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How to Calculate the Percentage of Students Who Travel Over Six Miles to School by Car
Mathematics
Grade 8 (Junior High School)
Question Content
Some students were asked how they travel to school. 39% of the students said they travel by car. Of these, 23% live more than six miles from their school. What percentage of the students travel over six miles to school by car?
Correct Answer
8.97%
Detailed Solution Steps
1
Step 1: Understand the problem. We need to find what percentage of all students are in the group that travels by car AND lives more than six miles from school.
2
Step 2: Recognize that "of these" refers to the 39% of students who travel by car. So we need to calculate 23% of 39%.
3
Step 3: Convert the percentages to decimals for calculation: 39% = 0.39, 23% = 0.23.
4
Step 4: Multiply the two decimals: 0.39 × 0.23 = 0.0897.
5
Step 5: Convert the result back to a percentage by multiplying by 100: 0.0897 × 100 = 8.97%.
Knowledge Points Involved
1
Percentage of a Percentage
This refers to calculating a proportion of an already proportional value. When you need to find what percentage of a subset makes up the whole, you multiply the two percentage values (after converting them to decimals). It is used in scenarios where you have nested proportional groups, like demographic or survey data analysis.
2
Percentage-Decimal Conversion
To convert a percentage to a decimal, divide the percentage value by 100 (or move the decimal point two places to the left). To convert a decimal back to a percentage, multiply the decimal by 100 (or move the decimal point two places to the right). This is essential for performing arithmetic operations with percentages.
3
Multiplication of Decimals
When multiplying decimals, multiply the numbers as if they were whole numbers, then count the total number of decimal places in the factors and place the decimal point in the product accordingly. This operation is used to calculate proportional values in real-world problems.
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