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

Multiplication is

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

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.

*click on the content to continue..*

`3` bananas cost `6` coins. What is the cost of `1` banana?

- `2` coins
- `2` coins
- `3` coins

The answer is "`2` coins"

Consider

`3` bananas

of price `2` coin per banana

with overall cost `6` coins.

the number of bananas is increased to `4`. What is the overall cost?

- `6` coins
- `8` coins
- `8` coins

The answer is "`8` coins". *Increase in number of bananas results in increase in overall cost, when the price remains unchanged.*

Consider

`3` bananas

of price `2` coin per banana

with overall cost `6` coins.

The number of bananas is decreased to `2` bananas. What is the overall cost?

- `4` coins
- `4` coins
- `8` coins

The answer is "`4` coins". *Decrease in number of bananas results in decrease in overall cost, when the price remains unchanged.*

Consider

`3` bananas

of price `2` coin per banana

with overall cost `6` coins.

The price increases to `3` coins per banana. The number of the bananas remain unchanged. What is the overall cost?

- `6` coins
- `9` coins
- `9` coins

The answer is "`9` coins". *Increase in the price of bananas results in increase in the overall cost, when the number of bananas remains unchanged.*

Consider

`3` bananas

of price `2` coin per banana

with overall cost `6` coins.

The price decreases to `1` coin per banana. The number of the banana remains unchanged. What is the overall cost?

- `3` coins
- `9` coins
- `9` coins

The answer is "`3` coins". *Decrease in the price of bananas results in decrease in the overall cost, when the number of bananas 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 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.

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

- change; difference in amount
- change; difference in amount
- couple; set of two things

The answer is "change; difference in amount".

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

- two parts; branching into two
- straight, without any irregularity
- straight, without any irregularity

The answer is "straight, without any irregularity".

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

- Pronunciation : Say the answer once

Spelling: Write the answer once

The answer is "direct variation".

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

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 `xx` 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.

*slide-show version coming soon*