QQuestionMathematics
QuestionMathematics
"When adding or subtracting fractions with different denominators, each fraction's denominator must be converted to an equal value. Which of the following terms describes that equal value?
A. Multiple
B. Reciprocal
C. Greatest Common Factor
D. Lowest Common Denominator"
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the key terminology
When adding or subtracting fractions with different denominators, we need to find a common denominator that allows us to combine the fractions.
Step 3:: Analyze the given options
- Reciprocal: A fraction flipped upside down ($$\frac{a}{b}$$ becomes $$\frac{b}{a}$$)
- Multiple: A number that can be divided by another number without a remainder - Greatest Common Factor: The largest number that divides two or more numbers without a remainder - Lowest Common Denominator: The smallest number that is a multiple of all the denominators
Step 4:: Identify the correct term
The term that describes the equal value needed to add or subtract fractions with different denominators is the "Lowest Common Denominator" (LCD).
Step 5:: Explain why LCD is correct
The Lowest Common Denominator is the smallest number that can be used as a common denominator for all fractions in the problem. It allows you to convert each fraction to an equivalent fraction with the same denominator, making addition or subtraction possible.
Final Answer
Lowest Common Denominator Explanation: When adding or subtracting fractions with different denominators, mathematicians use the Lowest Common Denominator to create equivalent fractions that can be combined. This ensures that the fractions have the same denominator before performing the arithmetic operation.
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