Divide Unit Fractions By Non-Zero Whole Number

Key Concepts

• Whole numbers
• Unit fractions
• Dividing whole numbers by unit fractions
• Dividing unit fractions by whole numbers

Unit fractions

What is a unit fraction? 

Any fraction with numerator 1 is defined as a unit fraction. In these types of fractions, we consider only one part of the whole, which is equally divided into a finite number of parts. Unit denotes one. Therefore, they are known as unit fractions.  

Example:  

If Abbey eats 1 slice of a large pizza containing 8 slices. Then Abbey ate 1/8 of pizza. 

Whole numbers

What are whole numbers? 

Whole numbers are referred to as the set of natural numbers along with ‘0’. The set of whole numbers is denoted by W. 

Whole numbers, W = {0, 1, 2, 3…………} 

Dividing whole numbers by unit fractions

To divide a whole number by a fraction, follow the steps listed below: 

Step 1: Find the reciprocal of the given fraction. 

Step 2: Multiply the given whole number by the reciprocal of the fraction.  

Step 3: The resultant product will be the required answer. 

Example: Divide 4 by 1/3. 

Solution: Observe that 4 here is a whole number, where 1/3 is a unit fraction. 

Step 1: Find the reciprocal of the given fraction. 

Reciprocal of 1/3 is 3/1. 

Step 2: Multiply the given whole number 4 by the reciprocal of the fraction, i.e., 3/1.  

4×3/1

= 4×3 = 12. 

Dividing unit fractions by non-zero whole numbers  

To divide a unit fraction by a whole number, follow the steps listed below: 

Step 1: Find the reciprocal of the given whole number. 

Step 2: Multiply the given unit fraction by the reciprocal of the whole number. 

Step 3: The resultant product will be the required answer. 

Example: Divide 1/8 by 9. 

Solution: We are asked to find the value of 1/8 ÷ 9. Observe that 9 is a whole number, whereas 1/8 is a unit fraction. 

Step 1: Find the reciprocal of the given whole number. 

Reciprocal of 9 is 1/9 . 

Step 2: Multiply the given unit fraction 1/8

by the reciprocal of the whole number, i.e.,1/9 .  

1 / 8 ×1 / 9 = 1×1/ 8×9 = 1/72. 

Dividing whole numbers by unit fractions

Example 1: There are four shipments of gas cans to auto supply stores. If each store received 1/10 shipment, how many stores are there in all? 

Method – I 

Solution: We observe that 4 shipments must be divided equally and shared among supply stores, where each store gets 1/10 of a shipment, i.e., 4÷ 1/10. 

Step 1: Divide each of the 4 shipments into 1/10 equal parts. Each part of 1 shipment is 1/10. 

Step 2: Since, there are 10 tenths in each whole, there are 4×10 = 40 tenths in 4 wholes. 

So, we can conclude that 4 ÷1/10 = 40. This explains that 40 stores can be supplied by 4 shipments. 

Method – II 

Solution: We will use a number line to find how many 1/10 ’s are there in 4. 

Step 1: We can observe there are ten 1/10’s in between each whole number. 

Step 2: There are ten 1/10’s in 1 whole, twenty 1/10’s in 2 wholes, thirty 1/10’s in 3 whole and forty 1/10’s in 4 wholes.  

So, we conclude that 4 ÷ 1/10

= 40.  

Hence, 40 supply stores receive gas cans from 4 shipments. 

Example 2: Kiara is putting sugar into a container. The container can hold 5 cups of sugar. How many scoops of sugar she needs, if each scoop can fill 1/3 of a cup? 

Method – I 

Solution: We observe that 5 cups of sugar equals 1 container. We must divide 5 by 1/3cups to find how many 1/3cups are required to fill the container, i.e., 5÷ 1/3. 

Step 1: Divide each of the 5 cups into 3 equal parts. Each part of 1 cup is 1/3. 

Step 2: Since, there are five thirds in each whole, there are 5×3 = 15 thirds in 5 wholes. 

So, we can conclude that 5÷1/3= 15. This explains that fifteen scoops are required to fill one container of sugar. 

Method – II 

Solution: We will use a number line to find how many 1/3’s are there in 5. 

