Question

list five rational numbers between 1/3 and 1/4

Answer 1

Hey mate

1/3 and 1/4 ( LCM of 3 and 4 is 12)

1/3×4/4 = 4/12

1/4×3/3 = 3/12

4/12 ×10/10 =40/120

3/12 × 10/10 = 30/ 120

31/120,32/120,33/120,37/120,38/120,39/120.

Hope my answer is right....

Answer 2

Given: Rational numbers $\frac{1}{3}$ and $\frac{1}{4}$

To find: Five rational numbers between these given numbers

Solution: According to the given question,

The given rational numbers have different denominators.

L.C.M. of their denominators 3 and 4 = 12.

To convert these rational numbers with same denominators, we have

$\frac{1}{3}$ × $\frac{4}{4} = \frac{4}{12}$ and $\frac{1}{4}$ × $\frac{3}{3}$ = $\frac{3}{12}$

Now, to insert 5 rational numbers, multiply numerator and denominator of each rational number with 5 + 1 = 6

⇒ $\frac{4}{12}$ × $\frac{6}{6} = \frac{24}{72}$ and $\frac{3}{12}$ × $\frac{6}{6} = \frac{18}{72}$

∵ 18 < 19 < 20 < 21 < 22 < 23 < 24

Hence, five rational numbers between $\frac{1}{3}$ and $\frac{1}{4}$ are

$\frac{19}{72}, \frac{20}{72}, \frac{21}{72}, \frac{22}{72}, and \ \frac{23}{72}$