COMPARAR FRACCIONES con distinto numerador y distinto denominador

Name: COMPARAR FRACCIONES con distinto numerador y distinto denominador
Uploaded: 2022-01-20T15:01:50.000Z
Duration: 34 min 5 s

Comparing Fractions: Understanding the Basics

Introduction to Comparing Fractions

The video introduces the concept of comparing fractions with different numerators and denominators, specifically focusing on determining which fraction is greater or lesser.

Comparing Fractions with Same Denominator

It is easier to compare fractions when they share the same denominator; for example, 2/4 and 3/4 can be compared directly by looking at their numerators.

In this case, 3/4 is greater than 2/4 , as visually represented by dividing a pizza into four parts.

Comparing Fractions with Same Numerator

When fractions have the same numerator, such as 5/4 and 5/8 , the one with the smaller denominator is larger. Thus, 5/4 > 5/8 .

Steps for Comparing Different Fractions

Step 1: Compare with Unity

To compare fractions that do not share numerators or denominators, first assess them against 1 (unity). This involves understanding proper and improper fractions.

An improper fraction (numerator > denominator), like 7/4 , indicates a value greater than 1. Conversely, a proper fraction (numerator < denominator), like 3/5 , is less than 1.

Step 2: Visual Representation

Graphically representing these fractions helps clarify their values; for instance, dividing a pizza into four pieces shows that taking seven pieces means exceeding one whole pizza.

Step 3: Reducing to Common Denominator

If both fractions are less than one, reduce them to a common denominator for accurate comparison. For example, comparing 1/2,; 2/3,; and; 3/4.

Importance of Common Denominators

Having a common denominator simplifies comparisons since it allows direct evaluation of numerators.

The video emphasizes that even if numbers appear larger (like in three-fourths vs. one-half), they may not necessarily represent larger values without proper comparison methods.

How to Find the Least Common Multiple (LCM) of 2, 3, and 4

Understanding Prime Factorization for LCM

The process begins with finding the least common multiple (LCM) of the numbers 2, 3, and 4 through prime factorization. The factors are identified as 2^2, 3^1, and 2^1.

According to LCM rules, we take all prime factors at their highest exponent: 2^2 from 4 and 3^1. Thus, the calculation is 4 times 3 = 12, making 12 the LCM.

Transforming Fractions to Equivalent Forms

With an established common denominator of 12, fractions need to be converted into equivalent forms. This involves adjusting each fraction so that they share this common denominator.

To convert a fraction, divide the common denominator by the original denominator and multiply by the numerator. For example:

For 1/2: 12/2 = 6; thus 1/2 = 6/12.

Comparing Equivalent Fractions

After conversion, fractions can be compared directly since they now have a common denominator. The new equivalents are:

1/2 = 6/12

2/3 = 8/12

9/12

The comparison shows that:

9/12 is largest,

followed by 8/12,

with 6/12 being smallest.

Ordering Fractions from Greatest to Least

Based on numerators after conversion:

Largest: 9/12

Middle: 8/12

Smallest: 6/12

This ordering allows for clear identification of which fractions are greater or lesser relative to one another.

Decimal Conversion Method for Comparison

Another method discussed is converting fractions into decimal form for comparison:

For example, converting three quarters (3/4) results in 0.75.

Converting two thirds (2/3) yields approximately 0.666....

Final Comparisons Using Decimals

By comparing decimals:

Since 0.75 > 0.666..., it confirms that three quarters is greater than two thirds.

Additional Fraction Comparisons

Further examples include comparing six eighths (6/8), nine twelfths (9/12), and four thirds (4/3).

Notably, four thirds exceeds one while others do not.

Finding Common Denominators Through LCM Again

To compare these fractions accurately again requires finding a new least common multiple among denominators (8, 12, and 3).

This involves breaking down each number into its prime factors.

Conclusion on Finding Common Denominators

Ultimately determining that the least common multiple here is also essential for transforming these fractions into equivalent forms suitable for direct comparison across different values.

Understanding Equivalent Fractions

Exploring Fraction Comparisons

The speaker discusses the comparison of fractions, specifically noting that 6/8 and 9/12 are equivalent, leading to the conclusion that they can be compared directly.

It is highlighted that 4/3 is greater than 1, with a focus on how to determine which fraction has a larger numerator when comparing fractions with different denominators.

The concept of cross-multiplication is introduced as a method to verify equivalence between fractions, using the example of 8 times 9 = 72 and 6 times 12 = 72 .

The speaker reflects on the importance of recognizing equivalent fractions early in problem-solving to simplify calculations and reach conclusions more efficiently.