Problem 53 - Algebra for College Students

Question

In a group of 12 children, 3 are girls. What percent are not girls?

Step-by-Step Solution

Answer

75% of the children are not girls.

Step 1: Identify Total Number of Children

The total number of children in the group is given as 12.

Step 2: Determine Number of Girls

It is stated that there are 3 girls in the group.

Step 3: Calculate Number of Boys

Subtract the number of girls from the total number of children: define \text{boys} = \text{total\text _children} - \text{number\text _girls}\[ boys = 12 - 3 = 9 \]

Step 4: Find Fraction of Boys in the Group

The fraction of boys in the group is the number of boys divided by the total number of children: \[ \text{fraction\text _of\text _boys} = \frac{9}{12} \]

Step 5: Convert Fraction to Percentage

Convert the fraction of boys to a percentage by multiplying by 100: \[ \text{percentage\text _of\text _boys} = \left(\frac{9}{12}\right) \times 100 = 75\% \]

Key Concepts

Fraction to Percentage Conversion

Understanding how to convert fractions into percentages is very important. Let’s break down the process. A fraction is made up of two numbers: the numerator (top number), which shows how many parts we have, and the denominator (bottom number), which shows how many total parts there are. To turn a fraction into a percentage, you multiply the fraction by 100. For example, if we have the fraction \(\frac{9}{12}\), we multiply it by 100 to get the percentage: \(\frac{9}{12} \times 100 = 75\%\). This shows that 75% of the children in the group are boys. Converting fractions to percentages helps to understand and compare parts of a whole more easily because percentages are a part of the number system you see commonly in daily life.

Basic Arithmetic Operations

Basic arithmetic operations are addition, subtraction, multiplication, and division. These operations are crucial for solving math problems. In the given exercise, subtraction helps to find the number of boys in the group. You subtract the number of girls from the total number of children: \(12 - 3 = 9\). This means there are 9 boys out of 12 children. It’s important to perform these operations correctly to get accurate results. For instance, if we swap the numbers and mistakenly subtract differently, we would get a wrong number of boys. Always double-check your arithmetic operations, they build the foundation for more complex problems.

Problem-Solving in Algebra

Problem-solving in algebra often involves setting up equations and solving for unknowns. In our example, we identify key quantities: total children (12), number of girls (3), and calculate the unknown quantity (number of boys) as a step in our solution. We also form a fraction and convert it to a percentage. These steps require logical reasoning and application of basic algebraic principles. Always break down the problem into smaller parts, address each part one step at a time, and use algebraic methods like forming equations or fractions to find solutions. This approach reduces errors and clarifies the path to the solution.