DIVIDING FRACTIONS BY WHOLE NUMBERS

Example 1 :

Divide 2/5 by 6.

Solution :

2/5 ÷ 6 

In the above division, change the division as multiplication and take reciprocal of the whole number 6. 

2/5 ÷ 6 = 2/5 ⋅ 1/6

= (2 ⋅ 1)/(5 ⋅ 6)

= (1 ⋅ 1)/(5 ⋅ 3)

= 1/15

Example 2 :

Divide 7/5 by 3.

Solution :

7/5 ÷ 3

In the above division, change the division as multiplication and take reciprocal of the whole number 3. 

7/5 ÷ 3 = 7/5 ⋅ 1/3

= (7 ⋅ 1)/(5 ⋅ 3)

= 7/15

Example 3 :

Divide 5/12 by 20.

Solution :

5/12 ÷ 20

In the above division, change the division as multiplication and take reciprocal of the whole number 20. 

5/12 ÷ 20 = 5/12 ⋅ 1/20

= (5 ⋅ 1)/(12 ⋅ 20)

= (1 ⋅ 1)/(12 ⋅ 4)

= 1/48

Example 4 :

Divide 2/19 by 6.

Solution :

2/19 ÷ 6

In the above division, change the division as multiplication and take reciprocal of the whole number 6. 

= 2/19 ⋅ 1/6

= (2 ⋅ 1)/(19 ⋅ 6)

= (1 ⋅ 1)/(19 ⋅ 3)

= 1/57

Example 5 :

David eats 1/4 of a pizza and divides the remaining in to two equal parts for his two kids. What is the part of the pizza will each kid receive ?

Solution :

Part of the pizza eaten by David is 1/4.

Remaining pizza is 3/4.

Given : Remaining pizza is divided in to equal parts for his two kids.

Then, the part of the pizza received by each kid is

= 3/4 ÷ 2

= 3/4 ⋅ 1/2

= (3 ⋅ 1)/(4 ⋅ 2)

= 3/8

So, each kid will receive 3/8 part of the pizza.

Example 6 :

David  donated one-fourth of his property to charity and divided the rest equally for his three sons. Find the share of each son.

Solution :

Given : One-fourth of the property donated to charity.

Then, 3/4^th of the property is remaining and it divided equally for the three sons.

Share of each son :

= 3/4 ÷ 3

= 3/4 ⋅ 1/3

= (3 ⋅ 1)/(4 ⋅ 3)

= 3/12

= 1/4

So, each son will get one-fourth of the property as share.

Example 7 :

What is the value of this expression?

1/5 ÷ 30

A)    1/150      B)  1/6    C) 6     D) 150

Solution :

= 1/5 ÷ 30

= 1/5 ÷ 30/1

= 1/5 x 1/30

= 1/150

So, option A is correct.

Example 8 :

Find the average of 1/4 and 3/4

Solution :

Let a = 1/4 and b = 3/4

Average of two numbers a and b = (a + b)/2

= [(1/4) + (3/4)]/2

= [(1 + 3)/4]/2

= (4/4)/2

= 1/2

Example 9 :

Find the average of -1/2 and 2/3

Solution :

Let a = -1/2 and b = 2/3

Average of two numbers a and b = (a + b)/2

= [(-1/2) + (2/3)]/2

= [(-3 + 4)/6]/2

= (1/6)/2

= 1/12

Example 10 :

Find the average of 1/2, 2/3 and 3/4

Solution :

Let a = 1/2, b = 2/3 and c = 3/4

Average of two numbers a and b = (a + b + c)/3

= [(1/2) + (2/3) + (3/4)]/3

= [(6 + 8 + 9)/12]/3

= (23/12)/2

= 23/24

Example 11 :

200 kg of sugar must be poured into packets so there is 2/5 kg of sugar per packet. How many packets will be filled?

Solution :

Amount of sugar = 200 kg

Quantity of sugar in each packet = 2/5 kg

Number of packets to be filled = 200 / (2/5)

= 200 x (5/2)

= 100 x 5

= 500 packets.

Example 12 :

2400 kg of icecream is put into plastic containers which hold 3/4 kg each. How many plastic containers are needed?

Solution :

Quantity of ice cream = 2400 kg

Quantity of ice cream holds = 3/4 kg

Number of plastic continers = 2400/(3/4)

= 2400 x (4/3)

= 800 x 4

= 3200 containers.

Example 13 :

Jon says that his income is now 3  1/2 times what it was 20 years ago. If his current annual income is $63 000, what was his income 20 years ago?

Solution :

3   1/2 x income 20 years ago = 63000

income 20 years ago = 63000 / (3  1/2)

= 63000 / (7/2)

= 63000 x (2/7)

= 9000 x 2

= 18000

So, income 20 years ago is $18000.

Example 14 :

If 3/8 of a shipping container holds 2100 identical  cartons, how many cartons will fit into:

a) 5/8 of the container     b) the whole container ?

Solution :

3/8 of container holds 2100 cartons.

1 container will hold = 2100 / (3/8)

= 2100 x (8/3)

= 700 x 8

= 5600 cartons.

a) Capacity of 5/8 of container = 5/8 of 5600

= (5/8) x 5600

= 5 x 700

= 3500

b) The capacity of whole container is 5600 cartons

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