Representing 7/4 on the number line:

To represent the number 7/4 on the number line, we need to first understand what the number represents. The fraction 7/4 can be interpreted as the result of dividing 7 by 4, or as the answer to the question "how many fourths are there in 7?".

To represent 7/4 on the number line, we can follow these steps:

1. Draw a horizontal line and mark a point as the origin (usually denoted by a 0).
2. Divide the line into equal parts. Since the denominator of 7/4 is 4, we need to divide the line into 4 equal parts.
3. Label the points on the number line. Starting from the origin, label the first point as 1/4, the second point as 2/4 (which simplifies to 1/2), the third point as 3/4, and the fourth point as 4/4 (which simplifies to 1).
4. To represent 7/4, we count 7 units from the origin. This will bring us to the point between 1/2 and 3/4, which represents 7/4 on the number line.

So, 7/4 can be represented on the number line between 1/2 and 3/4.

Explanation of Rational Numbers:

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers and the denominator is not zero. In other words, rational numbers are numbers that can be written in the form a/b, where a and b are integers and b is not equal to zero.

Rational numbers can be positive, negative, or zero. Examples of rational numbers include 1/2, -3/4, 5/1, and 0/7.

Key Points:
- Rational numbers can be represented on the number line.
- They can be positive, negative, or zero.
- Any integer can also be expressed as a rational number by writing it with a denominator of 1.
- Rational numbers can be added, subtracted, multiplied, and divided using the rules of arithmetic.
- Rational numbers can be converted to decimals by performing the division and expressing the result as a decimal. Some rational numbers, like 1/3, have repeating decimal representations.

Rational numbers are an important concept in mathematics and have various applications in real-life situations, such as measuring quantities, calculating proportions, and representing fractions in everyday situations.