Consider The Fraction $\frac{26}{200}$.Write The Equivalent Fraction That Has A Denominator Of 100.

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Understanding Equivalent Fractions

Equivalent fractions are fractions that have the same value, but differ in their numerators and denominators. In other words, two fractions are equivalent if they can be simplified to the same ratio. For instance, the fractions 12\frac{1}{2} and 24\frac{2}{4} are equivalent because they both represent the same proportion of a whole.

The Problem: Converting 26200\frac{26}{200} to a Denominator of 100

We are given the fraction 26200\frac{26}{200} and asked to write an equivalent fraction with a denominator of 100. To do this, we need to find a common multiple of 200 and 100 that will allow us to simplify the fraction.

Finding the Least Common Multiple (LCM)

The least common multiple (LCM) of 200 and 100 is 200. This means that we can multiply both the numerator and denominator of the fraction by 2 to get a denominator of 100.

Converting the Fraction

To convert the fraction 26200\frac{26}{200} to a denominator of 100, we can multiply both the numerator and denominator by 2:

26200×22=52400\frac{26}{200} \times \frac{2}{2} = \frac{52}{400}

However, we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 4.

Simplifying the Fraction

Dividing both the numerator and denominator by 4, we get:

52400=13100\frac{52}{400} = \frac{13}{100}

Therefore, the equivalent fraction with a denominator of 100 is 13100\frac{13}{100}.

Why is this Important?

Converting fractions to equivalent forms is an important skill in mathematics, particularly in algebra and geometry. It allows us to simplify complex fractions and make them easier to work with. In addition, it helps us to understand the relationships between different fractions and to make comparisons between them.

Real-World Applications

Converting fractions to equivalent forms has many real-world applications. For example, in cooking, we often need to convert fractions of ingredients to equivalent forms in order to make the right amount of a dish. In science, we use equivalent fractions to make measurements and to compare different quantities.

Conclusion

In conclusion, converting fractions to equivalent forms is an important skill in mathematics that has many real-world applications. By understanding how to convert fractions to equivalent forms, we can simplify complex fractions and make them easier to work with. Whether we are working in algebra, geometry, or real-world applications, equivalent fractions are an essential tool that can help us to solve problems and make comparisons between different quantities.

Additional Examples

  • Converting 15300\frac{15}{300} to a denominator of 100:
    • Multiply both the numerator and denominator by 2: 15300×22=30600\frac{15}{300} \times \frac{2}{2} = \frac{30}{600}
    • Simplify the fraction by dividing both the numerator and denominator by their GCD, which is 30: 30600=120\frac{30}{600} = \frac{1}{20}
  • Converting 24400\frac{24}{400} to a denominator of 100:
    • Multiply both the numerator and denominator by 2: 24400×22=48800\frac{24}{400} \times \frac{2}{2} = \frac{48}{800}
    • Simplify the fraction by dividing both the numerator and denominator by their GCD, which is 16: 48800=350\frac{48}{800} = \frac{3}{50}

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Q: What is an equivalent fraction?

A: An equivalent fraction is a fraction that has the same value as another fraction, but differs in its numerator and denominator.

Q: Why do we need to convert fractions to equivalent forms?

A: We need to convert fractions to equivalent forms in order to simplify complex fractions and make them easier to work with. This is particularly important in algebra and geometry, where equivalent fractions are used to make comparisons between different quantities.

Q: How do I convert a fraction to an equivalent form with a denominator of 100?

A: To convert a fraction to an equivalent form with a denominator of 100, you need to find the least common multiple (LCM) of the original denominator and 100. Then, multiply both the numerator and denominator by the necessary factor to get a denominator of 100.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. For example, the LCM of 200 and 100 is 200.

Q: How do I find the greatest common divisor (GCD)?

A: To find the greatest common divisor (GCD) of two numbers, you need to list the factors of each number and find the largest factor that they have in common. For example, the GCD of 52 and 400 is 4.

Q: Why do I need to simplify the fraction after converting it to an equivalent form?

A: You need to simplify the fraction after converting it to an equivalent form in order to get the simplest form of the fraction. This is done by dividing both the numerator and denominator by their GCD.

Q: Can I convert a fraction to an equivalent form with a denominator of 100 using a calculator?

A: Yes, you can convert a fraction to an equivalent form with a denominator of 100 using a calculator. Simply enter the fraction and the calculator will give you the equivalent fraction with a denominator of 100.

Q: Are there any real-world applications of converting fractions to equivalent forms?

A: Yes, there are many real-world applications of converting fractions to equivalent forms. For example, in cooking, we often need to convert fractions of ingredients to equivalent forms in order to make the right amount of a dish. In science, we use equivalent fractions to make measurements and to compare different quantities.

Q: Can I convert a fraction to an equivalent form with a denominator of 100 using a computer program?

A: Yes, you can convert a fraction to an equivalent form with a denominator of 100 using a computer program. Simply enter the fraction and the program will give you the equivalent fraction with a denominator of 100.

Q: Why is it important to understand equivalent fractions?

A: It is important to understand equivalent fractions because they are used in many mathematical operations, such as addition, subtraction, multiplication, and division. Equivalent fractions also help us to make comparisons between different quantities and to simplify complex fractions.

Q: Can I convert a fraction to an equivalent form with a denominator of 100 using a spreadsheet?

A: Yes, you can convert a fraction to an equivalent form with a denominator of 100 using a spreadsheet. Simply enter the fraction and the spreadsheet will give you the equivalent fraction with a denominator of 100.

Q: Are there any online tools that can help me convert fractions to equivalent forms?

A: Yes, there are many online tools that can help you convert fractions to equivalent forms. For example, you can use an online fraction calculator or a spreadsheet program to convert fractions to equivalent forms.

Q: Can I convert a fraction to an equivalent form with a denominator of 100 using a graphing calculator?

A: Yes, you can convert a fraction to an equivalent form with a denominator of 100 using a graphing calculator. Simply enter the fraction and the calculator will give you the equivalent fraction with a denominator of 100.