Question

Order the fractions from greatest from leastSolve a, b, c , d, e

Answer 1

Answer and Explanation:

Note that to be able to order fractions from the greatest to the least, we need to express the fractions with the same denominator using their least common multiple, then the fraction with the greatest numerator will be the greatest fraction while the one with the smallest numerator will be the least.

a) Let's go ahead and express the given fractions 4/7, 1/5, 2/3 with the same denominator as seen below;

`\begin{gathered} (4)/(7)=(4\cdot15)/(7\cdot15)=(60)/(105) \\ (1)/(5)=(1\cdot21)/(5\cdot21)=(21)/(105) \\ (2)/(3)=(2\cdot35)/(3\cdot35)=(70)/(105) \end{gathered}`

From the above, we can order the given fractions from the greatest to the least as 2/3, 4/7, 1/5

b) Given 5/8, 1/2, 3/4, let's express the given fractions with the same denominator;

`\begin{gathered} (5)/(8)=(5\cdot1)/(8\cdot1)=(5)/(8) \\ (1)/(2)=(1\cdot4)/(2\cdot4)=(4)/(8) \\ (3)/(4)=(3\cdot2)/(4\cdot2)=(6)/(8) \end{gathered}`

From the above, we can order the given fractions from the greatest to the least as 3/4, 5/8, 1/2

c) Given 5/6, 2/3, 7/9, let's go ahead and express the given fractions with the same denominator;

`\begin{gathered} (5)/(6)=(5\cdot3)/(6\cdot3)=(15)/(18) \\ (2)/(3)=(2\cdot6)/(3\cdot6)=(12)/(18) \\ (7)/(9)=(7\cdot2)/(9\cdot2)=(14)/(18) \end{gathered}`

From the above, we can order the given fractions from the greatest to the least as 5/6, 7/9, 2/3

d) Given 7/12, 1/8, 5/9, let's go ahead and express the given fractions with the same denominator;

`\begin{gathered} (7)/(12)=(7\cdot6)/(12\cdot6)=(42)/(72) \\ (5)/(8)=(5\cdot9)/(8\cdot9)=(45)/(72) \\ (5)/(9)=(5\cdot8)/(9\cdot8)=(40)/(72) \end{gathered}`

From the above, we can order the given fractions from the greatest to the least as 5/8, 7/12, 5/9

e) Given 2/5, 4/11, 3/7 let's go ahead and express the given fractions with the same denominator;

`\begin{gathered} (2)/(5)=(2\cdot77)/(5\cdot77)=(154)/(385) \\ (4)/(11)=(4\cdot35)/(11\cdot35)=(140)/(385) \\ (3)/(7)=(3\cdot55)/(7\cdot55)=(165)/(385) \end{gathered}`

From the above, we can order the given fractions from the greatest to the least as 3/7, 2/5, 4/11