Introduction to rational numbers quick check
Rational numbers are a subset of real numbers that can be expressed as a ratio or fraction of two integers. They can be positive or negative and include whole numbers, integers, and fractions. Rational numbers can be written in the form a/b, where a and b are integers and b is not equal to 0.
Rational numbers can be either terminating or repeating decimals when expressed in decimal form. For example, 1/2 is a rational number that can be expressed as 0.5, which terminates after the first decimal place. On the other hand, 1/3 is a rational number that can be expressed as 0.333..., which repeats the digit 3 indefinitely.
Rational numbers also follow certain operations, such as addition, subtraction, multiplication, and division. When adding or subtracting rational numbers, we need to have a common denominator to perform the operation. Multiplication and division of rational numbers are straightforward, as we simply multiply or divide the numerators and denominators.
In summary, rational numbers are numbers that can be expressed as fractions and include whole numbers, integers, and fractions. They can be expressed as terminating or repeating decimals and follow certain operations.
Introduction to Rational Numbers Quick Check:
1. What are rational numbers?
Rational numbers are numbers that can be expressed as a fraction (ratio) of two integers, where the denominator is not zero. They can be positive or negative, and include whole numbers, integers, and fractions.
2. How are rational numbers represented?
Rational numbers are represented using the fraction form, where a numerator is divided by a denominator, written as a/b, where a and b are integers and b ≠ 0.
3. Examples of rational numbers:
a) 1/2 - This is a rational number because it can be expressed as a fraction of two integers.
b) -3 - Whole numbers and integers are also considered rational numbers.
c) 0.6 - Decimal numbers that can be expressed as fractions are also rational numbers.
4. How are rational numbers ordered?
Rational numbers can be ordered on a number line according to their values. They follow the same principles of comparing numbers. For example, 1/2 is smaller than 3/4.
5. Operations with rational numbers:
Rational numbers can be added, subtracted, multiplied, and divided just like other numbers. When adding or subtracting rational numbers, the fractions need to have a common denominator to perform the operation. When multiplying or dividing, the fractions can be simplified if possible.
Remember, rational numbers are a fundamental concept in mathematics and are used in various applications, such as measurements, calculations, and comparisons.