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

Multiplication is

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

It is common to have multiplier as number of items. eg: Price of `10` pens is `200` coins.

When the multiplier is number of items, the multiplicand and product can be found for `1` item. This helps in simplifying solution to finding product for any number of items.

eg: Price of `1` pen is `20` coins. And with that it is easy to find price of `5` pens.

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A person took `2` bananas and `3` apples. How many fruits did she take?

- `2 xx 3 = 6` fruits
- `2 + 3 = 5` fruits
- `2 + 3 = 5` fruits

The answer is "`5` fruits". This is an example of finding sum of two given addends.

A person took `2` bananas and some apples. He had `5` fruits in total. How many apples did he take?

- `2+5 = 7` apples
- `5-2 = 3` apples
- `5-2 = 3` apples

The answer is "`3` apples". This is an example of finding difference from the given sum and one of the addends.

Addition in general terms is *addend + addend = sum *

For a given problem involving addition:

• if two addends are given, then sum is calculated by addition.

• if an addend and the sum are given, then the other addend is calculated by subtraction.

(Note: Subtraction is considered as inverse of addition. So, instead of referring as minuend and subtrahend, the numbers are referred as sum and addend.)

We understood the basics of problems involving addition, let us look at problems involving multiplication.

Banana is priced at `2` coins each. How much do `3` bananas cost?

- `2+3 = 5` coins
- `2xx3 =6` coins
- `2xx3 =6` coins

The answer is "`6` coins". This is an example of finding product of given multiplicand and multiplier.

A person buys `3` bananas for `6` coins. What is the price of a banana?

- `6xx3 = 18` coins
- `6//3 = 2` coins
- `6//3 = 2` coins

The answer is "`2` coins". This is an example of finding multiplier from given product and multiplicand.

Multiplication in general terms is *Multiplier `xx` multiplicand = product*

For a given problem involving multiplication,

• If multiplicand and multiplier are given, then product is calculated by multiplication.

• If the multiplicand and the product are given, then the multiplier is calculated by division.

(Note: Division is considered as inverse of multiplication. So, instead of referring as dividend, and divisor, the numbers are referred as product and multiplicand.)

`1` banana costs `2` coins. How much do `10` bananas cost?

- `2` coins
- `20` coins
- `20` coins

The answer is "`20` coins".

`3` bananas cost `6` coins. How much do `10` bananas cost?

- `2` coins
- `20` coins
- `20` coins

The answer is "`20` coins".

Consider the two given problems:

Problem A: `1` banana costs `2` coins. How much do `10` bananas cost?

Problem B: `3` bananas cost `6` coins. How much do `10` bananas cost?

It is easier to solve Problem A : as the cost is given for `1` item. But at times, the information available will result in a problem like the given Problem B, in which the cost of many items is given.

In solving the problems of type similar to given Problem B, it is simplified to Problem A first.

`3` bananas cost `6` coins. How much does `10` bananas cost?

Cost of `3` bananas `= 6` coins

Cost of `1` banana `= 6-:3 = 2` coins

Cost of `10` bananas `=2 xx 10 = 20` coins.

In the process of solving the problem, the value of `1` unit is found. That is, in this particular problem, value of `1` banana is `2` coins. For this reason, the method is named as *unitary method*.

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

- relating to one unit
- relating to one unit
- without a schedule

The answer is "relating to one unit".

What is the term used to refer "finding value for one unit"?

- Pronunciation : Say the answer once

Spelling: Write the answer once

The answer is "unitary method".

**Unitary Method** : Method of finding value of a single unit so that value of any number of units can be easily calculated.

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