A camp was organized in a school in which 12 students participated. The camp leader wanted to divide them into groups of 2 students. How many groups were there?

**Division
of Fractions**

** **

**Think about the situation 1**

A camp was organized in a school in which 12 students
participated. The camp leader wanted to divide them into groups of 2 students. How
many groups were there?

There were 6 groups which was got by the division
of 12 by 2.

That is 12 ÷ 2 = 6 which means there are six 2’s
in 12.

If the camp leader distributes 6 litres of water
in ½ litre water bottles to the students, then how many students will get water
bottles? This means finding how many 1/2 litres are there in 6 litres. For this
we need to calculate 6 ÷ 1/2 .

**Solution**

Let us describe
the situation

This means that if you share 6 litres of water into
1 litre bottles, 6 persons can get water. If you share in 1/2 litre water bottles,
12 persons can get water. If you share it in 1/4^{ }litre water bottles,
24 persons can get water. That is

We can illustrate this in the following diagram.
We divide each circle into halves such that each part is 1/2 of the whole. The number
of such halves would be 6 ÷ 1/2. In the figure how many halves do you see? There
are 12 halves. So 6 ÷ ½ = 6 × 2 = 12 . ^{}

As one circle has 2 halves, 6 circles will have
12 halves = 6 × 2. Therefore, 6 ÷ 1/2 = 6 × 2 = 12

Here, we can observe that, dividing a whole number
6 by a fraction 1/2 is the same as multiplying a whole number 6 by 2, where 2 is
the ** reciprocal** of 1/2 . Generally,
dividing a number by a fraction is the same as multiplying that number by the reciprocal
of the fraction.

Let us discuss the same situation in another way.
Let us take a bar of length 12 *cm* How many 2 *cm* bars are there in a
12 *cm* bar?

Now find how many 1/2^{ }*cm *bars are there in a 12 *cm* bar?

Let us observe and complete the following:

i) 3/7 × 7/3 = 21/21 = 1

ii) 1/9 × 9 = 9/9 = 1

iii) 8 × 1/8 = 8/8 = ?

iv) 13/4 × ? = 1

v) 4/3 × ? = 1

From the above, we can see that ** the Product of a fraction and its reciprocal is always 1**.

** **

__Example 19 __

Kandan shares 1/ 2 piece of a cake between 2 persons.
What will be the share 2 of each?

**Solution**

To know the
share, we need to find 1/2 ÷ 2

1/2 ÷ 2 = 1/2 × 1/2 (reciprocal of 2 is 1/2)

= 1/2 ÷ 2 = 1/2 × 1/2 (reciprocal of 2 is 1/2)

= 1/2 × 1/2 = [1 × 1] / [2 × 2] = 1 / 4

** **

**Try these**

**i) How many 6s are there in 18?**

Three 6 s are in 18.

**ii) How many ¼ s are there in 5?**

Twenty 1/4 s are there in
5.

**iii) 1/3 ÷ 5=?**

1/3 ÷ 5 = 1/3 × 1/5 = 1/15

** **

__Example 20__

Divide 4 1/2 by 3 1/2

**Solution**

** **

__Example 21__

An oil tin contains 7 1/2 litres of oil which
is poured in 2 1/2 litres bottles. How many bottles are required to fill 7 1/2 litres oil?

**Solution **

The number of bottles required = 15/2 ÷ 5/2 = 15/2
× 2/5 (reciprocal of 5/2 is 2/5)

= 3 bottles

** **

__Example 22__

A rod of
length 6m is cut into small rods of length 1 ½ * m *each. How many small rods can be cut?

**Solution**

The number of small rods = 6 ÷ 1 (1/2)

= 6 ÷
3/2

= 6 × 2/3
(reciprocal of 3/2 is 2/3 )

= 4 rods

** **

**Try these**

**i) Find the value of 5 ÷ 2(1/2).**

= 5 ÷ 2 1/2 = 5 ÷ 5/2.

= 5 × 2/5 = 2

**ii) Simplify: 1(1/2) ÷ 1/2**

3/2 ÷ 1/2

3/2 × 2/1 = 3

**iii) Divide 8 ½ by 4 ¼.**

8 1/2 ÷ 4 1/4

17/2 ÷ 17/4

17/2 ÷ 4/17 = 2

__ICT CORNER__

**Fractions**

Expected Outcome

**Step 1**

Open the Browser by typing the URL Link
given below (or) Scan the QR Code. GeoGebra work sheet named “Fraction Basic” will
open. Click on New Problem and solve the problem.

**Step 2**

Click the check boxes on right hand side
bottom to check respective answers

**Browse
in the link:**

Fraction Basic: https://ggbm.at/jafpsnjb or Scan
the QR Code.

**This puzzle involves fraction in Tamil song and its explanation**

கட்டியால் எட்டு
கட்டி

கால்அரை முக்கால் மாற்று

வியாபாரி சென்று
விட்டார்

சிறுபிள்ளை மூன்று
பேர்கள்

கட்டியும் புக் கொணாது

கணக்கிலும் பிச கொணாது

கட்டியாய் பகர வல்லார்

கணககினில் வல்லா ராவார்

Explanation

A jaggery merchant had 8 jaggery balls
with different weights such as 1/4 *kg* 1 /2 *kg* and
3/4 *kg*. He called his 3 children and asked
them to share those jaggery balls equally. How did the children share it equally
among themselves? (Hint: The number of jaggery balls with the given weights are
5, 2 and 1 respectively.).

Tags : Fractions | Term 3 Chapter 1 | 6th Maths , 6th Maths : Term 3 Unit 1 : Fractions

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

6th Maths : Term 3 Unit 1 : Fractions : Division of Fractions | Fractions | Term 3 Chapter 1 | 6th Maths

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