Select the best answer for the question.
13. Express the fractions $1 / 2, 3 / 16$, and $7 / 8$ with an LCD.
A. $4 / 8, 6 / 8$, and $14 / 8$
B. $1 / 4, 3 / 4$, and $7 / 4$
C. $1 / 32, 3 / 32$, and $7 / 32$
D. $8 / 16, 3 / 16$, and $14 / 16
Answer (2)
To express the fractions 2 1 , 16 3 , and 8 7 with a common denominator, we find the LCD, which is 16. The fractions convert to 16 8 , 16 3 , and 16 14 , matching option D. Therefore, the correct choice is D.
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Find the Least Common Denominator (LCD) of the denominators 2, 16, and 8, which is 16.
Express 2 1 with a denominator of 16: 2 1 = 16 8 .
Express 8 7 with a denominator of 16: 8 7 = 16 14 .
The fractions with a common denominator are 16 8 , 16 3 , and 16 14 , so the answer is D .
Explanation
Problem Analysis We need to express the fractions 2 1 , 16 3 , and 8 7 with a common denominator. The goal is to find the Least Common Denominator (LCD) and rewrite each fraction using this LCD.
Finding the LCD First, let's find the Least Common Denominator (LCD) of the denominators 2, 16, and 8. The LCD is the smallest number that is a multiple of all the denominators. From the tool, we found that the LCD is 16.
Expressing Fractions with LCD Now, we will express each fraction with the LCD of 16 as the new denominator.
For 2 1 , we need to find a number that, when multiplied by 2, gives 16. That number is 8. So, we multiply both the numerator and the denominator by 8: 2 1 = 2 × 8 1 × 8 = 16 8
For 16 3 , the denominator is already 16, so we don't need to change this fraction: 16 3 = 16 3
For 8 7 , we need to find a number that, when multiplied by 8, gives 16. That number is 2. So, we multiply both the numerator and the denominator by 2: 8 7 = 8 × 2 7 × 2 = 16 14
Comparing with Options So, the fractions expressed with the LCD are 16 8 , 16 3 , and 16 14 . Comparing these to the options provided, we see that option D matches our result.
Final Answer Therefore, the correct answer is D. 16 8 , 16 3 , and 16 14 .
Examples
When baking, you might need to combine different ingredients measured in fractions. To accurately add these fractions, you need to express them with a common denominator. For example, if a recipe calls for 2 1 cup of flour, 16 3 cup of sugar, and 8 7 cup of water, you would convert these fractions to have a common denominator of 16, making it easy to add them together: 16 8 + 16 3 + 16 14 = 16 25 cups total.
