RATIONAL NUMBERS | FIRST QUARTER GRADE 7 MATATAG TAGALOG MATH TUTORIAL

Summary

This tutorial explains rational numbers by exploring their representation as fractions, decimals, and percentages. It covers various types of fractions (proper, improper, and mixed numbers), decimal forms (terminating and repeating decimals), and the conversion between different forms. The video also emphasizes the concept of ratio, illustrating how numbers can be expressed as ratios of whole numbers. It concludes by discussing rational numbers, highlighting that they can be represented as fractions where the denominator is not zero, and contrasting them with irrational numbers like pi or the square root of 2. The tutorial aims to deepen understanding and prepare viewers for future lessons.

Takeaways

• 😀 Rational numbers are numbers that can be written as a ratio of two integers, where the denominator is not zero.
• 😀 A ratio is a comparison between two or more quantities of the same kind, expressed as a fraction or with a colon.
• 😀 Rational numbers include whole numbers, fractions, decimals, and percentages, and can be converted between these forms.
• 😀 A proper fraction has a numerator smaller than the denominator, while an improper fraction has a numerator larger than the denominator.
• 😀 Terminating decimals have a finite number of digits after the decimal point, while repeating decimals have a repeating pattern.
• 😀 Non-terminating and non-repeating decimals cannot be expressed as fractions or ratios, making them irrational numbers.
• 😀 A mixed number is a combination of a whole number and a fraction, which can be converted into an improper fraction.
• 😀 Whole numbers can be written as fractions with a denominator of 1 (e.g., 25 can be written as 25/1).
• 😀 When converting percentages to fractions, divide by 100 (e.g., 20% = 20/100).
• 😀 Numbers like pi (π) and square roots (e.g., √2) are irrational because they are non-terminating and non-repeating.
• 😀 Rational numbers can be written in the form of p/q, where p and q are integers, and q is not zero.

Q & A

What are rational numbers?

Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. They can be written in the form p/q, where p and q are integers and q ≠ 0.

How do you convert a decimal like 0.7 into a fraction?

To convert 0.7 into a fraction, note that the 7 is in the tenths place. Therefore, it can be written as 7/10.

What is the difference between a proper fraction and an improper fraction?

A proper fraction has a numerator smaller than the denominator, meaning its value is less than 1. An improper fraction has a numerator larger than the denominator, meaning its value is greater than or equal to 1.

What is a mixed number?

A mixed number is a number that combines a whole number and a fraction. For example, 3 4/5 is a mixed number, with 3 being the whole number and 4/5 being the fractional part.

Can repeating decimals be written as fractions?

Yes, repeating decimals can be written as fractions. For example, the repeating decimal 0.333... can be written as 1/3.

What is the difference between a terminating decimal and a non-terminating decimal?

A terminating decimal has a finite number of digits after the decimal point (e.g., 0.25), while a non-terminating decimal has an infinite number of digits that do not repeat in a regular pattern (e.g., π).

How do you convert 20% into a fraction?

To convert 20% into a fraction, write it as 20 out of 100, or 20/100. This can be simplified to 1/5.

Why is 5/0 considered undefined?

5/0 is undefined because division by zero is not possible in mathematics. The denominator cannot be zero in a rational number.

What is the significance of the vinculum (bar) in repeating decimals?

The vinculum (bar) is placed above the repeating part of a decimal to indicate that the numbers under the bar repeat infinitely. For example, in 0.666..., the vinculum is placed above the 6 to show it repeats.

What makes a number irrational?

An irrational number cannot be expressed as a ratio of two integers. These numbers are non-terminating and non-repeating, such as √2 or π, and they do not follow a regular pattern.