Calculating the Ratio of People in Different States

The problem asks us to find the ratio of the number of people in State C to the number of people in State E, based on the data provided in the table. A ratio compares two quantities.

Understanding the Table Data

Let's first look at the number of people listed for each state in the given table:

From the table, we can identify the number of people in State C and State E:

• Number of people in State C = 144
• Number of people in State E = 280

Calculating the Ratio of People in State C to State E

We need to find the ratio of the number of people in State C to the number of people in State E. This can be written as:

\text{Ratio of C to E} = \text{Number of people in State C} : \text{Number of people in State E}

Substituting the values from the table:

\text{Ratio of C to E} = 144 : 280

A ratio can also be expressed as a fraction:

\text{Ratio of C to E} = \frac{144}{280}

Simplifying the Ratio

To express the ratio in its simplest form, we need to divide both numbers by their greatest common divisor (GCD). Let's find common factors for 144 and 280.

We can start by dividing by small common factors:

• Both are even, so divide by 2: \frac{144 \div 2}{280 \div 2} = \frac{72}{140}
• Both are still even, divide by 2 again: \frac{72 \div 2}{140 \div 2} = \frac{36}{70}
• Both are still even, divide by 2 again: \frac{36 \div 2}{70 \div 2} = \frac{18}{35}

Now we have the fraction \frac{18}{35}. Let's check if 18 and 35 have any common factors other than 1.

• Factors of 18 are: 1, 2, 3, 6, 9, 18.
• Factors of 35 are: 1, 5, 7, 35.

The only common factor is 1. So, the fraction \frac{18}{35} is in its simplest form.

Therefore, the simplified ratio of the number of people in State C to the number of people in State E is 18 : 35.

Final Answer

The ratio of the number of people in state C to the number of people in state E is 18 : 35.

Revision Table: Key Ratio Concepts

Additional Information on Data Ratios

Ratios are frequently used when analysing data presented in tables or charts. They help us understand the proportional relationship between different data points. For example, in this problem, the ratio 18:35 tells us that for every 18 people in State C, there are 35 people in State E. This kind of comparison is useful in various fields, including demographics, finance, and science.

When working with data ratios, always ensure the quantities being compared are in the same units (which they are in this case - number of people). Also, pay close attention to the order required by the question (State C to State E, not State E to State C).