maths > commercial-arithmetics

Introduction Direct 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 multiplier is not changing, the multiplicand and product are in direct variation.

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

illustrative examples

3$3$ bananas cost 6$6$ coins. The cost of 1$1$ banana is 2$2$ coins.

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

the number of bananas is increased to $4$. The overall cost is $8$ coins.

Increase in number of bananas results in increase in overall cost, when the price remains unchanged.

The number of bananas is decreased to $2$ bananas. The overall cost is $4$ coins.

Decrease in number of bananas results in decrease in overall cost, when the price remains unchanged.

The price increases to $3$ coins per banana. The number of the bananas remain unchanged. The overall cost is $9$ coins.

Increase in the price of bananas results in increase in the overall cost, when the number of bananas remains unchanged..

The price decreases to $1$ coin per banana. The number of the banana remains unchanged. The overall cost is 3 coins.

Decrease in the price of bananas results in decrease in the overall cost, when the number of bananas remains unchanged.

summary of 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 number remains unchanged, increase in the price results in increase in the overall cost. And Decrease in the price results in decrease in the overall cost.

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

These two are direct variations. Increase in the multiplicand (or multiplier) results in increase in the product. Similarly, decrease in the multiplicand (or multiplier) results in decrease in the product.

The word "variation" means: change; difference in amount.

The word "direct" means: straight, without any irregularity.

summary

Direct Variation : If increase in one quantity causes a proportional increase in another quantity, then these two quantities are related by direct variation.

Multiplicand $\times$ Multiplier = Product

Increase in the multiplicand (or multiplier) results in increase in the product. Similarly, decrease in the multiplicand (or multiplier) results in decrease in the product.

If you are reading for the first time, please skip this. This is explained in the next two pages.

If you are revising, it is noted that the direct and inverse variations come as a pair in the same equation.

Multiplicand $\times$ Multiplier $=$ Product

•   "Multiplicand" and "Product" are in direct variation, when "Multiplier" does not change.

•   "Multiplier" and "Product" are in direct variation, when "Multiplicand" does not change.

•   "Multiplicand" and "Multiplier" are in inverse variation, when the "Product" does not change.

Outline