Writing, Simplifying and Ordering Fractions

Understanding Fractions and Their Equivalents

Introduction to Basic Fractions

• The lesson begins with identifying fractions of shapes, specifically focusing on how many parts are colored red.

• For the first shape, there are 6 total parts with 5 colored red, resulting in a fraction of 5/6.

• The second example shows 2 parts with 1 red, leading to a fraction of 1/2.

• In the third case, out of 4 parts, 3 are red (3/4), while the fourth has 5 parts with only 2 red (2/5).

Practice Problems

• Students are encouraged to try similar problems:

• First problem: 1 out of 3 is red (1/3).

• Second problem: Out of four parts, one is red (1/4).

• Third problem: Five out of eight are red (5/8).

• Fourth problem: Three out of five are red (3/5).

Equivalent Fractions

• The discussion shifts to equivalent fractions; for instance, both halves and two quarters represent the same amount.

• Another example shows that three-sixths also equals one-half. This illustrates how different fractions can represent the same value.

Finding Equivalent Fractions

• To find equivalent fractions, multiplying both numerator and denominator by the same number is key.

• Examples include:

• Multiplying by two gives two quarters from one half.

• Multiplying by three results in three sixths from one half.

Simplifying Fractions

• Simplification involves reducing fractions to their smallest form using common times tables.

• For example, simplifying three twelfths results in one quarter since both numbers share a common factor of three.

More Complex Simplifications

• When simplifying larger numbers like fifty over sixty:

• Both can be divided by ten yielding five-sixths but cannot be simplified further as they share no other common factors.

Additional Practice Questions

• Students are given practice problems such as simplifying fifteen over twenty-five which simplifies down to three-fifths through recognizing shared factors.

Understanding Fractions and Their Order

Introduction to Fractions

• The speaker introduces the concept of fractions, explaining that both 8 and 14 are in the two times table. This leads to a discussion on simplifying fractions, specifically focusing on converting them into equivalent forms.

Ordering Fractions

• Four fractions are presented: one half, 11 out of 24, five twelfths, and three eighths. The goal is to arrange these fractions in order from smallest to largest.

Finding Common Denominators

• To compare the fractions effectively, they need a common denominator. The speaker decides to convert all fractions to have a denominator of 24 since it is present in the two times table, twelve times table, and eight times table.

Converting Fractions

• The conversion process begins with one half being multiplied by 12/12 resulting in an equivalent fraction of 12 out of 24.

• Five twelfths is converted by multiplying both numerator and denominator by 2, yielding an equivalent fraction of 10 out of 24. Three eighths is converted similarly by multiplying by three for a result of nine out of 24.

Comparing Values

• After conversion:

• One half = 12/24

• Eleven twenty-fourths = 11/24

• Five twelfths = 10/24

• Three eighths = 9/24

The smallest fraction identified is three eighths (9/24), followed by five twelfths (10/24), eleven twenty-fourths (11/24), and finally one half (12/24).

Additional Practice with Ordering Fractions

• A new set of fractions is introduced for practice: seven tenths, thirty-one fortieths, three quarters, and sixteen twentieths. The speaker explains how to convert these into a common denominator of forty.

Conversion Steps Explained

• Each fraction undergoes conversion:

• Seven tenths becomes twenty-eight fortieths.

• Thirty-one fortieths remains unchanged.

• Three quarters converts to thirty fortieths.

• Sixteen twentieths converts to thirty-two fortieths.

Final Comparison

• After conversion:

• Five eighths = twenty-five fortieths (smallest)

• Seven tenths = twenty-eight fortieths

• Three quarters = thirty fortieth

• Thirty-one fortieth = thirty-one fortieth

• Sixteen twentieth = thirty-two fortieth

Simplifying Fractions

• The next task involves simplifying given fractions such as fourteen over twenty-eight using their greatest common divisor (GCD). Both numbers can be halved leading to seven over fourteen or simplified further down to one-half.

Further Simplification Examples

• For six over thirty: both numbers can be divided by six resulting in one-fifth.

More Complex Cases

• Eighteen over seventy-two requires multiple steps; first halving gives nine over thirty-six which simplifies further down through division by nine leading ultimately to one-quarter.

Conclusion on Ordering Sizes Again

• Another set for ordering includes five twelfths again needing conversion into a common denominator for comparison against other fractions like one quarter and three-eighth which will also be adjusted accordingly for proper ordering based on size.