Problem 57
Question
Convert \(62 \%\) to a fraction.
Step-by-Step Solution
Verified Answer
62% is \( \frac{31}{50} \) as a fraction.
1Step 1: Write the Percentage as a Fraction
To convert a percentage to a fraction, first recognize that a percentage is a number out of 100. Therefore, you can write 62% as the fraction \( \frac{62}{100} \).
2Step 2: Simplify the Fraction
Now simplify the fraction \( \frac{62}{100} \). To simplify, we find the greatest common divisor (GCD) of 62 and 100, which is 2. Divide both the numerator and the denominator by 2: \( \frac{62 \div 2}{100 \div 2} = \frac{31}{50} \).
3Step 3: Conclusion
The simplified fraction that represents 62% is \( \frac{31}{50} \).
Key Concepts
Simplifying FractionsGreatest Common DivisorMathematics Problem Solving
Simplifying Fractions
Simplifying fractions is an important step in percentage to fraction conversion. This involves reducing a fraction to its simplest form, which is the fraction with the smallest possible numerator and denominator while keeping the same overall value.
When a number, like a percentage, is converted to a fraction, often the fraction can be simplified. For example, converting 62% to the fraction \( \frac{62}{100} \) can be further simplified.
Simplification is achieved by dividing both the numerator and the denominator by their greatest common divisor (GCD). In our example, the GCD of 62 and 100 is 2. Dividing both terms of \( \frac{62}{100} \) by 2 gives \( \frac{31}{50} \).
Understanding this process makes it easier to work with fractions in everyday math problems.
When a number, like a percentage, is converted to a fraction, often the fraction can be simplified. For example, converting 62% to the fraction \( \frac{62}{100} \) can be further simplified.
Simplification is achieved by dividing both the numerator and the denominator by their greatest common divisor (GCD). In our example, the GCD of 62 and 100 is 2. Dividing both terms of \( \frac{62}{100} \) by 2 gives \( \frac{31}{50} \).
Understanding this process makes it easier to work with fractions in everyday math problems.
Greatest Common Divisor
The Greatest Common Divisor (GCD) is a crucial concept in simplifying fractions. The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.
To find the GCD of 62 and 100, we look for factors that both share. Doing this, we find that the greatest common factor is 2. It is important to note that 2 divides both 62 and 100, hence supporting the simplification of \( \frac{62}{100} \) into \( \frac{31}{50} \).
Understanding GCD aids not just in simplifying fractions but also in many areas of mathematics such as finding common denominators in fraction operations and solving problems involving proportions.
To find the GCD of 62 and 100, we look for factors that both share. Doing this, we find that the greatest common factor is 2. It is important to note that 2 divides both 62 and 100, hence supporting the simplification of \( \frac{62}{100} \) into \( \frac{31}{50} \).
Understanding GCD aids not just in simplifying fractions but also in many areas of mathematics such as finding common denominators in fraction operations and solving problems involving proportions.
- Helps in simplifying fractions
- Used in finding lowest terms
- Essential for solving equations and inequalities
Mathematics Problem Solving
Solving mathematics problems involves the use of various methods and techniques to find the solutions. In the exercise of converting a percentage to a fraction, mathematics problem solving encompasses several concepts, each building on the understanding of the previous.
The first step is knowing that a percentage can be expressed as a fraction out of 100. Once this is established, converting a percentage becomes straightforward. However, knowing how to simplify this fraction, as with turning \( \frac{62}{100} \) into \( \frac{31}{50} \), requires understanding simplification and the role of the GCD.
Problem solving involves breaking down the process:
The first step is knowing that a percentage can be expressed as a fraction out of 100. Once this is established, converting a percentage becomes straightforward. However, knowing how to simplify this fraction, as with turning \( \frac{62}{100} \) into \( \frac{31}{50} \), requires understanding simplification and the role of the GCD.
Problem solving involves breaking down the process:
- Convert the percentage to a fraction.
- Identify the GCD to simplify the fraction.
- Follow procedural steps for accuracy.
Other exercises in this chapter
Problem 57
Perform each operation. $$ 0-14 $$
View solution Problem 57
Find the value of each of the following. Use a calculator to check each result. $$ -(8-21) $$
View solution Problem 58
Perform each operation. $$ 5 \cdot(-2) $$
View solution Problem 58
Use the order of operations to simplify \(\left(5^{2}+3^{2}+2\right) \div 2^{2}\).
View solution