When measured amounts (number of units) are at the foundation of the concept of natural numbers, and number that can be seen as the target of big/little or additive/subtractive calculations may be treated as numbers that express quantity. Therefore, it is suitable to introduce fractional parts to children as the part less than a unit of a continuous quantity. For this reason , standard amounts such as 1 m, 1 l, and 1 kg are used as unit quantities for dividing fractions, as shown in the example of Figure 1 :
1/4 = 1÷4 , 3/4 = 1÷4×3
Also, fractions such as 3/4 m and 3/4 l are referred to as quantity fractions by such as m children recognize a quantity more than the unit such as 1 m. Thus, a fraction with a numerator of 1. Improper fraction and mixed fraction are usually introduced by the quantity fractions. A fraction with a numerator of 1 such as 1/4 or 1/5 is called a unit fraction in Japanese textbooks. A unit fraction is necessary to develops the ideas to recognize a fraction based on a unit fraction, such as 3/4 is three times of 1/4 , or 2/5 is two times of 1/5