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Welcome to our lesson on rational numbers. A rational number is any number that can be written as a fraction a over b, where a and b are integers and b is not equal to zero. This includes positive and negative fractions, whole numbers, and decimal numbers that can be converted to fractions. Let's look at some examples like one half, negative three fourths, zero point five which equals one half, and negative two which equals negative two over one. Now let's learn how to represent rational numbers on the number line. To place a fraction a over b on the number line, we first divide the unit interval into b equal parts, then mark the point at position a from zero. For example, to show one half, we divide the interval from zero to one into two equal parts and mark the first division. For negative three fourths, we divide the interval from zero to negative one into four equal parts and mark the third division. For five halves, we go to position two and a half on the number line. Now let's learn how to compare rational numbers. The first method is using common denominators. To compare two fractions, we convert them to have the same positive denominator, then compare their numerators. Let's see an example comparing two thirds and three fourths. First, we find a common denominator, which is twelve. Two thirds becomes eight twelfths, and three fourths becomes nine twelfths. Since eight is less than nine, we conclude that two thirds is less than three fourths. The second method for comparing rational numbers uses the number line. On a number line, any number that appears to the right is greater than any number to the left. All positive numbers are greater than zero, and zero is greater than all negative numbers. Let's compare negative one half and three fourths. On the number line, negative one half is to the left of three fourths, so negative one half is less than three fourths. This visual method makes it easy to see which number is larger. Let's summarize what we've learned about rational numbers. A rational number is any number that can be expressed as a fraction a over b, where a and b are integers and b is not zero. We can represent these numbers on a number line by dividing intervals into equal parts. We learned two methods to compare rational numbers: using common denominators and using the number line position. These concepts are fundamental in mathematics and have many applications in daily life, from measuring ingredients in cooking to calculating distances and proportions.