Statement I: An orchard has a total area of 1000 m². Given that 200 m² of the orchard has been used for mango trees, 500 m² has been used for apple trees and the remaining area is unused. The fraction of the orchard that is unused is $\dfrac{3}{10}$ .
Statement II: All natural numbers can be written as improper fractions.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.

Question

Statement I: An orchard has a total area of 1000 m². Given that 200 m² of the orchard has been used for mango trees, 500 m² has been used for apple trees and the remaining area is unused. The fraction of the orchard that is unused is $\dfrac{3}{10}$ .

Statement II: All natural numbers can be written as improper fractions.

Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.

KnowledgeBoat · Accepted Answer

According to Statement I,

Total area = 1000 m²

Area used = 200 + 500 = 700 m²

Unused area = 1000 - 700 = 300 m²

Fraction of unused area = $\dfrac{300}{1000} = \dfrac{3}{10}$ .

∴ Statement I is true.

According to Statement II, every natural number can be written with denominator 1.

For example, $5 = \dfrac{5}{1}$ , $21 = \dfrac{21}{1}$ , etc., which are improper fractions (numerator ≥ denominator).

∴ Statement II is true.

Both Statement I and Statement II are true.

Hence, option 3 is the correct option.

Mathematics

Fractions

Answer

Related Questions

The fraction whose numerator is the smallest odd prime number and denominator is the smallest composite number is
$\dfrac{3}{4}$
$\dfrac{2}{4}$
$\dfrac{4}{3}$
$\dfrac{4}{2}$

State whether the following statements are true (T) or false (F):
(i) The fraction $\dfrac{2}{3}$ lies between 2 and 3
(ii) To find an equivalent fraction to a given fraction, we may add or subtract the same (non-zero) number to its numerator and denominator.