maths > commercial-arithmetics

Introduction Inverse Variation

what you'll learn...

overview

Multiplication is
multiplicand × multiplier $\textrm{\mu < i p l i c \mathmr{and}} \times \textrm{\mu < i p l i e r}$ =product$= \textrm{\prod u c t}$

It is explained that

•  When product is not changing, the multiplicand and the multiplier are in inverse variation.

illustrative examples

Consider
3$3$ bananas
of price 2$2$ coin per banana
with overall cost is 6$6$ coins.

A person carries 6$6$ coins. The price of the banana is increased to $3$ coins per banana. The person can buy only $2$ bananas with the $6$ coins.

Increase in the price results in the decrease in the number of bananas one can buy, when the overall cost remains unchanged.

The price of the banana is decreased to $1$ coin per banana. The person can buy $6$ bananas.

Decrease in the price results in the increase in the number of bananas one can buy, when the overall cost remains unchanged.

Because of a change in price, the person could buy $6$ bananas. The revised price of a banana is $\frac{6}{6} = 1$ coin.

Increase in the number of banana was the result of decrease in the price, when the overall cost remains unchanged.

Because of a change in price, the person could buy only $2$ bananas. The revised price of a banana is $3$ coins.

Decrease in the number of banana was the result of increase in the price, when the overall cost remains unchanged.

summarizing the above

The underlying mathematical operation for the problem is product of two quantities.

•  Multiplicand: number of bananas

•  Multiplier: price of a banana

•  Product : Overall cost

number $\times$ price = overall cost

Multiplicand $\times$ Multiplier = Product

•  when overall cost remains unchanged, increase in the price results in decrease in the number.

•  when overall cost remains unchanged, increase in the number results in decrease in the price.

These two are inverse variations. Increase in the multiplier results in decrease in the multiplicand.. Similarly, Decrease in the multiplier results in increase in the multiplicand.

The word "inverse" means: opposite or reverse.

summary

Inverse Variation : If increase in one quantity causes a proportional decrease in another quantity, then these quantities are related by inverse variation.

Multiplicand $\times$ Multiplier = Product

When the product is constant.

•   Increase in the multiplier results in decrease in the multiplicand.

•   Decrease in the multiplier results in increase in the multiplicand.

Outline