Fraction RRB

Fraction

A fraction is a rational number of the form , q 0, p is called as numerator and q is called denominator.

Formula to remember

If the denominators of all the given fractions are equal then the fraction with greater numerator will be the greater fraction.

Example: $\frac{4}{7}$ , $\frac{2}{7}$ , $\frac{8}{7}$ , $\frac{9}{7}$ , $\frac{5}{7}$ then $\frac{9}{7}$ > $\frac{8}{7}$ > $\frac{5}{7}$ > $\frac{4}{7}$ > $\frac{2}{7}$ >

If the numerators of all the given fractions are equal then the fraction with smaller denominator will be the greater fraction.

Example: $\frac{7}{4}$ , $\frac{7}{2}$ , $\frac{7}{8}$ , $\frac{7}{9}$ , $\frac{7}{5}$ then $\frac{7}{2}$ > $\frac{7}{4}$ > $\frac{7}{5}$ > $\frac{7}{8}$ > $\frac{7}{9}$ >

When numerator is greater than denominator and the differences of numerator and denominator are equal, then the fraction with smaller numerator will be the greater fraction.

Example: $\frac{5}{2}$ , $\frac{7}{4}$ , $\frac{11}{8}$ , $\frac{8}{5}$ , $\frac{10}{7}$ then $\frac{5}{2}$ > $\frac{7}{4}$ > $\frac{8}{5}$ > $\frac{10}{7}$ > $\frac{11}{8}$ >

Quiker method (cross multiplication)

We can compare fractions by this method and easily take a decision.

Example- $\frac{11}{8}$ ? $\frac{7}{5}$ ? smaller or greater.

Ans. By cross multiplication

11 x 5 = 55 and 8 x 7 = 56 and 55 < 56 then < $\frac{11}{8}$ < $\frac{7}{5}$

Question 1:

Which of the following fraction is arranged in ascending order of their value?

a) $\frac{1}{4}$ , $\frac{2}{7}$ , $\frac{3}{4}$ , $\frac{4}{7}$ , $\frac{5}{7}$ , $\frac{6}{5}$

b) $\frac{1}{4}$ , $\frac{2}{7}$ , $\frac{4}{7}$ , $\frac{5}{7}$ , $\frac{3}{4}$ , $\frac{6}{5}$

c) $\frac{2}{7}$ , $\frac{1}{4}$ , $\frac{4}{7}$ , $\frac{3}{4}$ , $\frac{5}{7}$ , $\frac{6}{5}$

d) $\frac{2}{7}$ , $\frac{1}{4}$ , $\frac{4}{7}$ , $\frac{5}{7}$ , $\frac{3}{4}$ , $\frac{6}{5}$

Answer : b) $\frac{1}{4}$ , $\frac{2}{7}$ , $\frac{4}{7}$ , $\frac{5}{7}$ , $\frac{3}{4}$ , $\frac{6}{5}$

Solution :

Converting the given fractions into decimal numbers, we have

$\frac{1}{4}$ = 0.25

$\frac{2}{7}$ = 0.28

$\frac{3}{4}$ = 0.75

$\frac{4}{7}$ = 0.57

$\frac{5}{7}$ = 0.71

$\frac{6}{5}$ = 1.2

So, 0.25 < 0.28 < 0.57 < 0.71 < 0.75 < 1.2

Corresponding fraction is $\frac{1}{4}$ < $\frac{2}{7}$ < $\frac{4}{7}$ < $\frac{5}{7}$ < $\frac{3}{4}$ < $\frac{6}{5}$

Hence the answer is option b.

Question 2:

Which of the following fraction is the largest?

a) $\frac{8}{9}$

b) $\frac{18}{23}$

c) $\frac{16}{21}$

d) $\frac{14}{17}$

Answer : a) $\frac{8}{9}$

Solution :

Converting the given fractions into decimal form, we have,

$\frac{8}{9}$ = 0.88

$\frac{18}{23}$ = 0.78

$\frac{16}{21}$ = 0.76

$\frac{14}{17}$ = 0.82

From the above, 0.88 is the largest.
Corresponding fraction is $\frac{8}{9}$ .

Question 3:

Which of the following fraction is greater than $\frac{4}{5}$ and less than $\frac{6}{7}$ ?

a) $\frac{2}{3}$

b) $\frac{3}{4}$

c) $\frac{5}{6}$

d) $\frac{10}{11}$

Answer : c) $\frac{5}{6}$

Solution :

We have to find X such that $\frac{4}{5}$ < X < $\frac{6}{7}$

Converting each fraction into decimal form, we get:

$\frac{4}{5}$ = 0.8

$\frac{6}{7}$ = 0.85

We have to find the fraction which is greater than 0.8and less than 0.85.
Now,

$\frac{2}{3}$ = 0.66

$\frac{3}{4}$ = 0.75

$\frac{5}{6}$ = 0.83

$\frac{10}{11}$ = 0.91

Clearly, 0.83 lies between 0.8 and 0.85.
Required fraction is $\frac{5}{6}$

Question 4:

Which of the following fraction does not lie between $\frac{5}{6}$ and $\frac{8}{15}$ ?

a) $\frac{2}{3}$

b) $\frac{3}{4}$

c) $\frac{4}{5}$

d) $\frac{6}{7}$

Answer : d) $\frac{6}{7}$

Solution :

Converting each of the given fractions into decimal form, we get,

$\frac{5}{6}$ = 0.83

$\frac{8}{15}$ = 0.53

$\frac{2}{3}$ = 0.66

$\frac{3}{4}$ = 0.75

$\frac{4}{5}$ = 0.8

$\frac{6}{7}$ = 0.85

Clearly, 0.85 does not lie between 0.83 and 0.53
Hence the required fraction is $\frac{6}{7}$ .

Question 5: Which of the following is larger than 3/5?

Ans: Option A

Explanation: 3/5 = 6/10 , 1/2 = 5/10, 59/100 = 5.9/10 , 0.3/10 > 6/10.

so, 39/50 > 3/5