The reciprocal of an improper fraction

The reciprocal of an improper fraction is as follows:

Because an improper fraction is greater than or equal to 1, the reciprocal of an improper fraction is less than or equal to 1. According to the meaning of reciprocals, two numbers whose product is 1 are reciprocals of each other. An improper fraction is greater than or equal to 1, so the reciprocal of an improper fraction is less than or equal to 1.

Extended knowledge

Improper fraction (improper.fraction) refers to a fraction whose numerator is greater than or equal to the denominator. An improper fraction is greater than or equal to 1. A fraction whose value is greater than or equal to 1, that is, a fraction whose numerator is greater than or equal to the denominator, is called an improper fraction. If discussed within the entire range of rational numbers, a fraction whose absolute value is greater than or equal to 1 is an improper fraction. Improper fractions, as opposed to proper fractions, are usually discussed in the context of positive numbers.

Interesting Stories

In the Kingdom of Fractions, the situation is very tight. The cause of the matter is this: a group of real fractions and improper fractions joked: "We real fractions all look like kings. We have small upper bodies and big lower bodies. We are real fractions, and you improper fractions have fake characters in our names." , in fact, you don’t look like a king, with a big upper body and a small lower body, broad shoulders and thin legs, so you must be fake fractions.”

Unexpectedly, this joke actually angered the fake fractions. , they gathered together and quickly occupied the west side of the capital, intending to fight to the death with True Score, and True Score did not show any weakness, guarding the east side of the capital, preparing to fight. The two sides are at war with each other, and civil war is about to break out.

This naturally alarmed the king of the Fraction Kingdom. He told the ministers around him: "Go and check the history books. What's true and false?" After saying that, he set off for mediation. He rushed to the east and west sides of the capital respectively, and patiently persuaded the true and false fractions: "You are all subjects of the Kingdom of Fractions, and you have lived in harmony from generation to generation. Today is just a joke, and we have to fight with swords. You will regret it in the future." ."

The minister who went to check the history books hurried to the east and west of the capital and told everyone the results that the king asked him to check. The minister said: "According to historical records, the so-called fraction is to divide a unit into several equal parts, and the number indicating such one or several parts is called a fraction.

The numerator can be smaller than the denominator, or it can be smaller than the denominator. If the denominator is greater, it can be converted into an integer and a fraction. If the numerator is equal to the denominator, it can be converted into an integer. For the sake of distinction, this type of fraction is called an improper fraction in mathematics. Fractions are also fractions." Improper fractions jumped up and down with joy after hearing the minister's words.

The true fraction retorted: "Let's put it this way. Integers can also be turned into fractions with a denominator of 1." The minister said: Yes, I have a more important discovery. It turns out that the sum of integers and fractions is Decimals are called rational numbers. The characteristic of rational numbers is that they can be written as a ratio of two integers.