# Pick out the greatest fraction $8\dfrac{1}{4},2\dfrac{9}{{13}},4\dfrac{1}{2},1\dfrac{3}{6}.$

Last updated date: 26th Mar 2023

•

Total views: 307.2k

•

Views today: 5.84k

Answer

Verified

307.2k+ views

Hint: The value of mixed fraction $$a\dfrac{b}{c} = \dfrac{{(a \times c) + b}}{c}$$

Complete step-by-step answer:

The given mixed fractions are $8\dfrac{1}{4},2\dfrac{9}{{13}},4\dfrac{1}{2},1\dfrac{3}{6}.$

Converting these mixed fraction into fractions

$8\dfrac{1}{4} = \dfrac{{\left( {8 \times 4} \right) + 1}}{4} = \dfrac{{33}}{4}$

$2\dfrac{9}{{13}} = \dfrac{{\left( {13 \times 2} \right) + 9}}{{13}} = \dfrac{{35}}{{13}}$

$4\dfrac{1}{2} = \dfrac{{\left( {2 \times 4} \right) + 1}}{2} = \dfrac{9}{2}$

$$1\dfrac{3}{6} = \dfrac{{\left( {6 \times 1} \right) + 3}}{6} = \dfrac{9}{6} = \dfrac{3}{2}$$

The values of these fractions are

$$\dfrac{{33}}{4} = 8.25,\;\dfrac{{35}}{{13}} \approx 2.69,\;\dfrac{9}{2} = 4.5,\;\dfrac{3}{2} = 1.5$$

If we compare the values, we get $$\dfrac{3}{2} < \dfrac{{35}}{{13}} < \dfrac{9}{2} < \dfrac{{33}}{4}$$

$$ \Rightarrow \dfrac{{33}}{4}$$ is the greatest of the four fractions.

Corresponding mixed fraction for $$\dfrac{{33}}{4} = 8\dfrac{1}{4}.$$

$$\therefore $$ The greatest fraction of the four fractions is $8\dfrac{1}{4}.$

Note: We have to find the greatest mixed fraction of the given mixed fractions. We need to know the values of these mixed fractions to find the greatest fraction. So we converted mixed fractions to rational numbers to find their values easily.

Complete step-by-step answer:

The given mixed fractions are $8\dfrac{1}{4},2\dfrac{9}{{13}},4\dfrac{1}{2},1\dfrac{3}{6}.$

Converting these mixed fraction into fractions

$8\dfrac{1}{4} = \dfrac{{\left( {8 \times 4} \right) + 1}}{4} = \dfrac{{33}}{4}$

$2\dfrac{9}{{13}} = \dfrac{{\left( {13 \times 2} \right) + 9}}{{13}} = \dfrac{{35}}{{13}}$

$4\dfrac{1}{2} = \dfrac{{\left( {2 \times 4} \right) + 1}}{2} = \dfrac{9}{2}$

$$1\dfrac{3}{6} = \dfrac{{\left( {6 \times 1} \right) + 3}}{6} = \dfrac{9}{6} = \dfrac{3}{2}$$

The values of these fractions are

$$\dfrac{{33}}{4} = 8.25,\;\dfrac{{35}}{{13}} \approx 2.69,\;\dfrac{9}{2} = 4.5,\;\dfrac{3}{2} = 1.5$$

If we compare the values, we get $$\dfrac{3}{2} < \dfrac{{35}}{{13}} < \dfrac{9}{2} < \dfrac{{33}}{4}$$

$$ \Rightarrow \dfrac{{33}}{4}$$ is the greatest of the four fractions.

Corresponding mixed fraction for $$\dfrac{{33}}{4} = 8\dfrac{1}{4}.$$

$$\therefore $$ The greatest fraction of the four fractions is $8\dfrac{1}{4}.$

Note: We have to find the greatest mixed fraction of the given mixed fractions. We need to know the values of these mixed fractions to find the greatest fraction. So we converted mixed fractions to rational numbers to find their values easily.

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main