Question

The rational number (37/120) lies between (1/3) and (1/4) on the number line.

Answer 1

Step-by-step explanation:

-1/3 ,-2/3 ,-3/3 ,-4/3 -5/3 , -6/ 3, ....................... -4/4

Answer 2

Answer:

The given statement "The rational number $\frac{37}{120}$ lies between $\frac{1}{3}$ and $\frac{1}{4}$ on the number line." is TRUE.

Step-by-step explanation:

What is a Rational number?

A rational number is any number that can be represented in the form of p/q where p and q are integers and q≠0.

Given:

Two rational numbers:  $\frac{1}{3}$ and $\frac{1}{4}$

Given that,  $\frac{37}{120}$ lies between $\frac{1}{3}$ and $\frac{1}{4}$

Step 1:

Let us make the denominators equal.

$\frac{1}{3} = \frac{1 \times 40}{3 \times 40} = \frac{40}{120}$

$\frac{1}{4} = \frac{1 \times 30}{4 \times 30} = \frac{30}{120}$

Step 2:

Rational numbers between $\frac{30}{120}$ and $\frac{40}{120}$ include:

$\frac{31}{120}, \frac{32}{120}, \frac{33}{120}, \frac{34}{120}, \frac{35}{120}, \frac{36}{120}, \frac{37}{120}, \frac{38}{120}, \frac{39}{120}$

Therefore,

$\frac{37}{120}$ lies between  $\frac{30}{120}$ and $\frac{40}{120}$  'or'

$\frac{37}{120}$ lies between  $\frac{1}{4}$ and $\frac{1}{3}$

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