compare and order 7/12, 2/3, and 6/15
Find the equivalent fractions with a common denominator of 60.
Or you could find the equivalent decimals.
To compare and order the fractions 7/12, 2/3, and 6/15, we need to find a common denominator.
Step 1: Find a common denominator for all three fractions.
In this case, since the denominators are already different, we can simply find the least common multiple (LCM) of 12, 3, and 15. The LCM of these numbers is 60.
Step 2: Convert the fractions to have the same denominator.
To convert 7/12, we need to multiply the numerator and denominator by 5 to get a denominator of 60.
7/12 = (7 * 5)/(12 * 5) = 35/60
For 2/3, we need to multiply the numerator and denominator by 20 to get a denominator of 60.
2/3 = (2 * 20)/(3 * 20) = 40/60
And for 6/15, we need to multiply the numerator and denominator by 4 to get a denominator of 60.
6/15 = (6 * 4)/(15 * 4) = 24/60
Now, the fractions are 35/60, 40/60, and 24/60.
Step 3: Compare and order the fractions.
To compare the fractions, we only need to compare their numerators because the denominators are now the same.
Comparing the numerators:
35 is less than 40, and 24 is less than 35.
So, the order of the fractions from least to greatest is:
24/60, 35/60, 40/60
Alternatively, we can simplify the fractions to their lowest terms:
35/60 can be simplified to 7/12 by dividing both numerator and denominator by 5.
40/60 can be simplified to 2/3 by dividing both numerator and denominator by 20.
24/60 can be simplified to 2/5 by dividing both numerator and denominator by 12.
So, in simplest form, the fractions are:
7/12, 2/3, 2/5