NCERT Book Class 8 Mathematics (Part II) Chapter 3 Proportional Reasoning-2

PROPORTIONAL
3 REASONING–2

3.1 Proportionality — A Quick Recap
In an earlier chapter, we explored proportional relationships between
quantities and we used the ratio notation to represent such relationships.
When two or more related quantities change by the same factor, we call
that relationship a proportional relationship. For example, idli batter is
made by mixing rice and urad dal. The proportion of these two can have
regional variations. One of the proportions used is: for 2 cups of rice,
we add 1 cup of urad dal. We represent this relationship using the ratio
notation 2 : 1.

Viswanath made idlis by mixing 6 cups of rice with 3 cups of urad dal,
while Puneet made idlis by mixing 4 cups of rice with 2 cups of urad dal.
If cooked in the same way, would their idlis taste the same?
Viswanath’s mixture can be represented as 6 : 3 and Puneet’s mixture
as 4 : 2.
Recall that, to verify that these two ratios are proportional, we can
use the cross-multiplication method:
×

6:3 4:2

×
The two products are the same (12). So, the two ratios are proportional.
It is likely that the idlis would taste the same, if all the other ingredients
are proportional too!
In general, we can say that two ratios a : b and c : d are proportional if
a × d = b × c, or
a b.
c=d