__maths__>__Commercial Arithmetics__>__Unitary Method; Direct & Inverse Variations__### Introduction Inverse Variation

Multiplication is

`text(multiplicand ) xx text( multiplier )` `= text(product)`

It is explained that

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

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Consider

`3` bananas

of price `2` coin per banana

with overall cost is `6` coins.

A person carries `6` coins. The price of the banana is increased to `3` coins per banana. How many bananas can the person buy?

- `2` bananas
- `2` bananas
- `3` bananas

The answer is "`2` bananas". *Increase in the price results in the decrease in the number of bananas one can buy, when the overall cost remains unchanged. *

Consider

`3` bananas

of price `2` coin per banana

with overall cost `6` coins.

A person carries `6` coins. The price of the banana is decreased to `1` coin per banana. How many bananas can the person buy?

- `3` bananas
- `6` bananas
- `6` bananas

The answer is "`6` bananas". *Decrease in the price results in the increase in the number of bananas one can buy, when the overall cost remains unchanged. *

Consider

`3` bananas

of price `2` coin per banana

with overall cost `6` coins.

A person carries `6` coins. Because of a change in price, the person could buy `6` bananas. What was the revised price of a banana?

- `2` coin per banana
- `1` coin per banana
- `1` coin per banana

The answer is "`1` coin per banana". *Increase in the number of banana was the result of decrease in the price, when the overall cost remains unchanged. *

Consider

`3` bananas

of price `2` coin per banana

with overall cost is `6` coins.

A person carries `6` coins. Because of a change in price, the person could buy only `2` bananas. What was the revised price of a banana?

- `3` coin per banana
- `3` coin per banana
- `1` coin per banana

The answer is "`3` coin per banana". *Decrease in the number of banana was the result of increase in the price, when the overall cost remains unchanged. *

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 `xx` price = overall cost

Multiplicand `xx` Multiplier = Product

Consider

number `xx` price = overall cost

Multiplicand `xx` 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.

Which of the following is a meaning for the word "inverse"?

- opposite or reverse
- opposite or reverse
- within the limits

The answer is "opposite or reverse".

What is the term used to refer "increase in one causes a proportional decrease in another"?

- Pronunciation : Say the answer once

Spelling: Write the answer once

The answer is "inverse variation".

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

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