A method is used for solving a problem by first finding the value of a single unit and then finding the necessary value/ answer by multiplying the single unit value is called Unitary Method.

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**Unitary Method:**

The unitary method is a mathematical technique used to solve problems involving proportional relationships. It helps in finding the value of a single unit and then using it to find the value of a given number of units. This method is particularly useful when dealing with problems that involve ratios, proportions, or comparisons between different quantities.

**Examples:**

Here are a few examples to illustrate the concept of the unitary method:

1. **Example 1:**
- Suppose a car travels 240 kilometers in 4 hours. We can use the unitary method to find how far the car can travel in 10 hours.
- Step 1: Find the value of 1 hour. 240 km ÷ 4 hours = 60 km per hour.
- Step 2: Multiply the value of 1 hour by the given number of hours. 60 km/hour × 10 hours = 600 km.
- Therefore, the car can travel 600 kilometers in 10 hours.

2. **Example 2:**
- A recipe requires 3 cups of flour to make 24 cookies. We can use the unitary method to find how many cups of flour are needed to make 48 cookies.
- Step 1: Find the value of 1 cookie. 3 cups ÷ 24 cookies = 0.125 cups per cookie.
- Step 2: Multiply the value of 1 cookie by the desired number of cookies. 0.125 cups/cookie × 48 cookies = 6 cups.
- Therefore, 6 cups of flour are needed to make 48 cookies.

3. **Example 3:**
- A school has 720 students and wants to distribute 360 notebooks equally among them. We can use the unitary method to find how many notebooks each student will receive.
- Step 1: Find the value of 1 student. 360 notebooks ÷ 720 students = 0.5 notebooks per student.
- Therefore, each student will receive 0.5 notebooks.

**Proportion:**

Proportion is a mathematical concept that compares two ratios or fractions to determine if they are equal. In other words, it is a statement that shows that two ratios are equivalent. It is denoted using the symbol "=".

- Proportion can be used in various real-life scenarios, such as scaling maps, enlarging or reducing images, and solving problems involving ratios and percentages.
- The concept of proportion is closely related to the unitary method, as the unitary method often involves solving problems using proportions.
- Proportions can be solved by using cross-multiplication or by setting up equivalent fractions.
- If the cross-products of two ratios are equal, then the ratios are proportional.
- For example, if 2/3 = 4/6, we can cross-multiply to get 2 × 6 = 3 × 4, which shows that the two ratios are equal.
- Proportions are used in various mathematical concepts, such as solving equations, finding unknown values, and solving problems involving ratios and percentages.