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Correct Answer: divide the numerator by the denominator.
to effectively teach third graders how to convert fractions to decimals, it's important to clarify the process and offer straightforward examples. here's an expanded explanation on how to address the question of converting fractions to decimals:
**understanding fractions and decimals:**
before diving into conversion, ensure that the students understand what fractions and decimals are. a fraction consists of a numerator (top number) and a denominator (bottom number). the numerator represents how many parts are taken from a whole that is divided according to the denominator. a decimal, on the other hand, is another way to represent fractions, using powers of 10 (like tenths, hundredths, etc.).
**correct method to convert fractions to decimals:**
to convert a fraction into a decimal, you divide the numerator by the denominator. this method is straightforward and uses basic division. for example, to convert the fraction 3/4 into a decimal:
1. take the numerator (3).
2. divide it by the denominator (4).
3. the result is 0.75.
**clarifying common misconceptions:**
it's crucial to address common mistakes or misconceptions:
1. **dividing the denominator by the numerator** is incorrect and will not yield the right decimal representation of the fraction.
2. **inverting the fraction** and then trying to convert it into a decimal by dividing by 100 does not apply to general fraction-to-decimal conversion. this method is not only incorrect but also confusing.
3. **multiplying both the numerator and the denominator by 100** does not convert a fraction to a decimal. this action would actually just scale the fraction by 100, changing its value.
**examples and practice:**
after explaining, provide the students with multiple examples:
- convert 1/2 by dividing 1 (numerator) by 2 (denominator) to get 0.5.
- convert 2/5 by dividing 2 by 5 to get 0.4.
encourage students to practice with different fractions to ensure they grasp the concept.
**terminating and non-terminating decimals:**
explain that some decimals terminate (like 0.75 or 0.5) while others do not terminate and repeat indefinitely (like 1/3 = 0.333...). it's helpful to introduce the concept of repeating decimals and perhaps show how to denote them using a bar (e.g., 0.333... can be written as 0.3̅).
**summary:**
to sum up, converting fractions to decimals involves dividing the numerator by the denominator. it's a fundamental skill in math that helps students understand the relationship between fractions and decimals, enhancing their number sense and ability to handle real-world situations where decimals are used, such as in money calculations and measurements.
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