INTERPRETING FRACTIONS AS DIVISION

Problem 1 :

James shares 5/8 of cake between 6 people, what fraction of cake do they each receive ?

Solution :

Quantity of cake James has = 5/8 of cake

Number of people to be shared = 6

Part of cake each should get = 5/8 ÷ 6

Here 6 is a whole number, by imagining 6 as 6/1 it can be converted to fraction. 

= 5/8 ÷ 6/1

= (5/8) ⋅ (1/6)

= 5/48

So, each person will receive 5/48 part of cake.

Problem 2 :

John has 12 cans of dog food. He has two dogs and he gives each dog 2/3 of a can dog food each day. Does he have enough dog food to last one week ?

Solution :

Number of cans of dog food = 12

Each dog will have = 2/3 of cans food each day

Number of dogs = 2

Quantity of food for one week = 7(2) (2/3)

= 28/3

= 9.3 cans

Since 12 > 9.3, John has enough dog food.

Problem 3 :

Alisha has 7/8 liters of lemonade. She is pouring glasses that each contain 1/5 litters. How many full glasses can she pour?

Solution :

Quantity of lemonade = 7/8 liters

Capacity of each glass = 1/5 liters

Number of glasses = 7/8 ÷ (1/5)

= 7/8 ⋅ (5/1)

= 35/8

= 4.375

So, she can pour four glasses.

Problem 4 :

Helen is cutting lengths of string from a roll that is 9  1/3 meters long. Each length of string is 1/9 meters long. How many lengths of string can Helen cut from the roll?

Solution :

Length of string = 9  1/3 m

Length of each string = 1/9 m

Number of strings to be cut = 9  1/3 ÷ (1/9)

= 28/3 ÷ (1/9)

= 28/3 ⋅ (9/1)

= 28 ⋅ 3

= 84

Number of strings is 84.

Problem 5 :

Shown is a rectangle. Find the value of x.

Solution :

Area of rectangle = 20 cm²

Length of the rectangle = x cm

Width = 2  1/6 cm

= 13/6 cm

Length ⋅ width = 20

x ⋅ (13/6) = 20

x = 20 ÷ (13/6) 

x = 20 ⋅ (6/13)

x = 120/13

Converting into mixed fraction, we get

x = 9   3/13

So, the required length of the rectangle is 9  3/13 cm.

Problem 6 :

Daniel uses 3/4 of a roll of wrapping paper to wrap five equal sized presents. What fraction of the roll wrapping paper does each present use ?

Solution :

Amount of roll of wrapping paper spent = 3/4

Number of presents covered = 5

Amount of paper spent for each present = 3/4 ÷ 5

= 3/4 ⋅ (1/5)

= 3/20

So, each present uses 3/20 of roll wrapping paper for each present.

Problem 7 :

Meera uses 4/5 of a bag of chocolate chips to make eight muffins. What fraction of the bag of chocolate chips does each muffin contain ?

Solution :

Amount of chocolate chips she uses = 4/5

Number of muffing made = 8

Quantity of chocolate chips = 4/5 ÷ 8

= 4/5 ⋅ (1/8)

= 1/10

Each muffin contains 1/10 of muffin.

Problem 8 :

Little snail is going to visit his grandma, who lives 6 miles away. HE can crawl 1/2 mile a day. How many will it take him to get to his grandma's house ?

Solution :

Distance to be covered to reach grandma's house = 6 miles

Distance covered by little snail = 1/2 miles a day

Number of days required = 6 ÷ (1/2)

= 6 ⋅ (2/1)

= 12

So, the little snail needs 12 days.

Problem 9 :

Our aquarium holds 5 liters of water. IF we use a scoop that holds 1/6 of a liter of water, how many scoops will be needed to fill the aquarium ?

Solution :

Capacity of aquarium = 5 liters

Capacity of one scoop = 1/6 liters

Number of scoops needed = 5 ÷ (1/6)

= 5 ⋅ (6/1)

= 30

So, the number of scoops needed is 30.

Problem 10 :

There is 1/4 of a pan of brownies left. Jake and his three brothers are going to share equally. What fraction of the pan of brownies will each of 4 boys get ?

Solution :

Amount of brownies left = 1/4

Number of persons = 1 + 3 ==> 4

Fraction of pan of brownies = 1/4 ÷ (4/1)

= 1/4 ⋅ (1/4)

= 1/16

So, each boy will get 1/16 pan of brownies.

Problem 11 :

In an aquarium 3/8 of the fish are clown fish. The clown fish are shared equally between six fish tanks. What fraction of the fish in each tank are clown fish ?

Solution :

Amount of clown fish = 3/8 of fish

Amount of fishes to be shared for 6 tanks

Amount of clown fish in each tank = 3/8  ÷ (6/1)

= 3/8 ⋅ (1/6)

= 1/8 ⋅ (1/2)

= 1/16

Problem 12 :

Aziz uses 4/9 of a tub of ice cream to make six ice cream sundaes. what fraction of the tub of ice cream does each sundae contain ?

Solution :

Quantity of ice cream = 4/9

Number of ice cream sundaes made = 6

Quantity of ice cream used for each sundae = 4/9 ÷ (4/1)

= 4/9 ⋅ (1/4)

= 1/9

So, quantity of ice cream in each sundae is 1/9.