Summary of Fractions: Concept of Conversion between Fractions and Decimal Numbers

INTRODUCTION

The Relevance of the Theme
Fractions and decimal numbers are like two sides of the same coin in mathematics. Understanding how to switch from one to the other is like learning another language of mathematics. Thus, we can solve problems about money, measurements, and many other everyday things. Knowing how to convert fractions to decimal numbers and vice versa is a powerful tool!

Contextualization
Thinking about fractions is thinking about parts of a whole, and decimal numbers are another way to show these parts. This skill fits into the world of numbers and operations, one of the major themes of the elementary school mathematics curriculum. As mathematicians in training, it is essential to master this technique to excel in various topics of mathematics that will appear throughout the school journey.

THEORETICAL DEVELOPMENT

Components

• Fractions: Equal parts of an integer. Example: 1/2 is a half.

  • Numerator: The upper part of the fraction. Indicates how many parts we are considering.
  • Denominator: The lower part. Shows how many parts the whole was divided into.

• Decimal Numbers: A way to represent fractions whose denominator is a power of 10. For example: 0.5 is the same as 1/2.

  • Decimal Place: Each position after the comma in a decimal number. The first position is the tenth, the second is the hundredth, and so on.

Key Terms

• Conversion of Fractions to Decimals: Process of transforming a fraction into a decimal number through the division of the numerator by the denominator.
• Conversion of Decimals to Fractions: Process of writing a decimal number as a fraction, using the decimal place to define the denominator.

Examples and Cases

• Conversion of Fractions to Decimal Numbers:

  • Example: 3/4
    1. Divide 3 (numerator) by 4 (denominator).
    2. The result is 0.75.
    3. 3/4 is equal to 0.75.

• Conversion of Decimal Numbers to Fractions:

  • Example: 0.25
    1. Write the number without the comma as numerator (25).
    2. The denominator will be the number 1 followed by as many zeros as the number of decimal places (100).
    3. Simplify the fraction if possible.
    4. 0.25 converts to 25/100, which simplified is 1/4.

• Solving Problems with Conversions:

  • Case: João has 0.75 meters of rope and wants to cut it into pieces of 1/4 meter.
    1. Convert 0.75 to the fraction 3/4.
    2. Divide the fraction 3/4 by the pieces of 1/4 meter.
    3. João will be able to cut 3 pieces of rope.

Each step of the examples and cases is structured to facilitate the understanding of the conversion process between fractions and decimal numbers and to apply this knowledge to solve practical problems.

DETAILED SUMMARY

Relevant Points:

• Fractions and Parts of a Whole:

  • A fraction represents how many parts of a whole we have. It's like cutting a pie into pieces and each piece is a part of that pie.

• Decimal Numbers and Decimal Places:

  • Just as we can count whole balls, we can count little pieces of balls. The numbers after the comma (0.1; 0.01; 0.001) show these little pieces.

• From Fraction to Decimal:

  • To transform fractions into decimals, we do a "mathematical dive" by dividing the numerator by the denominator.

• From Decimal to Fraction:

  • To convert decimals into fractions, just think about how many "jumps" we took after the comma. Jumped once? It's a tenth. Twice? Hundredth!

• Simplification of Fractions:

  • If we find a number like 50/100, we can simplify! It's like realizing that we have much more of the same and can exchange it for something smaller. Thus, 50/100 becomes 1/2.

• Practical Use of Conversions:

  • In real life, we use these conversions to measure things like money (reais and cents) or distances (meters and centimeters).

Conclusions:

• Conversion Is Simple:

  • Transforming fractions into decimals and decimals into fractions is a walk in the park with some practice.

• Fractions Can Be Friends of Decimals:

  • Decimal numbers and fractions can help each other. When we have one, we can find the other.

• Practice Leads to Perfection:

  • The more we practice these conversions, the better we will get at solving them quickly.

Exercises:

1. Transformation of Fraction to Decimal:

   • Transform 7/10 into a decimal number.

2. Transformation of Decimal to Fraction:

   • Write 0.6 as a fraction.

3. Applying Conversion in Practical Problems:

   • If Maria has 1.2 meters of tape and needs to cut pieces of 1/5 meter, how many pieces can she cut?

These exercises are to practice the skill of converting fractions into decimal numbers and vice versa, and using this in everyday situations.