Learning objectives
● To recall the concept of ratio and proportion.
● To understand the concept of direct and inverse proportion.
● To be able to differentiate direct proportion and inverse proportion.
● To solve application problems using direct and inverse proportion.

__Chapter 4__

__Direct and Inverse Proportion____ __

** **

**Learning objectives**

● To recall the concept of ratio and proportion.

● To understand the concept of direct and inverse proportion.

● To be able to differentiate direct proportion and inverse proportion.

● To solve application problems using direct and inverse proportion.

** **

__Recap__

**Ratio
and Proportion**

In class VI we have learnt ratio and proportion.
Let us recall them now.

Ratio is the comparison of two quantities of the
same kind. If the quantity 'a' is compared with the quantity 'b',
the ratio can be written in the form a : b (read as a is to b)

When two ratios a : b and c : d are equal then we say that the ratios are in proportion.
This is denoted as a : b : : c : d and it is read as ‘a is
to b is
as c is
to d’.
In a :
b :
: c :
d, product
of the means is equal to product of the extremes, that is bc =
ad.

** **

**Try these**

**1. Find the ratio of the number of circles to number of squares.**

The number of circles: Number of squares

4:6

Divide by common 2

2:3

**2. Find the ratio (i) 555 g to 5 kg (ii) 21 km to 175 m**

**(i) 555 g to 5 kg **

555 : 5000

Divide by common 5

**111 : 1000**

**(ii) 21 km to 175 m **

21000 : 175

Divide by common 25

**840 : 7**

**3. Find the value of ‘x’ in the following proportions.**

**(i) 110 : x : : 8 : 88 (ii) x : 26 : : 5 : 65**

**(i) 110 : x : : 8 : 88**

*bc = ad*

* x* × 8 =110
× 88

* x* = [ 110 × 88 ] / 8 = 1210

*x = ***1210**

**(ii) x : 26 : : 5 : 65**

*x* × 65 = 26 × 5

*x* = [ 26 × 5 ] / 65 = 2

*x =* 2

** **

**Introduction**

We come across many situations in day-to- day life
where we see a change in one quantity brings a change in the other quantity. Let
us learn more about the concept of variation that helps us to handle situations
efficiently.

Now, let us consider such situations which we come
across in every day life.

We consider the task of cleaning a school,

(i) when more number of students are involved, the time taken
to clean will be less.

(ii) when the number
of students are more, the work done will also
be more.

In the first case, number of students is compared
with time taken and in the second case, the number of students is compared with
the amount of work. The quantities taken for comparison decides the type of variation.

**Situation 1** Manimala prepares vegetable soup for her family
of 4 members. She uses 2 cup of vegetables, 600 ml of water, 1 teaspoon of salt
and 1/2 teaspoon of pepper. Suddenly her aunt and uncle join them. What would be
the change in quantities of the ingredients to prepare soup for all the six members?

**Situation 2** In a military camp there are 200 soldiers. Grocery
for them are available for 40 days. If 50 more soldiers join them, how long will
these grocery last?

In the above situations a change in one quantity
results in the corresponding change in other quantity. That is in situation 1, more
the number of members, more will be the quantity of items. In situation 2, the more
number of soldiers in the group, the grocery needed will be more and so it will
last for less number of days.

In these situations when one quantity varies that
brings a change in other quantity in two ways, that is,

(i) both the quantities increase or decrease.

(ii) increase in one quantity causes decrease in
the other quantity or vice-versa.

If such quantities varies in constant ratio, they
are said to be in proportion. Two different variations give rise to two types of
proportion which will be discussed now.

MATHEMATICS ALIVE-DIRECT AND
INVERSE PROPORTION IN REAL LIFE

Tags : Term 1 Chapter 4 | 7th Maths , 7th Maths : Term 1 Unit 4 : Direct and Inverse Proportion

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