Problem 89 - Elementary Algebra

Question

Find the number of Haitians who live in poverty. Haiti occupies an area roughly the size of Maryland on the Caribbean island of Hispaniola, which it shares with the Dominican Republic. Nearly all of the \(8.7\) million residents are of African descent and speak Creole and French. The capital is Port-au-Prince. The country is the poorest in the Western Hemisphere, with four out of five people living in poverty and more than half in abject poverty. (Source: www nytimes.com, Dec. 27, 2011)

Step-by-Step Solution

Answer

6.96 million

Step 1: Identify Given Data

The total population of Haiti is given as 8.7 million. Additionally, four out of five people live in poverty.

Step 2: Calculate the Fraction of People in Poverty

Four out of five people living in poverty means that \( \frac{4}{5} \) of the population lives in poverty.

Step 3: Convert Percentage to Decimal

To facilitate the multiplication, convert \( \frac{4}{5} \) to a decimal which is 0.8.

Step 4: Multiply to Find Number of People in Poverty

Multiply the total population by the decimal obtained: \( 8.7 \times 0.8 = 6.96 \) million.

Key Concepts

Fraction to Decimal Conversion

A fraction represents a part of a whole number and when dealing with problems that require multiplication or division, converting a fraction to a decimal can simplify the process.
For the exercise, the fraction given is \(\frac{4}{5}\). To convert this fraction into a decimal, you divide the numerator by the denominator:
\[ \frac{4}{5} = 0.8 \]
This step is crucial because decimals are often easier to work with in multiplication and division calculations. Remember:

• Divide the top number (numerator) by the bottom number (denominator)
• You can also use a calculator to make this conversion faster
• Understanding and practicing fraction to decimal conversion will speed up your math tasks significantly

Population Statistics

Population statistics are crucial for understanding the demographics and economic conditions of a country. Here, we are provided with some key statistics about Haiti:

• Haiti has a population of 8.7 million
• Four out of five people live in poverty, which is 80 percent

These statistics help us understand that a significant majority of the population is living under challenging economic conditions.
To find how many people live in poverty, we use the fraction of the population that lives in poverty, which is \(\frac{4}{5}\). This type of analysis is vital for policymakers and organizations aiming to provide aid or create interventions.
Keep in mind:

• Always double-check the source of your data to ensure it is accurate
• Understand the importance of these statistics in real-world applications like aid distribution

Multiplication of Decimals

Multiplying decimals is a fundamental skill needed in many mathematical computations. After converting the fraction to a decimal, we multiply it by the total population to find the number of people living in poverty:
\[ 8.7 \times 0.8 = 6.96 \]
This means 6.96 million people live in poverty in Haiti.
Here are some tips for multiplying decimals:

• Line up the numbers by their place value instead of the decimal point
• Ignore the decimal points and multiply the numbers as if they are whole numbers
• Count the total number of decimal places in the factors
  Place the decimal in the product so it has that same number of decimal places

For example:
If you multiply 3.2 (one decimal place) by 2.5 (one decimal place), the result will have two decimal places:
\[ 32 \times 25 = 800 \]
Then adjust for the decimal places:
\[ 3.2 \times 2.5 = 8.00 \]