Step 1: We can observe there are three 1/3’s in between each whole number. 

Step 2: There are three 1/3’s in 1 whole, six 1/3’s in 2 wholes, nine 1/3’s in 3 whole and fifteen 1/3’s in 5 wholes.  

So, we conclude that 5÷1/ 3

= 15.  

Hence, fifteen scoops are required to fill the container. 

Dividing unit fractions by non-zero whole numbers

Example 1: Paul collected 1/2 a pound of strawberries. He must divide them equally among six wooden baskets. How many pounds of strawberries did Paul put in each wooden basket? 

Method – I (Area Model) 

Solution: We understand that 1/2 pound must be divided equally among the six wooden baskets, i.e., 1/2 ÷6. 

Step 1: Divide one pound into two equal parts. Each part of 1 pound is 1/2.

Step 2: Divide1/2 of a pound into six equal parts.  

Step 3: Each part of 1/2 of a pound is equal to 1/12 of a pound. 

Hence, each of the six baskets will have 1/12 of a pound. 

Method – II 

Solution: We are asked to divide 1/2 of a pound among six wooden baskets equally. Observe that 6 here is a whole number, where 1/2 is a unit fraction. 

Step 1: Find the reciprocal of the given whole number. 

Reciprocal of 6 is 1/6

Step 2: Multiply the given unit fraction 1/2 by the reciprocal of the whole number, i.e.,1/6 .  

1/2 ×1/6 = 1×1/2×6 = 1/12. 

Hence, each of the six wooden baskets will have 1/12 of a pound. 

Example 2: On the last day of the exam, the teacher had 1/5 of a bundle of blank papers left. She gave the papers to 10 of her students equally. How much of the bundle did every student take home? 

Method – I (Area Model) 

Solution: We understand that 1/5 of a bundle must be divided equally among the 10 students, i.e., 1/5÷10. 

Step 1: Divide one bundle into five equal parts. Each part of 1 bundle is 1/5. 

Step 2: Divide 1/5 of a bundle into ten equal parts.  

Step 3: Each part of 1/5 of a bundle is equal to 1/10. 

Hence, each of the 10 students will get 1/50 of a bundle. 

Method – II 

Solution: We are asked to divide 1/5 of a bundle among ten friends equally. Observe that 10 here is a whole number, where 1/5 is a fraction. 

Step 1: Find the reciprocal of the given whole number. 

Reciprocal of 10 is 1/10. 

Step 2: Multiply the given unit fraction 1/5 by the reciprocal of the whole number, i.e.,1/10 .  

15 ×1/10 = 1×1 / 5×10 =1/50. 

Hence, each of the ten friends will get 1/50 of a bundle. 

Exercise

1. Kate uses 2 packets of milk powder per day to feed her little bay. How many days will 1/3 of a packet will last?
2. A florist used 1/2  a basket of flowers to decorate 3 windows. How many baskets of flowers are used to decorate each window?
3. An oil factory uses 1/4 of a tin of peanuts to prepare 2 drums of peanut oil. How many tins of peanut are used to prepare each drum?
4. Jake prepares 1/3 pound of cake. He makes it into three equal pieces; what is the weight of each piece in pounds?
5. Wilson has a tray of cherries. His daughter ate 1/2 of the tray in three equal parts. How much of the tray did she eat each time?
6. A dog’s food bowl holds 4 cups of dog food. If each scoop can fill 1/4 of a cup. How many scoops are required to fill the bowl completely?
7. A vat of cement can hold 2 tons. If a bucket with 1/8 of ton capacity is used to empty the vat, find the number of buckets it takes to empty the vat.
8. Maddy has 4 storage box partitions. Each box has a partition that takes up 1/3 of the box. How many total partitions are there in the box?
9. Ruby is painting 4 walls of her room. If all the rooms take 1/2 a gallon of paint. How much paint was used for each room?
10. Cake batter is poured equally into 8 containers. If the total cake batter poured is 1/3 of gallon. How much batter is poured into each container

Concept Map

What have we learned

• Whole numbers
• Unit fractions
• Dividing whole numbers by unit fractions
• Dividing unit fractions by non-zero whole numbers