Which of the following sets of fractions has a lowest common denominator of 60 and is ordered from least to greatest? Is it A) one-fifth, one-third, seven twelfths; B) seven twelfths, one-third, one-fifth; C) one-third, one-fifth, seven twelfths; D) one-fifth, seven twenty-fourths, one-third; or E) seven twenty-fourths, one-fifth, and one-third.
Let’s first consider the lowest common denominator. 60 is not divisible by 24. Therefore, options D and options E cannot have a lowest common denominator of 60. The other three options have the same three fractions: one-fifth, one-third, and seven twelfths. The lowest common multiple of five, three, and 12 is equal to 60. Therefore, the lowest common denominator for options A, B, and C will be equal to 60. This means that option A, option B, and option C all satisfied the first condition — a lowest common denominator of 60.
The second condition was whether the fractions are ordered from least to greatest. In order to compare or order the three fractions, we must make the bottom numbers or denominators the same. In this case, the lowest common denominator is 60. One-fifth is equivalent to twelve sixtieths. In the same way, one-third is equivalent to twenty sixtieths. And finally, seven twelfths is equal to thirty-five sixtieths.
Remember that whatever you multiply the denominator by, you must do the same to the numerator or top of the fraction. Ordering these from least to greatest, we can see but the smallest fraction is one-fifth, the largest fraction is seven twelfths, and one-third lies between these two fractions.
This means that the correct option was option A. The fractions one-fifth, one-third, and seven twelfths have a lowest common denominator of 60. And they are also ordered from least to greatest.