Ratio

A ratio defines the comparison between two quantities or numbers by dividing them. It simply indicates how many times one value contains the other value. In math, there are mainly three approaches that can be used to write a ratio.

They are:

• As a fraction, by using the symbol (/). For example, 10/5
   
• The second method is with a colon (:), for instance, 1:5
   
• The third approach is to express it in words, for example, 10 to 5

A ratio compares the value of two quantities by dividing them. In this case, the divisor is referred to as the 'consequent' and the dividend as the 'antecedent.' To express the value of the ratio, the general formula is, a:b, which is read as ‘a’ to ‘b’.
 

Calculating a ratio is a simple mathematical operation. Several steps should be adhered to when calculating the ratio.

They are listed below:

Step 1: Identify the given quantities. For example, in a classroom, there are 20 chairs and 10 tables. Here, the given quantities are 20 and 10.

Step 2: Write the quantities in the correct ratio order. For instance, the correct order is 20:10.

Step 3: Try to simplify the ratio. Find the greatest common factor (GCF) of both numbers and then divide them by the GCF. Here, the GCF of 20 and 10 is 10.

To find the GCF, we have to list the factors of both the given numbers.

• The factors of 10 include 1, 2, 5, and 10.

• The factors of 20 include 1, 2, 4, 5, 10, and 20.

Now, we can identify the common factors of both the numbers:

1, 2, 5, and 10 are the common factors. Among these, the greatest common factor is 10.

Hence, the GCF of 20 and 10 is 10.

Next, we can divide the numbers by the GCF.

• 20 ÷ 10 = 2

• 10 ÷ 10 = 1

Therefore, the simplified ratio is 2:1.

Ratios are classified into different types according to their function and purpose. They are used to comparing two or more values.

The main types of ratios are as follows:

Simple Ratio:

A simple ratio shows the comparison between two numbers. In this type of ratio, the values are expressed in their simplest form. It explains how many times one value contains another value. A simple ratio can be denoted as fractions (/) or with a colon (:)

Take a close look at this example,

Suppose, in a garden, there are 10 roses and 15 sunflowers. The ratio of roses and sunflowers are at 10:15.

To get the simplified ratio, we have to find the GCF of the given numbers.

For that, we need to list the factors of 10 and 15.

• The factors of 10 are 1, 2, 5, and 10.

• Factors of 15 are 1, 3, 5, and 15.

Here, 1 and 5 are the common factors of the given numbers. So, the greatest common factor of 10 and 15 is 5.

Next, we can divide the values by the GCF:

• 10 ÷ 5 = 2

• 15 ÷ 5 = 3

The ratio of roses and sunflowers is 2:3. It means that for every 2 roses, there are 3 sunflowers in the garden.

Compound Ratio:

It is a ratio formed by multiplying two or more ratios together. Here, the numerator is the product of the numerators of the original ratios and the denominator is the product of the denominators of the original ratios. For instance, a compound ratio is represented as: a:b and c:d.
 

When we multiply these ratios, we get a compound ratio. To get a better idea of compound ratio, look at this example:
 

Milan drinks 2 liters of water every 3 days and eats 4 apples every 5 months. She wants to calculate the ratio of her drinking and eating habits. How can she find the compound ratio?

To find the compound ratio, we have to multiply these two ratios.

• (2 : 3) × (4 : 5)

• ((2 × 4) : (3 × 5)) = 8 : 15

Hence, the compound ratio of (2 : 3) and (4 × 5) is 8:15.

Inverse Ratio:

An inverse ratio is also known as an indirect or reciprocal ratio. This ratio expresses the relationship of two quantities, in which one value increases and the other decreases equally.
 

For example:

Building a house takes 100 days, 10 days if 10 workers are employed, and 5 days if 20 workers are engaged.

Now we can measure the workers' ratio and days ratio.

Workers Ratio = 10:20

To simplify this, we have to divide the numbers by the GCF. 10 is the GCF of 10 and 20.

• 10 ÷ 10 = 1

• 20 ÷ 10 = 2

The simplified ratio is 1:2.
 

To find the day's ratio, we have to divide both numbers by their GCF.

10:5

Here, 5 is the GCF of 10 and 5.

• 10 ÷ 5 = 2

• 5 ÷ 5 = 1

The simplified ratio of days ratio is 2:1

Learning the tips and tricks of ratios helps students get a proper understanding of the concept. It improves the calculation skills and problem-solving abilities of kids, and it will make complex calculations easier. 

• If both numbers in a ratio a:b are equal, then a:b = 1.

• In a ratio, if the first number is larger than the second number, then the ratio is greater than 1. 

• In a ratio, if the first number is smaller than the second number, then the ratio is less than 1. 

• Confirm the ratio has the same units before starting the calculation. For example, we could compare the ratio of a 50-meter rope to a 5-centimeter rope. Here, we need to convert the units from meter to centimeter or vice versa. 

Ratios help us in various real-life situations; from cooking and purchasing to solving complex mathematical problems. In the areas of business, construction, physics, and architecture, this essential concept is applicable. 

• In the field of culinary industry, ratios are used to calculate the correct proportion of recipes and food items. 

• To analyze the balance between colors, artists and painters use this concept for their work.

• Companies use ratios to divide financial assets, to check the profit of a company, and to determine discounts. 

• Golden Ratio (1.618:1) is a specific ratio used by artists or sculptors while sculpting or drawing.