Which fractions have 20 as the LCD (lowest common denominator)?
$\frac{2}{3}$
$\frac{5}{6}$
$\frac{7}{10}$
$\frac{1}{4}$
$\frac{3}{7}$
Answer (2)
The fractions that have 20 as the lowest common denominator are 10 7 and 4 1 . This is determined by checking if 20 is divisible by their respective denominators. Only these two fractions met the criteria for 20 being the LCD.
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List the denominators of the given fractions: 3, 6, 10, 4, and 7.
Check if 20 is divisible by each denominator.
Identify the fractions for which 20 is divisible by their denominator.
The fractions that have 20 as the LCD are 10 7 , 4 1 .
Explanation
Problem Analysis We need to determine which of the given fractions have 20 as their lowest common denominator (LCD). The fractions are 3 2 , 6 5 , 10 7 , 4 1 , and 7 3 . The LCD of a set of fractions is the smallest common multiple of their denominators. In this case, we want to check if 20 is the LCD for each fraction. This means we need to check if 20 is divisible by the denominator of each fraction.
Listing Denominators First, let's list the denominators of the given fractions: 3, 6, 10, 4, and 7. We will check if 20 is divisible by each of these numbers.
Checking Divisibility Now, let's check each denominator:
For 3 2 , the denominator is 3. Is 20 divisible by 3? No, 20 ÷ 3 = 6 with a remainder of 2.
For 6 5 , the denominator is 6. Is 20 divisible by 6? No, 20 ÷ 6 = 3 with a remainder of 2.
For 10 7 , the denominator is 10. Is 20 divisible by 10? Yes, 20 ÷ 10 = 2 .
For 4 1 , the denominator is 4. Is 20 divisible by 4? Yes, 20 ÷ 4 = 5 .
For 7 3 , the denominator is 7. Is 20 divisible by 7? No, 20 ÷ 7 = 2 with a remainder of 6.
Identifying Fractions with 20 as LCD From the above checks, we see that 20 is divisible by 10 and 4. Therefore, the fractions 10 7 and 4 1 have 20 as a possible LCD.
Final Answer Thus, the fractions that have 20 as the LCD are 10 7 and 4 1 .
Final Answer The fractions that have 20 as the LCD are 10 7 , 4 1 .
Examples
Understanding the lowest common denominator (LCD) is crucial when planning events with recurring schedules. For instance, imagine you're coordinating a school event with two activities: one occurs every 10 days and another every 4 days. To find out when both activities will happen on the same day, you need to determine the LCD of 10 and 4, which is 20. This means that every 20 days, both activities will coincide, helping you plan and coordinate the event effectively. The fractions 10 7 and 4 1 can be used to represent portions of these cycles, and knowing their LCD helps in aligning schedules.
