分数表示一个整体的一部分。分数由两个主要部分组成：分子在上面，告诉我们有多少部分；分母在下面，告诉我们整体被分成多少等份。比如二分之一表示我们有2个等份中的1份。四分之三表示我们有4个等份中的3份。不同的分数可以表示相同的数量，比如四分之二等于二分之一。
分数的加法和减法有两种情况。当分母相同时，分母保持不变，分子相加或相减。比如四分之一加四分之二等于四分之三。当分母不同时，需要先通分，找到最小公倍数作为新分母，然后将分数化为同分母，再进行计算。
分数的乘法比较简单，分子乘分子，分母乘分母，然后化简结果。比如三分之二乘以四分之三等于十二分之六，化简后是二分之一。分数的除法则是乘以被除数的倒数。比如三分之二除以四分之一，等于三分之二乘以一分之四，结果是三分之八。
分数和小数可以相互转换。分数转小数时，用分子除以分母。比如四分之三等于3除以4，得到0.75。小数转分数时，根据小数位数确定分母。一位小数分母是10，两位小数分母是100。然后化简到最简分数。
解分数应用题有固定的步骤。首先要理解题意，找出已知条件和要求什么。然后选择合适的运算方法，列式计算，最后检查答案是否合理。常见的题型包括求一个数的几分之几，已知一个数的几分之几求这个数，分数大小比较，以及分数的简单应用等。掌握这些基本技巧，就能解决大部分分数相关的问题。
Adding and subtracting fractions depends on whether they have the same denominator. With like denominators, we keep the denominator the same and add or subtract the numerators. For example, one-fourth plus one-fourth equals two-fourths, which simplifies to one-half. With unlike denominators, we must first find a common denominator, convert both fractions to equivalent fractions with that denominator, then add or subtract the numerators.
Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together, then simplify. We can visualize this with area models where we shade parts of a grid. For division, we multiply by the reciprocal - flip the second fraction and multiply instead. When working with mixed numbers, convert them to improper fractions first, then follow the same rules.
Decimals extend our place value system beyond whole numbers. Each place to the right of the decimal point represents a fraction with a power of ten in the denominator. The first place is tenths, then hundredths, then thousandths. We can see the connection between fractions and decimals: three-tenths equals zero point three, and twenty-five hundredths equals zero point two five, which also equals one-fourth.