MHB Big Denominator = Small Fraction

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A fraction with a larger denominator represents a smaller value, as illustrated by the comparison of 1/45 and 1/2. In practical terms, dividing one pizza into 45 pieces results in smaller individual portions than dividing it into 2 pieces. The mathematical reasoning behind this is that the denominator indicates how many equal parts a whole is divided into, making each part smaller with a larger denominator. Therefore, 1/45 is indeed less than 1/2. This concept is fundamental in understanding fractions and their relative sizes.
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Someone once told me that a fraction with a big denominator is a small fraction but no mathematical reason was given.

So, 1/45 < 1/2.

Why?
 
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RTCNTC said:
Someone once told me that a fraction with a big denominator is a small fraction but no mathematical reason was given.

So, 1/45 < 1/2.

Why?

1 pizza divided into 45 pieces vs. 1 pizza divided into 2 pieces

... which pieces are smaller?
 
To answer your question, (1 pizza)/2 is bigger.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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