which fraction is greatest 5/6 7/9 2/3 or 9/12
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To determine which fraction is the greatest among 5/6, 7/9, 2/3, and 9/12, we can either find the least common denominator (LCD) and compare the numerators or cross-multiply and compare the products.
Method 1: Comparing with a Common Denominator (LCD)
1. Find the least common denominator (LCD) of the fractions. It is the smallest number that the denominators (6, 9, 3, and 12) can all divide into evenly.
The LCD of 6, 9, 3, and 12 is 36.
2. Convert each fraction to an equivalent fraction with the LCD of 36:
5/6 = (5/6) * (6/6) = 30/36
7/9 = (7/9) * (4/4) = 28/36
2/3 = (2/3) * (12/12) = 24/36
9/12 = (9/12) * (3/3) = 27/36
3. Compare the numerators of the equivalent fractions to determine the greatest fraction:
The fractions in order of greatest to least are:
30/36, 28/36, 27/36, 24/36
Therefore, the greatest fraction is 5/6.
Method 2: Cross-Multiplication
1. Multiply the numerator of each fraction by the denominator of the other fraction.
For example:
5/6 * 9 = 45/6
7/9 * 12 = 84/9
2/3 * 12 = 24/3
9/12 * 6 = 54/12
2. Simplify each product if possible.
For example:
45/6 = 15/2
84/9 = 28/3
24/3 = 8
54/12 = 9/2
3. Compare the resulting values.
The fractions in order of greatest to least are:
15/2, 28/3, 9/2, 8
Therefore, the greatest fraction is 15/2.
Both methods lead to the same conclusion that the greatest fraction among 5/6, 7/9, 2/3, and 9/12 is 5/6.