Question

Which fraction is greater than 7/12

Answer 1

2/3 is greater

Explanation:

I took the long route, but I worked out the lowest common multiples of the denominator using prime factorization, which led me to 1980. I then divided each of the denominators by 1980 which would give me the number I would need to multiply the denominators by to get me to 1980. I then multiplied the numerator by the numbers that the denominators would be multiplied by to get to the 1980. For 7/12 I got 1155/1980 which meant that I only had to find a numerator higher than 1150. I did thus which the rest of the fractions and I got 1320/1980 which is higher than than the numerator for 7/12.

Answer 2

2/3, 7/9, 3/5

Explanation:

We can setup each fraction to compare each one to another by multiplying for common denominators

7/12 and 6/11 have a common denominator of 132, so multiple each fraction by the number that gets each denominator to 132

(7/12) * 11 = 77/132 and (6/11) * 12 = 72/32

77/132 > 72/132, so that is false

7/12 and 3/8 have a common denominator of 24, so multiply each fraction by the number that gets each denominator to 48

(7/12) * 4 = 28/48 and (3/8) * 6 = 18/48

28/48 > 18/48, so that is false

7/12 and 2/3 have a common denominator of 12, so multiply each fraction by the number that gets each denominator to 12

(7/12) * 1 = 7/12 and (2/3) * 4 = 8/12

7/12 < 8/12 so that is true

7/12 and 1/12 already share a common denominator, so we can already tell that 7/12 > 1/12, making it false

7/12 and 7/9 share a common denominator of 72, so multiply each number accordingly

(7/12) * 6 = 42/72 and (7/9) * 8 = 56/72

42/72 < 56/72, making it true

7/12 and 3/5 share a common denominator of 60, so multiply each number accordingly to get a matching denominator

(7/12) * 5 = 35/60 and (3/5) * 12 = 36/60

35/60 < 36/60, making it true