of bags we need to divide (3/4)/(1/8)
To divide simply find the reciprocal of the second rational number i.e. 8/1 and then multiply with first rational number
= 3/4*8/1
= 3*8/4*1
= 24/4
= 6
6. Jim bought 10 rolls of paper towel. He got 90 3/5 paper towels in all. How many rolls of paper towels were on each roll?
Solution:
To find the number of paper towels was on each roll we need to divide 90 3/5 by 10.
Firstly find the reciprocal of 10 i.e. 1/10
= (90 3/5)*1/10
=(453/5)*1/10
= (453*1)/(5*10)
= 453/50
= 9 3/50
Therefore, 9 3/50 rolls of paper towels were on each roll.
7. Simplify
(i) 4/5 · -7/12
(ii) -4 · (-4/15)
(iii) -12/5 · (-15)
(iv) (-1/8) · (-4/5)
Solution:
(i) 4/5 · -7/12
= (4/5)/(-7/12)
= (4/5)*(12/-7)
= 4*12/5*-7
= 48/-35
(ii) -4 · (-4/15)
= -4/(-4/15)
= -4*(15/-4)
= -60/-4
= 15/1
(iii) -12/5 · (-15)
= -12/5/(-15)
= -12/5*1/(-15)
= -12*1/5*(-15)
= -12/-75
= 12/75
(iv) (-1/8) · (-4/5)
= (-1/8)/(-4/5)
= 1/8*5/-4
= 1*5/(8*-4)
= 5/-32
= -5/32
8. Fill in the Blanks
(i) 8/4 · (_____) = -3/2
(ii) (_____) · (-7/5) = 10/19
Solution:
Let the number to be found be x
(i) 8/4 · (_____) = -3/2
(8/4)·x = 3/2
(8/4)/x/1 = 3/2
8/4*1/x = 3/2
8/4x= 3/2
12x= 16
x = 2
The number to be divided is 2.
(ii) (_____) · (-7/5) = 10/19
Consider the number to be found as x
x÷ (-7/5) = 10/19
x/(-7/5) = 10/19
x*(5/-7) = 10/19
x = (10/19)/(5/-7)
= 10/19*(-7/5)
= 10*-7/19*5
= -70/95
= -14/19