Introduction Inverse Variation

overview

Multiplication is

multiplicand × multiplier multiplicand × multiplier =product=product

It is explained that

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

illustrative examples

Consider

33 bananas

of price 22 coin per banana

with overall cost is 66 coins.

A person carries 66 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 66=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 × price = overall cost

Multiplicand × 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 × 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

The outline of material to learn "commercial arithmetics" is as follows.

Note: * Click here for the detailed ouline of commercial arthmetics.*

• **Ratio, Proportion, Percentage**

→ __Comparing Quantities__

→ __Introduction to Ratio__

→ __Ration & Fraction Differences__

→ Proportions__P__

→ __Percentages__

→ __Conversion to percentage__

• **Unitary Method**

→ __Introduction to Unitary Method__

→ __Direct Variation__

→ __Inverse Variation__

→ __DIV Pair__

• **Simple & Compound Interest**

→ __Story of Interest__

→ __Simple Interest__

→ __Compound Interest__

• **Rate•Span=Aggregate**

→ __Understanding Rate-Span__

→ __Speed • Time=Distance__

→ __Work-rate • time = Work-amount__

→ __Fill-rate • time = Filled-amount__

• **Profit-Loss-Discount-Tax**

→ __Profit-Loss__

→ __Discount__

→ __Tax__

→ __Formulas__