Question

when two fractions refer to the same whole, explain why the fraction with a lesser denominator has larger pieces than the fraction with a greater denominator

Answer 1

Answer with explanation:

Consider a Rectangular room, in which four people are residing and another congruent room,in which six people are dwelling.

If Area Occupied by two rooms are same

Then, Area occupied by each person in first room,if there are four person in first room, if represented in terms of fraction is equal to one fourth$\frac{1}{4}=0.25 m^2$.

And, Area occupied by each person in second room,if there are six person in second room, if represented in terms of fraction is equal to one sixth$\frac{1}{6}=0.17 m^2$.

So,→→ Area occupied by each person in which four people are residing>Area occupied by each person in which six people are residing.

→→So,Fraction with a lesser denominator has larger pieces(Larger area) than the fraction with a greater denominator smaller pieces(smaller area).

Answer 2

Answer:

when two fractions refer to the same whole than the  fraction with a lesser denominator has larger pieces than the fraction with a greater denominator because:

for example: let us consider a pizza is to be divided in two ways such that each gets the equal amount:

• the pizza is divided among 4 people.

      Hence the will get 1/4 part of the pizza.

• the pizza is divided among 8 people

    Hence they will get 1/8 part of the pizza.

Hence, in the first case the people will get more amount as compared to the second case.

Hence, if as a whole the denominator is less the fraction is bigger.