maths > commercial-arithmetics

Unitary Method : Introduction

what you'll learn...

overview

Multiplication is
multiplicand × multiplier $\textrm{\mu < i p l i c \mathmr{and}} \times \textrm{\mu < i p l i e r}$ =product$= \textrm{\prod u c t}$

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

When the multiplier is number of items, the multiplicand and product can be found for 1$1$ item. This helps in simplifying solution to finding product for any number of items.
eg: Price of 1$1$ pen is $20$ coins. And with that it is easy to find price of $5$ pens.

A person took $2$ bananas and $3$ apples.

The total number of fruits is $2 + 3 = 5$ 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. From this, we can calculate that he took, $5 - 2 = 3$ 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.

examining multiplication

Banana is priced at $2$ coins each. $3$ bananas cost

$2 \times 3 = 6$ coins.

This is an example of finding product of given multiplicand and multiplier.

A person buys $3$ bananas for $6$ coins. The price of a banana is

$6 / 3 = 2$ coins

This is an example of finding multiplier from given product and multiplicand.

Multiplication in general terms is
Multiplier $\times$ 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.)

simplify

Problem A : Given that, $1$ banana costs $2$ coins. It is easy to calculate that $10$ bananas cost 20 coins.

Problem B :Given that, $3$ banana costs $6$ coins. It can also be calculated that, $10$ bananas cost 20 coins.

Consider the two given problems. 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.

unitary method

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

Cost of $3$ bananas $= 6$ coins

Cost of $1$ banana $= 6 \div 3 = 2$ coins

Cost of $10$ bananas $= 2 \times 10 = 20$ 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.

The word "unitary" means: relating to one unit.

summary

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

Outline