91Ó°ÊÓ

Ratios are a way to compare two quantities. Think of it as a division between two numbers. For example, if you have a ratio of 2:3, it means for every 2 parts of one quantity, there are 3 parts of another.
Ratios can be written in different forms:
• Using a colon, like 2:3
• As a fraction, \(\frac{2}{3}\)
• In words, '2 to 3'
This can be very useful in real-life situations, like cooking or mixing solutions.
In our example, when we express numbers as ratios of integers, it is essentially writing them in fraction form. For instance, \-16\ can be written as \(\frac{-16}{1}\). Similarly, a decimal like 4.399 can be expressed as \(\frac{4399}{1000}\). This conversion helps in understanding and comparing numbers better.

Fractions are another essential concept when dealing with rational numbers. A fraction consists of a numerator (top part) and a denominator (bottom part). For example, in \(\frac{3}{4}\), 3 is the numerator, and 4 is the denominator. Fractions represent parts of a whole.
Key points about fractions:
• Proper fractions have numerators smaller than denominators, like \(\frac{3}{4}\).
• Improper fractions have numerators larger than or equal to denominators, such as \(\frac{5}{4}\).
• Mixed numbers combine integers and fractions, like 1 \(\frac{1}{2}\).
• Any integer can be written as a fraction by putting it over 1, like \(\frac{-16}{1}\).
For decimals, converting them to fractions involves using place values. For instance, 4.399 becomes \(\frac{4399}{1000}\), since 4.399 is 4399 thousandths.

Integers are whole numbers that can be positive, negative, or zero. Examples include -16, 0, and 4. They are foundational in mathematics and everyday calculations.
Key characteristics of integers:
• Do not have fractional or decimal parts.
• Can be added, subtracted, multiplied, and divided (except division by zero).
• Zero (0) is neutral, meaning it is neither positive nor negative.
Understanding integers is crucial because they are often involved in ratios and fractions.
For instance, expressing an integer like -16 as a ratio or fraction is simple. Just write it over 1, resulting in \(\frac{-16}{1}\). This shows how integers easily fit into other mathematical concepts like rational numbers.