Understanding Rational Numbers: Examples and Arithmetic Operations

Rational Numbers (Q)

p divided by q where p and q are integers and q is not zero

Rational numbers (Q) are numbers that can be expressed as a ratio of two integers (a/b), where b is not equal to zero. This means that rational numbers can be written as a fraction with a denominator that is a non-zero integer.

Examples of rational numbers include:

– 1/2
– 5/6
– -3/4
– 0 (which can be expressed as 0/1)

Note that every whole number can also be expressed as a rational number (by setting the denominator equal to 1). For example, 3 can be expressed as 3/1.

Rational numbers can be compared, added, subtracted, multiplied, and divided using the standard rules of arithmetic. For example:

– To compare two rational numbers, find a common denominator and then compare the numerators. For example, to compare 1/2 and 3/4, we would find a common denominator of 4 and then compare 2 and 3 (which tells us that 3/4 is larger).
– To add or subtract rational numbers, find a common denominator and then combine the numerators. For example, to add 1/2 and 3/4, we would find a common denominator of 4 and then add the numerators: 1/2 + 3/4 = 2/4 + 3/4 = 5/4.
– To multiply rational numbers, multiply the numerators and denominators separately. For example, to multiply 1/2 and 3/4, we would multiply 1 * 3 = 3 for the numerator and 2 * 4 = 8 for the denominator, giving us 3/8.
– To divide rational numbers, invert the second number and then multiply. For example, to divide 1/2 by 3/4, we would invert 3/4 to get 4/3 and then multiply: 1/2 ÷ 3/4 = 1/2 * 4/3 = 4/6 = 2/3.

It is important to note that not all numbers are rational. For example, square roots that are not perfect squares (such as √2) are irrational numbers, and cannot be expressed as a ratio of two integers.

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