Understanding Equivalent Fractions and Decimals

Oct 13, 2025 by miodeya.com 24 views

Which of the Following is NOT Equivalent to the Others?

Understanding Equivalent Fractions and Decimals

In mathematics, equivalent fractions and decimals are expressions that represent the same value. They can be written in different forms, but they all convey the same amount or quantity. In this article, we will explore the concept of equivalent fractions and decimals, and we will examine a set of expressions to determine which one is not equivalent to the others.

What are Equivalent Fractions and Decimals?

Equivalent fractions are fractions that have the same value, even though they may have different numerators and denominators. For example, the fractions 1/2 and 2/4 are equivalent because they both represent the same amount. Similarly, equivalent decimals are decimals that have the same value, even though they may have different digits in the decimal places. For example, the decimals 0.5 and 0.50 are equivalent because they both represent the same amount.

Analyzing the Given Expressions

Now, let's analyze the given expressions:

A. 1.25 B. $$1 \frac{25}{100}$$ C. $$1 \frac{75}{1,000}$$ D. $$1 \frac{1}{4}$$

At first glance, it may seem like all of these expressions are equivalent. However, upon closer inspection, we can see that they are not all equivalent.

Breaking Down the Expressions

Let's break down each expression to understand its value:

A. 1.25: This is a decimal expression that represents 1 and 25/100.

B. $$1 \frac{25}{100}$$: This is a mixed number expression that represents 1 and 25/100.

C. $$1 \frac{75}{1,000}$$: This is a mixed number expression that represents 1 and 75/1000.

D. $$1 \frac{1}{4}$$: This is a mixed number expression that represents 1 and 1/4.

Comparing the Expressions

Now, let's compare the expressions to determine which one is not equivalent to the others.

Expression A (1.25) and Expression B ($$1 \frac{25}{100}$$) are equivalent because they both represent 1 and 25/100.

Expression C ($$1 \frac{75}{1,000}$$) is not equivalent to the others because it represents 1 and 75/1000, which is a different value than the others.

Expression D ($$1 \frac{1}{4}$$) is equivalent to Expression A (1.25) and Expression B ($$1 \frac{25}{100}$$) because it represents 1 and 1/4, which is the same value as 1 and 25/100.

Conclusion

In conclusion, the expression that is not equivalent to the others is Expression C ($$1 \frac{75}{1,000}$$). This is because it represents a different value than the others, whereas the other expressions all represent the same value.

Key Takeaways

Equivalent fractions and decimals are expressions that represent the same value.
Equivalent fractions and decimals can be written in different forms, but they all convey the same amount or quantity.
To determine which expression is not equivalent to the others, we need to compare their values and identify any differences.

Real-World Applications

Understanding equivalent fractions and decimals is essential in various real-world applications, such as:

Cooking: When a recipe calls for a certain amount of an ingredient, it's essential to understand equivalent fractions and decimals to ensure that the correct amount is used.
Finance: When working with money, it's crucial to understand equivalent fractions and decimals to ensure that the correct amount is paid or received.
Science: When working with measurements, it's essential to understand equivalent fractions and decimals to ensure that the correct amount is used.

Common Misconceptions

Some common misconceptions about equivalent fractions and decimals include:

Assuming that all fractions and decimals are equivalent.
Not understanding that equivalent fractions and decimals can be written in different forms.
Not recognizing that equivalent fractions and decimals can have different denominators and decimal places.

Conclusion

In conclusion, understanding equivalent fractions and decimals is essential in mathematics and various real-world applications. By recognizing which expressions are equivalent and which are not, we can ensure that we are working with the correct values and amounts.
Frequently Asked Questions: Equivalent Fractions and Decimals

Understanding Equivalent Fractions and Decimals: A Q&A Guide

In our previous article, we explored the concept of equivalent fractions and decimals, and we examined a set of expressions to determine which one is not equivalent to the others. In this article, we will answer some frequently asked questions about equivalent fractions and decimals.

Q: What is the difference between equivalent fractions and decimals?

A: Equivalent fractions and decimals are expressions that represent the same value. Fractions are written in the form of a/b, where a is the numerator and b is the denominator. Decimals are written in the form of a decimal point followed by digits. For example, the fraction 1/2 and the decimal 0.5 are equivalent because they both represent the same value.

Q: How do I determine if two fractions are equivalent?

A: To determine if two fractions are equivalent, you need to find a common denominator. A common denominator is a number that both fractions can be divided by. For example, to determine if 1/2 and 2/4 are equivalent, you can find a common denominator, which is 4. Then, you can rewrite both fractions with the common denominator: 1/2 = 2/4.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you need to divide the numerator by the denominator. For example, to convert the fraction 1/2 to a decimal, you can divide 1 by 2, which equals 0.5.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you need to find the place value of the last digit. For example, to convert the decimal 0.5 to a fraction, you can find the place value of the last digit, which is 5. Then, you can rewrite the decimal as a fraction: 0.5 = 5/10.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction. For example, 2 1/2 is a mixed number. An improper fraction is a fraction where the numerator is greater than the denominator. For example, 3/2 is an improper fraction.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, to convert the mixed number 2 1/2 to an improper fraction, you can multiply 2 by 2 and then add 1, which equals 5/2.

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator and then write the remainder as a fraction. For example, to convert the improper fraction 5/2 to a mixed number, you can divide 5 by 2, which equals 2 with a remainder of 1. Then, you can write the remainder as a fraction: 2 1/2.

Q: Why are equivalent fractions and decimals important in real-world applications?

A: Equivalent fractions and decimals are important in real-world applications because they allow us to work with different forms of numbers. For example, in cooking, we may need to use fractions to measure ingredients, but we may also need to convert those fractions to decimals to use a digital scale. In finance, we may need to work with decimals to calculate interest rates, but we may also need to convert those decimals to fractions to use a calculator.

Conclusion

In conclusion, equivalent fractions and decimals are essential concepts in mathematics and real-world applications. By understanding how to determine if two fractions are equivalent, how to convert fractions to decimals, and how to convert decimals to fractions, we can ensure that we are working with the correct values and amounts.