LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

ALGEBRA - UNITARY METHOD (OTHER WAY OF UNDERSTANDING)

__UNITARY METHOD -__

**The unitary method is a technique used in mathematics, particularly in arithmetic, to solve problems involving ratios, proportions, and rates. It involves finding the value of a single unit and then scaling it up or down to find the value of the required number of units. Here's a step-by-step guide to using the unitary method:Example 1: Cost Calculation**

**Identify the Given Information: Start by noting what is given in the problem. This usually involves a ratio, rate, or proportion.****Find the Value of One Unit: Determine the value or quantity of a single unit. This often involves dividing the given quantity by the number of units it represents.****Calculate the Required Value: Use the value of one unit to find the value of the required number of units by multiplying.**

**Example 1: Cost Calculation**

**Problem: If 5 apples cost $10, how much would 8 apples cost?**

**Solution:**

**Find the cost of 1 apple: 10 / 5 = 2 dollars per apple.****Find the cost of 8 apples: 2 × 8 = 16 dollars.**

**Example 2: Distance Travelled**

**Problem: A car travels 60 miles in 2 hours. How far will it travel in 5 hours?**

**Solution:**

**Find the distance travelled in 1 hour: 60 / 2 = 30 miles per hour.****Find the distance travelled in 5 hours: 30 × 5 = 150 miles.**

**Example 3: Unit Price**

**Problem: A pack of 12 pens costs $24. What is the cost per pen?**

**Solution:**

**Find the cost of 1 pen: 24 / 12 = 2 dollars per pen.**

**A method in which the value of a unit quantity is first obtained to find the value of any required quantity is called unitary method.**

**For simplification, always write the things to be found on the right-hand side and things known on the left-hand side. In the above problem, we know the amount of the number of apples and the value of the apples is unknown. It should be noted that the concept of ****ratio** **and proportion**** is used for problems related to this method.**

**Example of Unitary Method -**

**Consider an example, a car runs 150 km on 15 litres of fuel, how many kilometre will it run on 10 litres of fuel?**

**In the above question, try and identify units (known) and values (unknown). Kilometre = Unknown (Right Hand Side)**

**No of litres of fuel = Known (Left Hand Side) Now we will try and solve this problem.**

**15 litres = 150 km**

**1 litre = 150 / 15 = 10 km**

**10 litres = 10 x 10 = 100 km**

**The car will run 100 kilometres on 10 litres of fuel.**

**Applications of Unitary Method -**

**The unitary method finds its practical application everywhere ranging from problems of speed, distance, time to problems related to calculating the cost of materials.**

**The unitary method is quite versatile and can be applied to various types of problems involving direct proportions. It simplifies the process of finding unknown quantities by focusing on the value of a single unit.**