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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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mathsCommercial ArithmeticsUnitary 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.

click on the content to continue..

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.

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