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Question

Arrange $$\displaystyle \frac{5}{8}, \frac{3}{16}, -\frac{1}{4}$$ and $$\displaystyle \frac{17}{32}$$ in descending order of their magnitudes.Identify the largest rational number.


Solution

Consider the given numbers $$\dfrac {5}{8},\dfrac {3}{16},-\dfrac {1}{4}$$ and $$\dfrac {17}{32}$$. 

The LCM of the denominators $$8,16,4,32$$ is $$32$$. Therefore, the given numbers will be:

$$1]\dfrac { 5\times 4 }{ 8\times 4 } =\dfrac { 20 }{ 32 } $$

$$2]\dfrac { 3\times 2 }{ 16\times 2 } =\dfrac { 6 }{ 32 } $$

$$3]-\dfrac { 1\times 8 }{ 4\times 8 } =-\dfrac { 8 }{ 32 }$$

$$4]\dfrac {17}{32}$$

Thus, the numbers in descending order are shown below:

$$\dfrac { 20 }{ 32 } ,\dfrac { 17 }{ 32 } ,\dfrac { 6 }{ 32 } ,-\dfrac { 8 }{ 32 } \\ \Rightarrow \dfrac { 5 }{ 8 } ,\dfrac { 17 }{ 32 } ,\dfrac { 3 }{ 16 } ,-\dfrac { 1 }{ 4 }$$  

Thus the largest rational number is $$\dfrac{5}{8}$$.



Mathematics

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