A fraction is a number we need for measuring. For counting, we have the natural numbers: 1, 2, 3, 4. But when we measure something, such as a length, it will not always be a whole number. Therefore we need numbers that are less than 1 -- numbers that are the parts of 1: half of 1, a third, a fourth, a fifth, a millionth.
A number written with a numerator and a denominator, in which both are natural numbers.
The denominator and the numerator
The denominator names the number of equal parts into which number 1 has been divided. We read the denominator as an ordinal number. The numerator, which we read as a cardinal number, names how many of those parts.
The fraction 3/10 signifies that number 1 has been divided into 10 equal parts and -- starting from the left -- we are counting 3 of them.
Number 1, in other words, has been divided into tenths. At this point, the student should be clear about the language of division into equal parts, and why we use ordinal numbers: third, fourth, fifth, sixth, and so on.
Every fraction is constructed in this way from number 1, which is the source of every number of arithmetic. The whole numbers are the multiples of 1. The fractions are its parts: its halves, thirds, fourths, fifths, and so on.
Since the numerator and denominator are natural numbers, the numerator has a ratio to the denominator. (3 is three tenths of 10.) And the fraction itself has that same ratio to 1. (3/10 is three tenths of 1.).
Proper Fraction
Proper fraction is A fraction that is less than 1 and the numerator is smaller than the denominator. Since the numerator and denominator are natural numbers, they have a ratio to one another. And a proper fraction has the same name as that ratio.
Mixed number fraction
Mixed number is A whole number plus a proper fraction.
Improper fractions
If we divide each whole unit into thirds, say, and keep counting them -- then we will come to 3/3, 4/3, 5/3, and so on. That is, we will come to fractions that are equal to or greater than 1. We call those improper fractions. We can recognize an improper fraction when the numerator is greater than or equal to the denominator.
In fact, when the numerator is equal to the denominator, then the fraction is equal to 1. We say that those fractions also are improper.
This article was originally published on The math page. Read the original article.
Source:
https://www.themathpage.com/ARITH/fractions.htm
Fraction
Common fractionA number written with a numerator and a denominator, in which both are natural numbers.
The denominator and the numerator
The denominator names the number of equal parts into which number 1 has been divided. We read the denominator as an ordinal number. The numerator, which we read as a cardinal number, names how many of those parts.
The fraction 3/10 signifies that number 1 has been divided into 10 equal parts and -- starting from the left -- we are counting 3 of them.
Number 1, in other words, has been divided into tenths. At this point, the student should be clear about the language of division into equal parts, and why we use ordinal numbers: third, fourth, fifth, sixth, and so on.
Every fraction is constructed in this way from number 1, which is the source of every number of arithmetic. The whole numbers are the multiples of 1. The fractions are its parts: its halves, thirds, fourths, fifths, and so on.
Since the numerator and denominator are natural numbers, the numerator has a ratio to the denominator. (3 is three tenths of 10.) And the fraction itself has that same ratio to 1. (3/10 is three tenths of 1.).
Proper Fraction
Proper fraction is A fraction that is less than 1 and the numerator is smaller than the denominator. Since the numerator and denominator are natural numbers, they have a ratio to one another. And a proper fraction has the same name as that ratio.
Mixed number fraction
Mixed number is A whole number plus a proper fraction.
Improper fractions
If we divide each whole unit into thirds, say, and keep counting them -- then we will come to 3/3, 4/3, 5/3, and so on. That is, we will come to fractions that are equal to or greater than 1. We call those improper fractions. We can recognize an improper fraction when the numerator is greater than or equal to the denominator.
In fact, when the numerator is equal to the denominator, then the fraction is equal to 1. We say that those fractions also are improper.
This article was originally published on The math page. Read the original article.
https://www.themathpage.com/ARITH/fractions.htm
