## Questions and Answers

What is the process for simplifying a fraction?

Dividing the numerator and denominator by the greatest common divisor

How is 25% written as a decimal?

0.25

What does the decimal 1.3 represent as a fraction?

13/10

When multiplying a whole number by a fraction, what should be done first?

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Why are decimals particularly useful in representing money?

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Explain the process of simplifying a fraction and why it is important in mathematics.

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How are fractions and percentages related in expressing values?

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Explain the significance of finding common denominators when adding or subtracting fractions.

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Describe how decimals are used to represent fractions and why they are considered convenient.

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Why is it important to understand percentages in everyday life and mathematical calculations?

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## Study Notes

## Introduction to Mathematics

Mathematics is an essential field of study that provides foundational knowledge for various disciplines, including physics, economics, engineering, and computer science. It involves understanding shapes, numbers, and quantities, among other concepts. This article will delve into five key areas within mathematics: probability, polygons, fractions, percentages, and decimals.

### Probability

Probability is concerned with predicting the likelihood of events occurring based on available data. For example, if two dice are rolled, there are 36 possible outcomes, each having an equal chance of occurring. To calculate the probability, you would divide the number of favorable outcomes by the total number of possible outcomes. In this case, since only one pair appears on both dice, the probability of rolling double sixes is 1 out of 36.

### Polygons

A polygon is a flat shape with sides made up of straight lines. Common types include triangles, squares, rectangles, pentagons, hexagons, heptagons, octagons, nonagons, decagons, undecagons, dodecagons, and so on. These geometric figures can be classified according to their angles and sides. For instance, a triangle has three sides, while a square has four sides of equal length arranged at right angles.

### Fractions

Fractions represent parts of a whole. They consist of two main components: a numerator, which represents the quantity being considered, and a denominator, which signifies the total quantity of interest. A fraction can also be simplified by dividing both its numerator and denominator by the greatest common divisor until neither value changes. For example, when simplifying the mixed fraction 3 + 1/2, we first multiply the whole number (3) by the denominator (2), resulting in 6, and then divide it by the original denominator (2), yielding 3. Therefore, the reduced fraction becomes 3 + 1/2 = 3.

### Percentages

Percentages express a part of a whole as a percentage of 100. They are often used to compare different quantities or measure increases and decreases in values over time. Calculating percentages involves finding a proportion of a given value, usually expressed as a decimal. For instance, if 25% of apples cost $10 each, and you want to know how much 100 apples would cost, you would multiply 25 by 100, giving you $250.

### Decimals

Decimals represent fractions where the numerator is smaller than the denominator. For example, 2.5 represents 2/5, while 1.3 represents 1/8. Decimal notation allows us to work with small portions of money more easily than fractions. Additionally, decimals make it easier to perform arithmetic operations such as addition, subtraction, multiplication, and division.

In conclusion, mathematics encompasses numerous concepts, from basic arithmetic calculations to complex problem-solving skills. Understanding these fundamental aspects of math sets the stage for further exploration into advanced mathematical principles.

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