· To understand the concept of fraction

· 理解分数的概念

· To learn about different types of fractions

· 学习不同类型的分数

We have 50 candies. These are to be served in 10 plates. Each plate will have 5 candies. What happens if we are asked to divide one chocolate slab in 5 equal parts? How do we say how much part has been served in a plate. So here we are talking about parts of a whole.

我们有50个糖果。将它们装在10个盘中。每个盘子将装5个糖果。如果要求我们将一个巧克力条平均分为5部分，会怎样？怎样表达装在盘中的部分。在这里，我们将讨论一个整体的部分。

Let us understand this by considering an example. We have a circular disk. We divide it into two equal parts. Each part is half of the whole and is called a fraction. It is written as and read as one half or one by two. The upper number or the number above the line is called the Numerator and indicates the number of equal parts selected, the lower number or the number below the line is called the Denominator and indicates the number of equal parts into which the whole is divided. Now let us divide the disk in four equal parts, each part is called one fourth and is written as. If we combine two one fourths then it makes half. When an object is divided into a number of equal parts then each part is called a fraction.

举一个例子来理解这个概念。我们有一个圆盘，将其平均分成两部分。每一部分是整体的一半，称为一份。它被写作或读作一半或二分之一。上部数字或分数线上面的数称为分子，表示所选的相同部分数，下部数字即分数线下部的数字称为分母，表示整体被划分的相同的部分数。现在，让我们将圆盘平分为四等份，每一份称为四分之一写做。如果我们将两个四分之一组合会得到一半。当一个物体被等分为若干部分，那么每部分被称为一份。

Let us consider a watermelon. Divide the watermelon into 15 equal parts, each part will be called 15^th. If we take seven fifteenth parts, it will be written as. The whole has been divided into 15 parts, so 15 is the denominator and out of these seven fifteenth parts have been selected which appear as the numerator. Note that the denominator is never taken to be a zero. Observe different arrangements of ten cubes used in the following shapes. Each of the cubes is one tenth of the shape formed. In this, there are three cubes shaded out of ten that together form the shape and the fraction is written as. Notice here, that all the shapes have the same fraction shaded. These shapes have ten parts each and three of the parts have been shaded. Thus, in all these cases, irrespective of the shape of the figure, the shaded part remains the same, that is 3/10.

再来看另一个西瓜的例子。将西瓜平分为15等分每一份称为十五分之一。如果我们拿出十五分之七份，写做。因为整体被分成了15份，所以15为分母，从中取的7份为分子。注意，分母决不能为零。观察下面形状中所用的十个立方体的不同排列。每一个立方体为所组成形状的十分之一。这里，十个由立方体组成的形状中有三个加阴影的立方体，此分数写做。注意，在此处所有的形状的相同部分都被加了阴影。这样，在所有这些情形中，无论图形为何种形状，阴影部分保持不变。即十分之三。

Let us consider another illustration and divide the circle into more parts say 8. Shade two parts of the circle. The shaded part is 2/8. Take three such parts and combine, what do we get? We now have 6 eighth parts written as 6/8. In all the fractions discussed so far that is, 1/2, 1/4, 7/15, 3/10; and 6/8, we notice that all of them have their numerator smaller than the denominator. Such fractions are called proper fractions. Now consider two circles and three fourths of a circle. Counting all the parts we have 11 fourth parts. We can write it as. The fraction which has the numerator greater than the denominator is called an improper fraction.

来看另一个实例，将圆盘分等为更多部分，例如8份。将其中的两部分加阴影。加阴影的部分为八分之二。取三个这样的部分并将它们组合，我们会得到什么？现在我们得到八分之六部分，写做八分之六。在所有迄今为止讨论的分数即二分之一，四分之一，十五分之七，十分之三和八分之六中，我们注意到这些分数的分子都小于分母。这种分数被称为真分数。现在来看两个圆盘和四分之三个圆盘的组合。数出所有的部分，我们得到四分之十一部分。写做。分子比分母大的分数被称为假分数。

Remember there is also another way of writing such a fraction. We can say that we have two circles and three fourths of a circle. All taken together can be written as. We write it as. Since we have a combination of whole and part, we call it a mixed fraction. We can convert a mixed fraction into an improper fraction and vice versa. Divide the numerator by denominator. The quotient gives the whole, remainder is the numerator and divisor is the denominator. To convert a mixed fraction into an improper fraction; multiply the whole with the denominator and added to it the numerator to get the numerator of the mixed fraction, with denominator remaining the same.

记住，还有另一种书写这种分数的方法。我们可以说我们有两个圆盘和四分之三个圆盘。加在一起可以写做。我们将其写做。因为将整体和部分进行了组合，我们称它为带分数。一个带分数转化为假分数，反之亦然。用分子除以分母，商为带分数的整数部分，余数作为分子，除数为分母。 将一个带分数转化为假分数：用分母乘以整个分数并加上分子，获得带分数的分子，分母保持不变。

In this session we have understood the concept of a fraction and also the types of fractions.

本节中我们了解了分数的概念和类型。

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